Social structure modulates the evolutionary consequences of social plasticity A social network perspective on interacting phenotypes
Pierre-Olivier Montiglio1 emsp|emspJoel W McGlothlin2 emsp|emspDamien R Farine345
ThisisanopenaccessarticleunderthetermsoftheCreativeCommonsAttributionLicensewhichpermitsusedistributionandreproductioninanymediumprovidedtheoriginalworkisproperlycitedcopy2017TheAuthorsEcology and EvolutionpublishedbyJohnWileyampSonsLtd
AbstractOrganismsexpressphenotypicplasticityduringsocialinteractionsInteractingpheno-typetheoryhasexploredtheconsequencesofsocialplasticityforevolutionbutitisunclearhow this theory applies to complex social structuresWeadapt interactingphenotypemodelstogeneralsocialstructurestoexplorehowthenumberofsocialconnectionsbetweenindividualsandpreferenceforphenotypicallysimilarsocialpart-nersaffectphenotypicvariationandevolutionWederiveananalyticalmodelthatig-noresphenotypicfeedbackandusesimulationstotestthepredictionsofthismodelWefindthatadaptingpreviousmodelstomoregeneralsocialstructuresdoesnotaltertheirgeneralconclusionsbutgeneratesinsightsintotheeffectofsocialplasticityandsocialstructureonthemaintenanceofphenotypicvariationandevolutionContributionofindirectgeneticeffectstophenotypicvarianceishighestwheninteractionsoccuratintermediatedensities anddecrease at higherdensitieswhen individuals approachinteractingwithallgroupmembershomogenizingthesocialenvironmentacrossindi-vidualsHoweverevolutionaryresponsetoselectiontendstoincreaseatgreaternet-workdensitiesastheeffectsofanindividualrsquosgenesareamplifiedthroughincreasingeffectsonothergroupmembersPreferentialassociationsamongsimilar individuals(homophily) increase both phenotypic variancewithin groups and evolutionary re-sponsetoselectionOurresultsrepresentafirststepinrelatingsocialnetworkstruc-turetotheexpressionofsocialplasticityandevolutionaryresponsestoselection
InteractionsamongorganismsareubiquitousinnatureForexamplein-dividualsinteractwithconspecificswhenacquiringordefendingfoodrefuges or mates (Clutton-Brock 1989 Giraldeau amp Caraco 2000HuntingfordampTurner1987KrauseampRuxton2002)andwithhet-erospecificsinmutualismantagonismandcompetition(egCrowleyampCox2011MillerAmentampSchmitz2014ShusterLonsdorfWimp
BaileyampWhitham2006Thompson1982) Inresponsetosuch in-teractionsindividualsmayadjusttheirphenotypeasafunctionofthephenotypeof thosewithwhich they interact (FawcettampJohnstone2010West-Eberhard1989)Forexample individualsmightexpressstronger aggression in the presence of more aggressive individualsthaninthepresenceofmorepassiveindividuals(WilsonGelinPerronampReacuteale2009)Thechangeinphenotypethatresultsfrominteractionsisaformofphenotypicplasticity(hereaftersocialplasticity)
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Interacting phenotypes theory has used quantitative geneticmodels to show how evolutionary trajectories are altered by socialplasticity (BaileyampHoskins 2014BaileyampZuk2012BijmaMuirEllenWolf amp Van Arendonk 2007 Bijma Muir amp Van Arendonk2007BijmaampWade2008McGlothlinMooreWolfampBrodie2010MooreBrodieampWolf1997WolfBrodieampMoore1999)Indirectgenetic effectswhichoccurwhenone individualrsquos genes affect an-other individualrsquos phenotype may either amplify or decrease theamountofgeneticvarianceavailabletoselectionThisprocesscouldquickenorslowthepaceofevolutionarychangeandmayalsocausecoevolutionofotherwiseuncorrelatedtraits(Mooreetal1997)Theeffectof social plasticityonevolutionaryprocesses including thosecapturedbyquantitativegeneticmodelsdependsonthepatternofsocial interactionsoccurringwithin a population that iswho inter-actswithwhomandwithwhatfrequencyorintensityEarlyinteract-ing phenotypemodels focused solely on simple dyadic interactions(Mooreetal1997)and laterattempts includedunstructured inter-actionswithin largergroups (AgrawalBrodieampWade2001BijmaampWade2008BijmaMuirEllenetal2007McGlothlinampBrodie2009McGlothlinetal2010)HowevernoneofthesemodelshaveexploredmorerealisticallystructuredinteractionswherethestrengthofassociationsmayvaryacrossdyadsandwhereindividualsmaynotinteractwitheveryothermemberoftheirgroupItisthereforeunclearwhethertheconclusionsfrominteractingphenotypemodelsaregen-erallyapplicabletomostanimalpopulations
Innaturesocialinteractionsmoreoftenresemblestructurednet-worksthandyadsornonoverlappinggroupsSocialnetworkanalysisprovidesapowerfultoolforquantifyingthestructureofsuchinterac-tions(FarineampWhitehead2015Whitehead2008)anditsimpactsonsocialprocesses(AplinFarineetal2015VanderWaaletal2016)Social network analysis uses information aboutwho interacts withwhomtolinkindividualinteractionstooverallpopulation-levelsocialstructure(Hinde1976Whitehead2008)Incontrasttosimplermod-elsofsocialstructuresocialnetworkscancapturevariation inboththe immediate social environment that individuals experience (iewhoeachindividualinteractswithdirectly)andtheindividualsrsquoposi-tionswithintheoverallsocialstructureofthegroup(iehowcentralanindividualisinstabilizingorfavoringaparticularsocialstructure)Combiningthisgreaterrealismwhenquantifyingsocialstructurethatisthepatternsofconnectionsinasocialnetworkwiththeabilitytomakeformalpredictionsaboutphenotypicevolutionhasthepotentialto significantly expandour understandingof the evolutionof socialtraits(FisherampMcAdam2017)
Inthisstudyweinvestigatehowsocialstructuresshapethe im-pactofsocialplasticityontheamountofphenotypicvarianceavailableforselectionandontheevolutionaryresponseoftraitstoselectionFirstweexpandmodelsofinteractingphenotypes(McGlothlinetal2010Mooreetal1997Wolfetal1999)todescribehowvaryingaspectsofsocialstructuresuchasstrengthsofconnectionsbetweengroupmembersandpreferentialassociationbasedonphenotypicsim-ilarityimpactphenotypicvariationandevolutionSecondwecreatereplicategroupsofindividualswithstructuredsocialinteractionsusingagent-based simulations to analyze how social structure influences
distributionsofphenotypesandtheabilitytorespondtonaturalselec-tionWefocusonthenumberofconnectionsobservedamonggroupmembers (ienetworkdensity thesumofallpresentedgeweightsdividedbythepossiblesumofedgeweightsifthenetworkwerefullyconnected)andthedegreetowhichindividualscanbiasthestrengthof their interactionswith others that have a similar phenotype (ienetworkhomophily)Althoughtheparametersofouranalyticalmodelarenotidenticaltothoseofoursimulationmodeltheyareanalogous(iemeanconnectionstrengthisrelatedtonetworkdensityandphe-notypicassortment isrelatedtohomophily)allowingustocomparetheconclusionsofthetwoapproaches
Wepredictthatsocialplasticityshouldhaveaminimaleffectonphenotypesandontheirvariationwhenconnectionsamongindividu-alsareweak(atlownetworkdensitiesFigure1leftpanels)becauseall individuals experience weaker effects of the same social envi-ronment (they are disconnected) Likewisewepredict therewill beminimalvariation in indirectgeneticeffectsamong individualswhenconnectionsarestrong(athighnetworkdensitiesFigure1rightpan-els)becauseall individuals interactequallyandwiththesamegroup(everyoneexcludingthemselves)Thusthesocialenvironmentexpe-riencedbyeachindividualshouldbeveryclosetotheaveragepheno-typeofthepopulationNetworkswithintermediatenetworkdensities(Figure1middle panel) have a greater scope to exhibitvariation inlocal social structure resulting invariation in thesocialenvironmentexperiencedbyindividualsNextwepredictthathomophilyandsocialplasticityshouldinteractinasimilarwayasdorelatednessandindirectgeneticeffectsindyadicmodels(McGlothlinetal2010)Specificallywhensocialplasticitycausesindividualstobecomemoresimilaradd-ingpreferentialassortmentshouldleadtoanincreaseinphenotypicvariation and anenhanced response to selectionConverselywhenindividualsexpressheterophily (disassortativeassociationbypheno-type)weexpectindirectgeneticeffectstodecreasetheabilityofthetraittoexhibitchangeinresponsetoselection
2emsp |emspMETHODS
21emsp|emspAn analytical model integrating connection strength and phenotypic assortment
Wedevelopananalyticalmodelofinteractingphenotypesinagen-eralized social network In our model the average social plasticityofagroupofindividualsisrepresentedbyaninteractioncoefficient(ψg)whichmeasurestheoverallphenotypiceffectofanindividualrsquossocial partnersrsquo phenotypes on its own phenotype The phenotypicchangesresultingfromsocialplasticityaremodulatedbytheoverallmeanstrengthoftheconnectionsamongindividuals(ieindividualsareembeddedwithinaweightednetworkwithconnectionstrengthsranging from0to1andthenetworkdensity is thesumofallpre-sentedgeweightsdividedbythepossiblesumofedgeweightsifthenetworkwerefullyconnected)Whiletheproductofsocialplasticityandconnectionstrengthcouldbemodeledasasingleparameterweprefertoretainthedistinctionbetweenconnectionstrengthandplas-ticitytokeepourmodelcompatiblewithempiricalstudiesofindirect
emspensp emsp | emsp1453MONTIGLIO eT aL
geneticeffects(egCappaampCantet2008)andallowextensionsofthismodel in the futureWeallowconnection strengths todependupon the nonplastic component of the phenotype (phenotypic as-sortment)Suchassortmentisanalogoustohomophilywhenassort-ment is positive (individuals seek similar partners) and heterophilywhenassortment isnegative(individualsavoidsimilarpartners)WefollowedtheapproachofMooreetal (1997) ignoringthepotentialfordirectsocialeffectsonfitness(socialselectionorgroupselectionWolf etal 1999)Althoughourmodel considers only a single traitforsimplicityitdoesnotconsiderthepossibilityforfeedbackeffectsonphenotypesmakingourmodelanalogoustothetwo-traitmodelwithnonreciprocaleffectsofMooreetal(1997)Wewilltreatphe-notypicfeedbackinafuturecontributionThemodelispresentedinitsentiretyintheAppendixbutwereportitsmainresultsbelow(seeResults)
22emsp|emspSimulation overview
Toinvestigatehowsocialplasticityandsocialstructurecanaffecttheextentofphenotypicvariationobservedwithinpopulationsandevo-lutionarychangewesimulategroupsofindividualswithafixedinter-actioncoefficient(ψg)butvaryingsocialstructures(networkdensityandhomophilyheterophily)EachgrouphasitsownuniquenetworkofinteractionsFromtheseinteractionswecalculatethephenotypethateachindividualinthegroupwouldexpressgivensocialplasticityWe then calculate thephenotypicmeanof the group the varianceinindirectgeneticeffectsexperiencedamongindividualgroupmem-bersthecorrelationbetweenindividualsrsquogenetictendenciesandtheindirectgeneticeffects theyexperienceandtheoverallphenotypicvarianceofthegroupWealsocalculatetheoverallgeneticvariance
WesimulatereplicatednetworksofvaryingdensityandhomophilyEachreplicatecanbeconsideredasa (small)populationorasadis-tinct group embeddedwithin a largermetapopulation To generatenetworksofinteractionwefirstgeneratepairsofcoordinatesfromauniformdistribution(range0ndash1)forindividualsToalloweachindivid-ualtointeractmorestronglywithsomeofitsconspecificsrelativetoothersweallowindividualstomovetowardtheirnearestneighborby15ofthedistancebetweenthemVaryingthispercentagedoesnotinfluenceourresults(resultsnotshown)Todeterminetheconnectionstrengthsbetweeneachpairof individuals inoursimulations(s)wecalculatetheEuclideandistancebetweenthemanduseanexponentialdecayfunctiongeneratingadecreasingconnectionstrengthasafunc-tionof thedistancebetweenany two individualsThusweassumethattheconnectionstrengthbetweentwoindividualsiss=eminusdistance
F IGURE 1emsp (a)Samplenetworksgeneratedusingthreevaluesofr(005015and09)creatingnetworksofvaryingdensitieslow(left)intermediate(center)andhighdensities(rightNgroup=12)(b)Foreachlevelofdensityindividualsalsovariedinthenumberofinteractionswithothergroupmembersshownatlow(left)intermediate(center)andhigh(right)networkdensities(Ngroup=500)
Becausetheresultingnetworkdensity(thesumofallpresentedgeweightsdividedby thepossible sumofedgeweights if thenetworkwerefullyconnected)foragivenvalueofrisstochasticnotdetermin-isticwereportourresultsasafunctionofnetworkdensitywhichwascalculatedusingtheRpackageassortnet(Farine2014)Statedanotherwaynetworkdensityisanemergentpropertyofvaryingrnotaparam-eterofoursimulationsOurapproachismostimmediatelyapplicabletosituationswhereindividualsareactuallydistributedintwo-dimensionalspaceandinteractmoreorlessintenselyasafunctionofthedistance(Farine 2015) Such an interaction structure applies directly to situ-ations such as competition amongneighboringplants (egCappaampCantet2008)orterritorialityinanimals(egRoyleHartleyOwensampParker1999)butisgeneralizableawidevarietyofothermorecomplexsituationsthatmaynotinvolveaspatiallyexplicitcomponent
Individualscanoftenchoosetoconnectmorestronglywithsomeindividuals than others In many species individuals preferentiallyinteractwithpartnersthataresimilar (ieunderassortativematingor during cooperative interactions) or dissimilar to them (ie underdisasortativemating or because of division of labor and social het-erosis seeNonacsampKapheim 2007)Hence networks can exhibitassortment (associations between individuals that are similar andor avoidance of dissimilar individuals Farine 2014) Firstwe studythe effect of randomly occurring network assortment in the sim-ulated groups To explicitly investigate the impact that interactionpreferencescanhaveonevolutionaryprocesseswethenallowindi-vidualstoreducethestrengthoftheirinteractionwithnonpreferredaffiliates (eg with dissimilar individuals in the case of homophilyorwithsimilar individuals inthecaseofheterophily)Wethusmod-ify the function used to calculate the strength of interaction (s) tos=eminusdistance
2∕rtimesH(
1
1+expminus20|xminusy| minus05)+05 which generates a sig-
moidalfunctionwithamagnitudeofH(thelevelofhomophilyrang-ingbetween0and02) as a functionof |xminusy| or thedifference inthephenotypesoftheindividualsIftwoindividualsareidenticalthestrengthoftheirinteractionismultipliedbyeither~0or~1ifmodelingheterophily or homophily respectivelyTheir connection strength ismultipliedby05iftheirphenotypicdifference(|xminusy|)isaverageAswithnetworkdensitywe report themeasurednetworkassortmentcalculatedusingtheRpackageassortnet(Farine2014)
strengthoftheirsocialinteractionssiIndividualswithnoconnectionstrengthdonotcontributetothephenotypeassi =0Inoursimula-tionsall individualshavethesameinteractioncoefficient(ψg)Wealsoinvestigatewhetherourresultsdependedonthedistributionofbreedingvaluesbyrunningadditionalsimulationswhereindividualbreedingvaluesare sampled fromanormaldistribution (mean=0andvariance=1)IntheresultswepointoutwheresuchachangeindistributionaffectsourresultsInpreviousmodels(McGlothlinampBrodie2009McGlothlinetal2010)ψghasbeenconstrainedtoliebetweenminus1and1fortworeasonsFirstvaluesofψggreaterthan1canleadtounreasonablephenotypicvalues(particularlyinmodelsthat include phenotypic feedback) Second phenotypic values areoftenstandardizedtoameanofzeroandunitvarianceforanalysiswhichshouldresult inψgvaluesbetweenminus1and1 Inoursimula-tionsthemeanandvarianceofindividualphenotypesvariedineachgroup because of samplingwhichmade such standardization dif-ficultWechose touseunstandardized traitvaluesanda largeψg value(4)inallsimulationsSuchavalueofψgwhichwouldyieldanaveragestandardizedvalueofψgof~030whichiscomparabletoempiricalψgvaluesreportedintheliterature(egBaileyampHoskins2014BaileyampZuk2012)Usingthislargevaluefacilitatesvisual-izing social effects anddoesnot lead tounreasonablephenotypicvalues due to the absence of phenotypic feedback in ourmodelAs noted in theAppendixψg ismultiplied by average connectionstrength (network density) when calculating phenotypes whichwillreducetheeffectofψgexceptinfullyconnectednetworksAspredictedbytheanalyticalmodel increasingthestrengthofsocialplasticity(iehowmuchanindividualchangedhisphenotypeinre-sponsetohissocialpartnerstheabsolutevalueofψg)amplifiesallthe patternswe report below (seeResults section)However be-causesuchincreasesareintuitiveandoflesserinterestwedonotreporttheresultsofanalysesvaryingψgUsingthecodeavailableasFigureS1 the reader cangenerate figures that are comparable totheoneswepresentbelowforanyvalueofψg
where G indicates additive genetic variance andE indicates envi-ronmental variance The third term above represents the among-individual variance due to social interactions This term shouldincreasesomewhatwithhomophilybutshoulddependmostheav-ily on network density The variance in social environment expe-rienced by individuals should be at amaximum at intermediate
becomemorehomogenous(ieeveryoneinteractswitheveryone)Thefourthtermwillbemost influencedbyhomophily (orhetero-phily)becauseassociatingwithsimilar(ordifferent)individualswillcause the covariance to increase (ordecrease)Themultiplicationbyψgwillcausephenotypicvariancewithinagrouptoincreasewithhomophilyunderpositivevaluesofψganddecreasewithhomophilywhenψg isnegativeThistermshouldalsobe influencedbyaver-ageconnectionstrength(
where R is a general measure of the strength of homophily (seeEquationA19 in Appendix) and β is the selection gradient (seeAppendix)Thisequationshowsthattheamountofgeneticvarianceavailableforresponsetoselectionatthepopulationlevelshouldde-pendon(1)thedegreeofsocialplasticity(2)theaverageconnectionstrength(whichshouldincreasewithmeanconnectionstrength)and(3)theamountofassociationbetweenindividualsthatisbasedonge-neticvaluesimilarity(homophilyorheterophily)Thismodelisnearlyidenticaltopreviousmodelswithsimplergroupstructure(McGlothlinetal 2010) except for the inclusion of the connection strength (
=s)
and the replacementof relatednesswithhomophilyheterophily (R)Theseanalyticalresultsprovidepredictionsthatwetestbelowusingindividual-basedsimulations
32emsp|emspNetwork density
Inoursimulationsincreasingnetworkdensitywhichisanalogoustoincreasing mean connection strength in the analytical model doesnot lead to an increase inphenotypicmeanonaverage (ie acrossallgroupsFigure2red line)Howeverathighernetworkdensitiesthere is much greater variation among groups in their phenotypicmean (Var[
=z ] Figure2 gray dots) This occurs because although
themeangeneticvalueacrossall simulations iszero thisvaluecandiffer across groups due to sampling As predicted by Equation2increasing network density (or
=s) increases the importance of the
group genotypic composition in determining the effects of indirectgeneticeffectsmagnifyingdifferencesamonggroupsingeneticvalue(=a) across replicate simulation runs This amplification effect is also
Thephenotypicvariance in indirecteffectswithineachgroup ismaximalatintermediatenetworkdensities(Figure3a)Whenindivid-ualshave fewconnections (and connection strength isweaker) thescopeforindirecteffectstodifferamongmembersofagivengroupisnarrowtherebydecreasingthecontributionofsocial interactionstophenotypicvariance(Figure3a)Likewiseingroupswhereindividualsarehighlyconnected (highnetworkdensity) thesocialenvironmentexperiencedbyeachindividualisclosertotheaveragebreedingandenvironmentalvalueofthepopulation(whichis0inoursimulations)In otherwordsVar[aprime] and consequentlyVar[saprime]within groups issmallathighdensities(seeEquation3)Howeveratintermediateden-sities indirecteffectshadthepotentialtomakealargecontributiontophenotypicvariancealthoughthiseffectwashighlyvariableacrosssimulations
Intheabsenceofhomophilyheterophilyhighnetworkdensityleadstoanegativecorrelationbetweendirectandindirectgeneticeffects(Figure3b)Atlownetworkdensitiesthiscorrelationisex-pectedtobezerobecauseindividualsassociateatrandom(althoughthiswouldnotbe thecase if therewasanyspatial assortmentbyphenotype) However at high densities this correlation becomesnegativeeventhoughindividualassociationisalsorandomThisef-fectarisesbecauseindividualsarenotcountedaspartoftheirownsocial environment andasnetworkdensities increase the impor-tanceofthisdifferencebecomesmagnifiedAtthehighestnetwork
(3)Var[z]=G+E+ψ2gVar
[sa + se
]+2ψgCov
[a +e sa + se
]
(4)Δ=zasymp
(1+ψg
=s)G(1+Rψg
)β
F IGURE 2emspThechangeinaveragephenotypeofindividualsinanetworkasafunctionofthenetworkdensity(redline)Thechangeinaveragephenotypeisexpressedrelativetothephenotypeexpectedinabsenceofinteractionsamongindividuals(ie0)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4Asdensityincreasedweobservedagreatervariationinmeanphenotypeamonggroups(graydots)
1456emsp |emsp emspensp MONTIGLIO eT aL
densitiessocialenvironmentsare indistinguishableexceptforthiseffect of excluding oneself thus leading to a directndashindirect cor-relationofminus1Smallergroupswillexhibitthispatterntoastrongerextent than larger groups (see FigureS5 also McDonald FarineFosterampBiernaskie2017)Thecombinedimpactoftheeffectsofnetworkdensityonthevariancein indirectgeneticeffectsandonthecovariancebetweendirectandindirectgeneticeffectsisarel-ativedecrease inphenotypicvariationwithingroups(comparedtothephenotypicvariationinabsenceofanyinteractions)asnetworkdensityincreases(Figure3c)Oppositepatternsareobservedwhenψg isnegative(FigureS6)Finallywenotethatalthoughthemeanphenotypic variationwithin each group decreaseswith increasingnetworkdensitywefindthatthevariationamonggroups(eachdotin each panel of Figure3c represents one group) ismaximized atintermediatenetworkdensities
Although the phenotypic variance typically decreases with in-creasednetworkdensitythevarianceintotalbreedingvalues(rela-tivetothegeneticvarianceinabsenceofanysocialinteraction)hasthe greatest increase at highest network densities (Figure3d redline)Thisisbecausetheexpectedvarianceintotalbreedingvaluesisequalto
(1+ψg
=s)2
G(seeEquationA12)Thatisthevarianceintotalbreedingvaluesdoesnotdependonthevarianceinindirectgeneticeffects noron the covariancebetweendirect and indirect geneticeffectswhich leadtothedecrease invarianceshowninFigure3cRatherthevarianceintotalbreedingvaluesisafunctionofdirectge-neticeffectsandeffectsofanindividualrsquosgenesonothersthelatter
ofwhichbecomesinflatedathigherdensitiesTheresponsetoselec-tiondependsonthecovariancebetweentotalbreedingvaluesandphenotypicvalueswhichisexpectedtoincreaselinearlywithdensity(EquationA15)Whenwesubjectgroupstoaselectiongradientof02networkswithincreasingdensitiesexhibitedanincreasedevolu-tionaryresponsetoselection(Figure4redline)Increasingnetworkdensityalso increases thevariance in responsetoselectionamonggroups (Figure4 gray dots) This likely happened because individ-ualsadjusttheirphenotypetotheaveragesocialenvironmentthattheyexperienceThusathighernetworkdensitiesindividualswithextreme phenotypicvalues have a disproportionate impact on theaveragesocialenvironmentexperiencedbyindividualsSmalldiffer-encesinthephenotypicvaluesofextremeindividualsfromgrouptogroupcreatedifferencesinthecovariancebetweenthephenotypicvarianceandthetotalbreedingvaluesamonggroupsandincreasingthevariance in response to selection amonggroups In agreementwiththisextremeindividualsalsogenerategreaterphenotypicvari-anceamonggroupsathighernetworkdensities(Figure2)andwhenindividualphenotypesfollowauniformdistribution(moreindividualswithextremephenotypes)thananormaldistribution(fewerindivid-ualswithextremephenotypesSeeFigureS3)
F IGURE 3emspEffectsofnetworkdensityon(a)thevarianceinindirecteffectsexperiencedbyindividuals(b)thecorrelationbetweendirectandindirectgeneticeffectsexperiencedbyindividuals(c)thechangeinphenotypicvariancewithingroupsrelativetothegeneticvariance(iethephenotypicvarianceinabsenceofinteractions)and(d)thechangeintotalgeneticvariationrelativetothegeneticvariance(ievarianceofindividualdirectgeneticeffectsandindirectgeneticeffectsimposedtoothers)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψg of4
emspensp emsp | emsp1457MONTIGLIO eT aL
hasnoeffectonthemeanphenotypeofeachgroup(Figure5)whichis consistent with our analytical model (Equation2) However in-creasednetworkassortmentisassociatedwithanincreaseinthevari-anceinindirectgeneticeffectsexperiencedbyindividualsinagivengroup(seethethirdterminEquation3Figure6a)Becauseindividu-alsinteractmorestronglywithconspecificsthathavesimilarbreedingvalues(highwithhighlowwithlow)thedirectandindirectgeneticcontributions to phenotypes act in concert and covary positively(fourthterm inEquation3Figure6b)Thesetwoeffectscontributetowardincreasingphenotypicvarianceobservedwithinagivengroup(Figure6c)Theseeffectsarereversedwhenψgisnegativedirectandindirect contributions to individual phenotypes act to oppose eachothertherebyreducingtheamountofphenotypicvarianceobservedin the population (see FigureS7) Increasing network assortmentalsoleadstoasmalldecreaseinthevarianceintotalbreedingvalues(Figure6dredline)Thisisattributabletotheslightdecreaseinden-sityassociatedwithhigherlevelsofnetworkassortment(ieindividu-alshavetheabilitytoreducetheconnectionstrengthwithparticulargroupmembers)aphenomenonnotcapturedbyouranalyticalmodel
Applying selection to groups with varying network assortmentshowsthatasynergybetweendirectandindirectgeneticeffectsleadstoanincreaseinevolutionarychangewithincreasingnetworkassort-ment(Figure7redline)Thisresultisinaccordwiththepredictionsofouranalyticalmodelwhichpredictsanincreasedresponsetoselec-tionwithincreasingR(Equation4)AlthoughEquation4suggestsden-sityandhomophilyshouldhavesymmetricaleffectstheincreaseseeninFigure7isnotasdramaticasthatinFigure4perhapsbecauseoftheconcomitantdecreaseindensitycausedbyallowinghomophilyinoursimulationsUnlikenetworkdensitynetworkassortmentdoesnotaffectthevariationofevolutionaryresponsesamonggroups(Figure7graydots)
4emsp |emspDISCUSSION
Inthisstudyweexploretheconsequencesofsocialplasticityandthestructureofinteractionsinshapingtheamountofphenotypicvariationwithingroupsof interactingindividualsandtheevolutionaryresponseofthesegroupstoselectionWeconsiderreplicategroupswithvary-ingstructuresofinteractionsSuchreplicatescouldbeseenasmultiplegroups of individualswithin a given population (eg tribes packs orcolonies)orasmultipleisolatedpopulationswithinanecologicalcom-munityThroughananalyticalmodelandagent-basedsimulationsweshowthatthestructureofsocialnetworksmodulatedtheimpactofin-directgeneticeffectsontheamountofphenotypicvarianceavailablefor selectionOur resultsemphasize that thenumberandstrengthofconnectionsamongindividuals(networkdensity)aswellaspreferentialassociations among individualswith a similar phenotype (network as-sortment)haveimportanteffectsonthecontributionofindirectgeneticeffectsNetworkdensityandassortmentalsomodulatetheabilityfortraitstoexhibitevolutionarychangeinresponsetoselectionIncreasingthenumberofinteractionsamonggroupmembers(networkdensity)in-creasestheaverageevolutionaryresponseofgroupstoselectionandin-creasesthevariationinresponsetoselectionamonggroupsBycontrastincreasednetworkassortmentleadstoanincreaseintheaverageevolu-tionaryresponseofgroupstoselectionbutdoesnotaffectthevariationinevolutionary responseamonggroupsOur resultshavewidespreadimplicationsforstudiesofsocialevolutionmultilevelselectionandtheemergenceofkeystoneindividuals(ModlmeierKeiserWattersSihampPruitt2014)andniche-constructingtraits(egSihampWatters2005)
41emsp|emspComparison with earlier interacting phenotype models
Our analytical results show that given some simplifying assump-tions (most importantly ignoring the potential for phenotypic
F IGURE 4emspEvolutionaryresponseofphenotypetoaselectiongradientvarieswithnetworkdensityTheaveragechangeinphenotypemeanresultingfromselectionincreasedwithnetworkdensity(redline)Groupswithdensernetworksofinteractionsexhibitedmorevariationinthechangeinphenotypicmean(graydots)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4
F IGURE 5emspTheaveragephenotypeofindividualsasafunctionofnetworkhomophily(redline)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4Networkscouldnotreachhomophilyvaluesof1becauseweusedacontinuoustraitvalueratherthandiscretevalues(seeFarine2014)
1458emsp |emsp emspensp MONTIGLIO eT aL
feedback) considering more general social structures does notgreatlyalter theconclusionsofearliermodelsof interactingphe-notypeevolution(egMcGlothlinetal2010Mooreetal1997)First indirect genetic effects still alter the response to selectionby increasing the amount of genetic variance exposed to selec-tionNote thatbecausewedonotmodel feedback thiseffect is
directional with positiveψg (ie becomingmore similar to onersquosneighbors)increasingtheresponsetoselectionandnegativevalues(iebecomingmoredifferentfromonersquosneighbors)decreasingitSecondhomophilyheterophilyplaysa rolesimilar to relatednessinpreviousmodelsinalteringtheresponsetoselection(McGlothlinetal2010)IndeedMcGlothlinetal(2010)noted(ashavemanyothers)thatrelatednessperseisjustaspecialcaseofphenotypicassortment
Themostnotabledifferencebetweenourmodelandearliermod-elsisthatindividualsareallowedtodifferintheirinfluenceonsocialplasticityduetovariation inconnectionstrength (s)Perhapsunsur-prisingly responsetoselection ismorestrongly influencedbysocialinteractions indensernetworkswhere interactionsarestrongerandmorecommonaneffect that isapparent inbothouranalyticalandsimulation results Inour simulation resultswealso find thatvaria-tioninresponsetoselectionamongincreaseswithgreaterconnectionstrengthThis could occur because in some groups themostwell-connectedindividualshappentohaverelativelyhighorlowbreedingvaluesThesewell-connected individualswould thenhaveadispro-portionateeffectonthephenotypeofothers (relativeto individualsclosertothepopulationrsquosaveragebreedingvalue)byexertingastrongeffectonthemeansocialenvironmentexperiencedbyindividualsIndoingsowell-connectedextremeindividualscangeneratevariabilityinthecovariancebetweenbreedingvaluesandphenotypeandthusintheresponsetoselectionFuturemodelsshouldallowconnectionstrength to display a heritable component which would allow thesocialnetworkstructureitselftoevolveinresponsetosucheffects
F IGURE 6emspEffectofnetworkhomophilyon(a)thevariationinindirecteffects(b)thecorrelationbetweendirectandindirectgeneticeffects(c)therelativechangeinphenotypicvariancewithingroupsand(d)therelativechangeintotalgeneticvariationEachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4HomophilysimultaneouslyincreasesvariationamongindividualsinindirectgeneticeffectswithingroupsandgeneratesastrongpositivecovariancebetweendirectandindirectgeneticeffectstherebysubstantiallyincreasingthephenotypicvarianceobservedwithingroupsHoweverthisincreaseinphenotypicvarianceisnotassociatedwithanychangeatthegeneticlevel
F IGURE 7emspEvolutionaryresponseofphenotypetoaselectiongradientincreaseswithnetworkhomophily(redlineandgraydots)Eachdotrepresentsthechangeinmeangenotypeacrossgenerationsinasinglesimulatednetworkorgroupof50individuals(Ngroup=50)TheredlinerepresentstheaverageevolutionaryresponseasafunctionofnetworkdensityIndirectgeneticeffectsweregeneratedusingaψgof4
emspensp emsp | emsp1459MONTIGLIO eT aL
Studiesinthewildhaveshownthatpositioninasocialnetworkmaybe repeatable and have fitness consequences suggesting that con-nectionstrengthmaybeanevolvabletrait (AplinFirthetal2015FormicaWoodCookampBrodie2017Formicaetal2012)
42emsp|emspGroups with denser connections exert a stronger ldquopull to the meanrdquo
Our simulations show that groupswhere individuals have an in-termediatenumberorstrengthofsocialconnections (iegroupswithintermediatenetworkdensities)allowforthegreatestwithin-groupvariationinsocialenvironmentsexperiencedamongindivid-ualsThispatternariseswithinagenerationduetosocialplasticityratherthanasaresponsetoanyselectivepressureBygeneratinga greater range of phenotypes and social environments groupswithan intermediatedensityof social interactionscouldprovidethe basis for the emergence and evolution of alternative socialphenotypes (Bergmuumlller amp Taborsky 2010 Sinervo amp Calsbeek2010) When social phenotypes are subject to indirect geneticeffects the maintenance of variation in social behavior shouldthus be observed more frequently in groups with intermediateconnectedness
Whilelowtointermediatedensitiesofsocialinteractionsofferthewidestscopeforpromotingindividualvariationinphenotypegroupswith high densities exhibit a very different patternAs the numberand strengths of interactions increases among group members in-direct genetic effects experienced by each individual becomemoresimilarbecauseallgroupmembersstarttobecomeconnectedtooneanotherand theseconnectionsareuniformlystrong Inadditionasnetworksbecomemoreconnectedindividualsattheextremesofthedistributionofgenetic tendencies in thegroups (ie the individualsfurthest from the averagebreedingvalue) tend to experience a so-cialenvironmentexertinganopposingeffectontheirphenotype(ieCov[a+esa +se] in Equation3 becomes more negative) This ldquopullto themeanrdquo is stronger in smaller groups than in larger ones (seeFigureS5) anddecreases thepopulationphenotypicvariancewhenψg ispositive (egwhen individuals increasetheiraggressiveness inresponse to the aggression they receive) and increases it whenψg is negative (egwhen individuals inhibit their aggressiveness in re-sponsetotheaggressiontheyreceive)Whenindividualsexhibit im-portantphenotypicplasticitysuchaneffectappearssimilartosocialconformity where individuals express more similar phenotypes asgroupsthan in isolation (egHerbert-Readetal2013MagnhagenampBunnefeld2009)Conformity isusually thought toemergewhendissimilarindividualsareatafitnessdisadvantageForexamplepred-ators tend topick individuals that standout amonggroupsofpreyselecting forhomogeneousgroups (LandeauampTerborgh1986)Weshowherethatconformist-likepatternsinbehaviorcanemergefromverysimpleformsofsocialplasticity Importantlyweshowthatbe-havioralconformitycanemergeevenwhenindividualsarenotactivelycopyingthemostabundantphenotypeoftheirgroup inabsenceofanyselectivepressureExamplesofhighlyconnectedgroupsinnatureincludechorusesofmalesinsomespeciesoffrogsproducingmating
calls or leks ofmales displaying to attract females and adjust theirsignalingeffortinresponsetothesignalingoftheirrivals(Boatright-HorowitzHorowitzampSimmons2000SimmonsSimmonsampBates2008)Whenmalesareclosetoeachotherandeachmalecanadjustits signaling intensity to that of all the othermaleswe expect thisldquopulltothemeanrdquotodecreasethevariationinmalesignals(althoughsocialplasticitycantakemorecomplexpatternsthenismodeledhereGreenfieldampRand2000)Thiscandecreasetheeffectivenessoffe-malematechoiceandtheintensityofsexualselection
43emsp|emspGroups with denser connections potentiated the effect of keystone individuals
Aninsightfromoursimulationsisthatwheneverindividualsadjusttheirphenotypetotheaveragesocialenvironmentthattheyexperi-enceindividualsattheextremesofthegenotypicorphenotypicdis-tributionhavethegreatestimpactonthephenotypeofothergroupmembers This phenomenon arises because these individuals havethestrongest impacton themeansocialenvironmentexperiencedbytheirconspecificsTheevolutionofniche-constructingtraitsal-lowingsomeindividualstomanipulatetheirgroupinawaythatfa-vorstheirownsuccess(SaltzGeigerAndersonJohnsonampMarren2016) or to have a disproportionate effect on their group (Keiseramp Pruitt 2014 Modlmeier etal 2014 Pruitt amp Pinter-Wollman2015)hasbeenthefocusofmuchinterestrecentlySurprisinglynostudyhasexplored the implicationsof theexactpatternsofsocialplasticity for the identity and impact of such ldquokeystone individu-alsrdquo (Modlmeier etal 2014) It is reasonable to assume thatmostanimalsexhibitingsocialplasticityshouldadjusttheirphenotypeinresponse to theaverage socialconditions that theyexperience (al-thoughinsomecasessomeindividualscanadjusttheirphenotypeto themaximumor to theminimumphenotypicvalueof the indi-vidualswithwhomtheyinteractseeDyerCroftMorrellampKrause2009 for a potential example) Thus our simulations suggest thattheemergenceofkeystoneindividualsmightbeaphenomenonfarmore common than previously envisioned Keystone individualscouldemergeinanygroupofinteractingindividualsexhibitingphe-notypicplasticityanddenseinteractionnetworks(asinthelekkingexampleabove)Hencetheemergenceofkeystoneindividualsmightnotrequireacomplexsocialsystemdivisionoflabor(PruittBolnickSihDiRienzoampPinter-Wollman2016) collectivebehavior (PruittampPinter-Wollman2015)orniche-constructingtraits (egaggres-sivenesspolicingorelseChangampSih2013)butshouldbemostcommon in specieswhere individuals respond to thebehaviors ofthemajorityofgroupmembers
Denserinteractionsamongindividualswithinagrouppotentiatetheimpactofindividualswithextremephenotypicvaluesbyallow-ing these to interact and affect themajority of their groupmem-bersHencetheconsequencesofindividualsocialplasticitytendtobecomemuchgreater ingroupsasnetworkdensity increasesThisldquoamplificationrdquoeffectisalsostrongerwhengenotypesfollowauni-formdistribution (iewhenextremegenotypesaremorefrequentwithin groups) thanwhen they followaGaussiandistribution (ie
1460emsp |emsp emspensp MONTIGLIO eT aL
whenextremegenotypesarerarewithingroups)Networkdensityincreases the evolutionary response of groups on average groupswith denser connections also exhibit increasedvariation in evolu-tionaryresponsetoagivenselectiongradientSuchan increase inthevariationinevolutionaryresponseobservedinourstudyisap-parentbecauseourapproachallowsustorelaxtheassumptionthatindividualswithingroupsinteractequallywithallothergroupmem-bersbyintroducinganewparameter(averageconnectionstrength=s)intoourmodelandinsteadtoexplicitlyexploretheeffectofcon-nectiondensity
44emsp|emspHomophily affects the amount of phenotypic variation within groups
Our simulations also investigate the consequencesof social struc-turewhenindividualscaninteractpreferentiallywithindividualsthathaveasimilar(iehomophily)ordissimilar(ieheterophily)pheno-typeNetworkassortment(thenetworkmeasureofhomophily)doesnot have any impact on groupsrsquomean phenotype but can gener-ateagreatervariationinsocialenvironmentswithingroupsHenceassuming that different immediate social environments can favordifferent (alternative) phenotypes within groups our simulationssuggest that homophily should be associatedwith the emergenceof phenotypic variation among individuals (or social specializationBergmuumlller amp Taborsky 2010 Montiglio Ferrari amp Reacuteale 2013)Homophilyalsohasdirectconsequencesfortheevolutionofalter-nativephenotypesbycreatingsynergyoroppositionbetweendirectand indirect genetic effectsWhen social plasticity (ψg) is positive(egwheninteractingwithanaggressiveindividualincreasesafocalindividualrsquosaggression)andindividualsshowatendencytointeractwithsimilarphenotypesthesocialenvironmentactstoshapetheirphenotypeinthesamedirectionastheirgenotypeAsaresultsocialinteractionsandsocialplasticityincreasethephenotypicvarianceofthetraitrelativetoasituationinwhichconnectionsarerandominterms of their traits It also tends to increase the strength of theevolutionaryresponsetoselectioninresponsetoagivenselectiongradientThisincreaseinevolutionaryresponsearisesfromthesyn-ergybetweendirectandindirecteffect(orbetweensocialplasticityandhomophily)ratherthanfromachangeintotalgeneticvariationwithingroups
45emsp|emspPossible applications and tests of the model and future directions
differentialandmatechoicebyfemalesThestrengthofconnectionsbetweenmales of known phenotype could be increased artificiallyusingplaybacks tosimulatemore frequent interactionsamong indi-viduals(DabelsteenampPedersen1990Otteretal2001)tomonitorhowsuchincreasesinconnectionstrengthaffecttheextentofpheno-typicandgeneticadditivevariationAlternativelyonecanmanipulatethedistributionofterritoriesavailableandthepatternsofinteractionsby controlling the locationof nest boxes foodpatches or refugesSuchapproachescouldbeparticularlysuitableforcavity-nestingbirds(Both1998)
Ourmodel also studied the consequences of homophily for theevolutionary responses of phenotypic traits Assuming individualshave some level of control on their interactions homophily can beobservedwhen individualsexhibitpreferences to interactwithcon-specificsthatare(dis)similartothemSuchpreferencescouldexplainthemaintenanceofaltruisticbehaviorbecauseoftheirpotentialroleinshapingtheselectionpressuresactingonaltruismSomeworkonfruitflieshavereportedthatindividualpreferencesforparticularsocialenvironmentsisassociatedwithgeneticvariationandcanthuspoten-tiallyevolve (egSaltzampFoley2011)Onecould testourmodel insuchstudysystemsbyeitherallowingorpreventingtheexpressionofsocialpreferences(throughmixingofindividualsormanipulatingtheirinteractions) Alternatively homophily can also be observed whenindividualssegregateintheenvironmentasafunctionoftheirphe-notype(HelfensteinDanchinampWagner2004Ward1993WardampPorter1993)Forexamplemoreandlessaggressiveindividualsseg-regateinpatcheswithdifferentdensitiesofconspecifics(Duckworth2006)Thusbymanipulatingtheheterogeneityandthescaleatwhichitisobserved(iethesizeofpatchesofdifferenthabitat)onecouldtestthepredictionsofourmodelFutureworkwillexpandthemodelwe presented here to analyze the consequences of such traits forthemaintenanceofphenotypicvariationandtheevolutionofsocialstructure
One limitationofourmodel is thatweassumebothphenotypicfeedback(Mooreetal1997)andsocialselection(Wolfetal1999)tobeabsentIncludingfeedbackmayaltertheconclusionswehavepre-sentedhereasfeedbackeffectsmaycausesocialplasticitytomovethroughnetworksincounterintuitivewaysItispossiblethatnetworkmetricsbeyondconnectionstrength (suchasclusteringcoefficientsbetweennessetc)may influencewhetherfeedbackcontributessig-nificantly to variation and response to selection Regarding socialselectionwehaveshownherethatconnectionstrengthcontributestoamong-groupvariancewhichshould intensifyresponsetohigherlevelsofselectionsuchassocialselectionWewilltreatbothfeedbackandsocialselectioninfuturecontributions
5emsp |emspCONCLUSION
Wepresentbothananalyticmodelandsimulationsextendingpre-vious work on social phenotypic plasticity to more general socialstructuresOurstudygeneratesafirstsetofverygeneralandtest-able predictions on the role of social structure in modulating the
emspensp emsp | emsp1461MONTIGLIO eT aL
consequencesofsocialplasticityWeshowthatthebasiccharacter-isticsofthestructureofinteractionsamongindividualsingroupsandpopulationscanhaveimpactsontheconsequencesofsocialplasticityforthemeanphenotypeexpressedbytheindividualstheextentofphenotypicvariationavailableforselectionandfortheabilityofthepopulation to respond to selectivepressuresWehope that futurestudieswillbeabletotestourpredictionsempiricallybyapplyingourapproachtothestudyofsocialbehavior(egaggressionandcoop-eration)socialinformationuseoralternativematingtacticsinpopu-lationswithvaryingpatternsofsocialormatinginteractionsFromatheoreticalperspectivefutureresearchwouldwarrantinvestigatingthelinkbetweenindividualpositioninsocialnetworksandtheindi-rect genetic effects it experiences and thuswhether factors otherthan individualsrsquo breeding values can lead to keystone individualsFurtherinourstudyweassumethatallindividualsexpressedplas-ticityidenticallyHoweverindividualshavealsobeenshowntovaryintheirplasticity(DingemanseKazemReacutealeampWright2010NusseyWilsonampBrommer2007WestneatHatchWetzelampEnsminger2011)andsuchvariationmayalterthepredictionsofinteractingphe-notypemodels(KazancıoğluKlugampAlonzo2012)Linkingindividualdifferencesinbothsocialpositionandplasticitycouldyieldnewin-sightsandagreaterunderstandingoftheevolutionarymechanismsthatunderpinphenotypicvariationwithinindividualsbetweenindi-vidualsandamongpopulations
ACKNOWLEDGMENTS
We thank the Reader Hendry and Barrett laboratories in McGillUniversity forconstructivecommentsonadraftof thismanuscriptPOMwas supported by aNSERCpostdoctoral fellowshipDRF re-ceived funding from a grant to theBBSRC (BBL0060811 toBCSheldon)andtheMaxPlanckSociety
CONFLICT OF INTEREST
Nonedeclared
AUTHOR CONTRIBUTIONS
POMandDRFbuiltthesimulationsandJWMdevelopedthemodelPOMdrafted themanuscript andproduced the figuresAll authorscontributedtorevisionsandapprovedthefinalversionofthearticle
AplinLMFarineDRMorand-FerronJCockburnAThorntonAamp SheldonBC (2015) Experimentally induced innovations lead topersistentcultureviaconformityinwildbirdsNature518538ndash541
Aplin LMFirthJAFarineDRVoelklBCratesRACulinaAhellipSheldonBC (2015)Consistent individual differences in the so-cialphenotypesofwildgreattits(Parusmajor)Animal Behaviour108117ndash127httpsdoiorg101016janbehav201507016
BaileyNWampHoskins J L (2014)Detecting cryptic indirect geneticeffectsEvolution681871ndash1882httpsdoiorg101111evo12401
Bailey N W amp Zuk M (2012) Socially flexible female choice differsamongpopulationsofthePacificfieldcricketGeographicalvariationin the interaction coefficient psi (Ψ)Proceedings of the Royal Society of London Series B Biological Sciences 279 3589ndash3596 httpsdoiorg101098rspb20120631
Bergmuumlller R amp Taborsky M (2010) Animal personality due to socialnichespecialisationTrends in Ecology amp Evolution25504ndash511httpsdoiorg101016jtree201006012
Bijma P ampWade M J (2008) The joint effects of kin multilevel se-lection and indirect genetic effects on response to genetic selec-tion Journal of Evolutionary Biology 21 1175ndash1188 httpsdoiorg101111j1420-9101200801550x
Boatright-HorowitzSLHorowitzSSampSimmonsAM(2000)Patternsof vocal interactions n a BullfrogRana catesbeiana chorus preferen-tial responding to farneighborsEthology106701ndash712httpsdoiorg101046j1439-0310200000580x
BothC(1998)Experimentalevidencefordensitydependenceofrepro-ductioningreattitsJournal of Animal Ecology67667ndash674httpsdoiorg101046j1365-2656199800228x
Cappa E P amp Cantet R J C (2008) Direct and competition additiveeffects in treebreedingBayesianestimation froman individual treemixedmodelSilvae Genetica5745ndash56
ChangAampSihA (2013)Multilevel selection andeffects of keystonehyperaggressivemalesonmatingsuccessandbehaviorinstreamwaterstridersBehavioral Ecology241166ndash1176httpsdoiorg101093behecoart044
Clutton-BrockTH(1989)MammalianmatingsystemsProceedings of the Royal Society B236339ndash372httpsdoiorg101098rspb19890027
Crowley P H amp Cox J J (2011) Intraguild mutualism Trends in Ecology amp Evolution 26 627ndash633 httpsdoiorg101016jtree201107011
Duckworth R A (2006) Aggressive behaviour affects selection onmorphology by influencing settlement patterns in a passerine birdProceedings of the Royal Society B 273 1789ndash1795 httpsdoiorg101098rspb20063517
Farine D R (2014) Measuring phenotypic assortment in animal so-cial networks Weighted associations are more robust than binaryedges Animal Behavior 89 141ndash153 httpsdoiorg101016janbehav201401001
FarineDRampWhiteheadH(2015)Constructingconductingandinter-preting animal social network analysis Journal of Animal Ecology841144ndash1163httpsdoiorg1011111365-265612418
Fawcett TW amp Johnstone RA (2010) Learning your own strengthWinner and loser effects should change with age and experienceProceedings of the Royal Society of London Series B Biological Sciences2771427ndash1434httpsdoiorg101098rspb20092088
Fisher D N amp McAdam A G (2017) Social traits social networksand evolutionary biology Journal of Evolutionary Biology httpsdoiorg101111jeb13195Inpress
FormicaVAWood CW LarsenW B Butterfield R EAugatMEHougenHYampBrodieIIIED(2012)Fitnessconsequencesofsocialnetworkpositioninawildpopulationofforkedfungusbeetles(Bolitotherus cornutus) Journal of Evolutionary Biology 25 130ndash137httpsdoiorg101111j1420-9101201102411x
Greenfield M D amp Rand S A (2000) Frogs have rules selective at-tention algorithms regulate chorusing in Physalaemus pustulosus (Leptodactylidae)Ethology106131ndash147
Helfenstein FDanchin E ampWagner RH (2004)Assortativematingand sexual size dimorphism in blacklegged kittiwakes Waterbirds27 350ndash354 httpsdoiorg1016751524-4695(2004)027[0350AMASSD]20CO2
Herbert-Read J E Krause S Morrell L J Schaerf T M Krause JampWardAJW (2013)The roleof individuality in collectivegroupmovementProceedings of the Royal Society B- Biological Sciences28020122564
KeiserCNampPruittJN (2014)Personality composition ismore im-portantthangroupsizeindeterminingcollectiveforagingbehaviourinthewildProceedings of the Royal Society of London Series B Biological Sciences28120141424httpsdoiorg101098rspb20141424
Krause J amp Ruxton GD (2002) Living in groups Oxford UKOxfordUniversityPress
Landeau L ampTerborgh J (1986)Oddity and the ldquoconfusion effectrdquo inpredationAnimal Behavior341372ndash1380httpsdoiorg101016S0003-3472(86)80208-1
Magnhagen C amp Bunnefeld N (2009) Express your personality or goalong with the group What determines the behaviour of shoalingperchProceedings of the Royal Society B- Biological Sciences2763369ndash3375httpsdoiorg101098rspb20090851
McDonaldG C FarineD R Foster K R ampBiernaskie JM (2017)Assortment and the analysis of natural selection on social traitsEvolution712693ndash2702httpsdoiorg101111evo13365
McGlothlin JW amp Brodie III E D (2009) How to measure individ-ual genetic effects The congruence of trait-based and variance-partitioning approaches Evolution 63 1785ndash1795 httpsdoiorg101111j1558-5646200900676x
McGlothlin J W Moore A J Wolf J B amp Brodie III E D(2010) Interacting phenotypes and the evolutionary pro-cess III Social evolution Evolution 64 2558ndash2574 httpsdoiorg101111j1558-5646201001012x
MillerJRBAmentJMampSchmitzOJ (2014)Fearon themovePredatorhuntingmodepredictsvariation inpreymortalityandplas-ticityinpreyspatialresponseJournal of Animal Ecology83214ndash222httpsdoiorg1011111365-265612111
ModlmeierAPKeiserCNWattersJVSihAampPruittJN(2014)The keystone individual concept An ecological and evolutionaryoverview Animal Behavior 89 53ndash62 httpsdoiorg101016janbehav201312020
MontiglioP-OFerrariCampReacutealeD(2013)Socialnichespecializationunder constraints Personality social interactions and environmentalheterogeneityPhilosophical Transactions of the Royal Society of London Series B Biological Sciences36820120343httpsdoiorg101098rstb20120343
Moore A J Brodie III E D ampWolf J B (1997) Interacting pheno-types and the evolutionary process I Direct and indirect geneticeffects of social interactions Evolution 51 1352ndash1362 httpsdoiorg101111j1558-56461997tb01458x
NonacsPampKapheimKM(2007)Socialheterosisandthemaintenanceof genetic diversity Journal of Evolutionary Biology 20 2253ndash2265httpsdoiorg101111j1420-9101200701418x
Nussey D H Wilson A J amp Brommer J E (2007) The evolution-ary ecology of individual phenotypic plasticity in wild popula-tions Journal of Evolutionary Biology 20 831ndash844 httpsdoiorg101111j1420-9101200701300x
OtterKAStewartIRKMcGregorPKTerryAMRDabelsteenTampBurkeT(2001)Extra-pairpaternityamonggreattitsParus major following manipulation of male signals Journal of Avian Biology 32338ndash344httpsdoiorg101111j0908-88572001320408x
Pruitt J N Bolnick D I Sih A DiRienzo N amp Pinter-Wollman N(2016)Behavioralhypervolumesofspidercoloniespredictscommu-nity performance and disbandmentProceedings of the Royal Society B- Biological Sciences 283 20161409 httpsdoiorg101098rspb20161409
PruittJNampPinter-WollmanN(2015)Thelegacyeffectsofkeystonein-dividualsoncollectivebehaviourscaletohowlongtheyremainwithina group Proceedings of the Royal Society B- Biological Sciences 28220151766httpsdoiorg101098rspb20151766
RoyleNJHartley IROwens I P FampParkerGA (1999) Siblingcompetition and the evolution of growth rates in birds Proceedings of the Royal Society B 266 923ndash932 httpsdoiorg101098rspb19990725
SaltzJBampFoleyBR(2011)Naturalgeneticvariationinsocialnicheconstruction Social effects of aggression drive disruptive sexual se-lectioninDrosophila melanogaster American Naturalist177645ndash654httpsdoiorg101086659631
ShusterSM LonsdorfEVWimpGMBaileyJKampWhithamTG (2006) Community heritabilitymeasures the evolutionary conse-quencesofindirectgeneticeffectsoncommunitystructureEvolution60991ndash1003httpsdoiorg101111j0014-38202006tb01177x
SimmonsAMSimmonsJAampBatesMA (2008)Analyzingacous-tic interactions in natural bullfrog (Rana catesbeiana) chorusesJournal of Comparative Psychology 122 274ndash282 httpsdoiorg1010370735-70361223274
Sinervo B R amp Calsbeek R (2010) Behavioral concepts of selectionExperiments and genetic causes of selection on the sexes In D FWestneatampCWFox(Eds)Evolutionary behavioral ecologyLondonUKOxfordUniversityPress
Thompson J N (1982) Interaction and coevolution Chicago USA TheUniversityofChicagoPress
emspensp emsp | emsp1463MONTIGLIO eT aL
VanderWaal K L ObandaV Omondi G P McCowan BWang HFushingHampIsbellLA (2016)Thestrengthofweaktiesandhel-minth parasitism in giraffe social networks Behavioral Ecology 271190ndash1197httpsdoiorg101093behecoarw035
Ward P I (1993) Micro-habitat segregation and the mating systemof Gammarus pulex Animal Behavior 45 191ndash192 httpsdoiorg101006anbe19931019
Ward P I amp PorterAH (1993)The relative role of habitat structureandmale-malecompetition in thematingsystemofGammarus pulex (CrustaceaAmphipoda)AsimulationstudyAnimal Behavior45119ndash133httpsdoiorg101006anbe19931011
West-EberhardMJ(1989)Phenotypicplasticityandtheoriginsofdiver-sityAnnual Review of Ecology and Systematics20249ndash278httpsdoiorg101146annureves20110189001341
Westneat D F Hatch M IWetzel D P amp Ensminger A L (2011)IndividualvariationinparentalcarereactionnormsIntegrationofper-sonalityandplasticityAmerican Naturalist178652ndash667httpsdoiorg101086662173
Wilson A J Gelin U Perron M-C amp Reacuteale D (2009) Indirect ge-neticeffectsandtheevolutionofaggression inavertebratesystemProceedings of the Royal Society of London Series B Biological Sciences276533ndash541httpsdoiorg101098rspb20081193
Additional Supporting Informationmay be found online in the sup-portinginformationtabforthisarticle
How to cite this articleMontiglioP-OMcGlothlinJWFarineDRSocialstructuremodulatestheevolutionaryconsequencesofsocialplasticityAsocialnetworkperspectiveoninteractingphenotypesEcol Evol 201881451ndash1464 httpsdoiorg101002ece33753
APPENDIX
PHENOTYPIC MEAN AND VARIANCE
FollowingMooreetal(1997)wemodelasinglephenotypeofanindi-vidual (z)asanadditivecombinationoftheeffectsof itsowngenes(iedirectgeneticeffectsa)thenonsocialenvironmentitexperiences(e)andaplasticcomponentthatissomefunctionofthephenotypesinitssocialgroupMooreetal(1997)originallymodeledthesocialeffectasafunctionofthephenotypeofoneinteractingindividualMcGlothlinandBrodie (2009)andMcGlothlinetal (2010)consideredsocialef-fectsinapopulationconsistingofgroupsofnindividualswhereinter-actionswereassumedtooccursimultaneouslywithinagroupwithallindividuals within a group having the same strength of interactionHereweconsideramoregeneralsocialstructurewhereindividualsinteractwithallpossiblesocialinteractantsingroupsizenwithvaria-bleconnectionstrengthsirangingfrom0to1giving
wherethesummationistakenacrossalln minus1possiblesocialinterac-tionsforeachindividualsandψrepresentstheinteractioncoefficientwhichdetermines thestrengthanddirectionof the indirectpheno-typic effect of individual social interactantsHere and elsewhere aprimeindicatesaparameterbelongingtoasocialpartnerAnysocialnetworkstructurecanbemodeledbychangingthedistributionofs High-densitysocialnetworkswithstrongconnectionswillhavemanylargevaluesofswhilesparsernetworkswithweakerconnectionswillhavemanyweaksvalueswithmanyequaltozeroConsideringphenotypicfeedback(asdoMooreetal1997)insuch
The value of the two covariance terms represents how stronglystrengthofinteractiondependsonthegenesandenvironmentofin-dividualsocialpartnersThiscovarianceisdeterminedforeachindi-vidualandmayvaryacrossindividualsTheseshouldbepositiveunderhomophilyandnegativeunderheterophilyTakingthemeanandas-suming
=e=0
where double overbars indicate global means and large overbarswithintheparenthesesindicatemeanstakenacrossindividualsbasedonsummarystatisticsoftheirsocialgroupsThiscanbeexpandedasaboveto
The remainingcovariance terms represent theaveragedegree towhichindividualconnectionstrengthsareadjustedbasedonthephe-notypeofpotentialinteractantsInthecaseofhomophilyorheteroph-ilyindividualswillmakethisadjustmentbasedontheirownphenotypewithlargeindividualshavingapositivecovarianceandsmallindividu-alshavinganegativecovariance(orviceversa)ThereforeweexpecttheseaveragecovariancetermstotendtowardzeroMakingthisas-sumptionandrearrangingprovidesEquation2inthetext
EXTENSION TO MULTIPLE GROUPS
EquationA8iswrittenassumingthatthepopulationconsistsofasin-gle social networkwhere individualsmay interact in anywayNowassumethatthepopulationisdividedintomultiplegroupswhereindi-vidualsmay interactwithanystrengthswithinagroupanddonotinteract at all between groups Assuming the covariance terms inEquationA8arezeroandthatenvironmentaldeviationsdonotvaryamonggroupsthemeanofeachgroupwillbe
where overbars now indicate within-groupmeans Assuming equalgroupsizethepopulationmeanisnow
(IfgroupsvaryinsizethenEquationA10canbemodifiedtogiveaweightedmean) Ifconnectionstrengthhasnoheritablebasis thenthe covariance term become zero and EquationA10 collapses toEquation2inthetextWemaycalculateamong-groupvariancemosteasilybymakingafewassumptionsthatarealsomadeinoursimula-tionsFirstasaboveweassumethatgroupsareofequalsizeSecondweassume thatmean interactiondoesnotvaryacrossgroups ands=
=sMakingtheseassumptions
Thisshowsthat indirectgeneticeffectswillmagnifyslightdiffer-ences in genetic values across groups regardless of sign Strongermeanconnectionstrengthswillintensifythiseffect
RESPONSE TO SELECTION
FollowingMoore etal (1997) andMcGlothlin etal (2010) and as-suming that thecovariance terms inEquationA8areeither zeroorpopulation parameters that do not have a heritable component anindividualrsquostotalbreedingvaluecanbewrittenasthegeneticcontri-butiontothepopulationmean
where Ristheregressionofsaprimeonaandisthusanalogoustorelated-ness This assumes thatCov[aseprime] is negligible Positive values ofR indicatehomophilyandnegativevaluesindicateheterophilyMakingthissubstitutiongivesEquation4inthetextEquation4canalsobeexpresseddifferentlybyrearrangingas
Interacting phenotypes theory has used quantitative geneticmodels to show how evolutionary trajectories are altered by socialplasticity (BaileyampHoskins 2014BaileyampZuk2012BijmaMuirEllenWolf amp Van Arendonk 2007 Bijma Muir amp Van Arendonk2007BijmaampWade2008McGlothlinMooreWolfampBrodie2010MooreBrodieampWolf1997WolfBrodieampMoore1999)Indirectgenetic effectswhichoccurwhenone individualrsquos genes affect an-other individualrsquos phenotype may either amplify or decrease theamountofgeneticvarianceavailabletoselectionThisprocesscouldquickenorslowthepaceofevolutionarychangeandmayalsocausecoevolutionofotherwiseuncorrelatedtraits(Mooreetal1997)Theeffectof social plasticityonevolutionaryprocesses including thosecapturedbyquantitativegeneticmodelsdependsonthepatternofsocial interactionsoccurringwithin a population that iswho inter-actswithwhomandwithwhatfrequencyorintensityEarlyinteract-ing phenotypemodels focused solely on simple dyadic interactions(Mooreetal1997)and laterattempts includedunstructured inter-actionswithin largergroups (AgrawalBrodieampWade2001BijmaampWade2008BijmaMuirEllenetal2007McGlothlinampBrodie2009McGlothlinetal2010)HowevernoneofthesemodelshaveexploredmorerealisticallystructuredinteractionswherethestrengthofassociationsmayvaryacrossdyadsandwhereindividualsmaynotinteractwitheveryothermemberoftheirgroupItisthereforeunclearwhethertheconclusionsfrominteractingphenotypemodelsaregen-erallyapplicabletomostanimalpopulations
Innaturesocialinteractionsmoreoftenresemblestructurednet-worksthandyadsornonoverlappinggroupsSocialnetworkanalysisprovidesapowerfultoolforquantifyingthestructureofsuchinterac-tions(FarineampWhitehead2015Whitehead2008)anditsimpactsonsocialprocesses(AplinFarineetal2015VanderWaaletal2016)Social network analysis uses information aboutwho interacts withwhomtolinkindividualinteractionstooverallpopulation-levelsocialstructure(Hinde1976Whitehead2008)Incontrasttosimplermod-elsofsocialstructuresocialnetworkscancapturevariation inboththe immediate social environment that individuals experience (iewhoeachindividualinteractswithdirectly)andtheindividualsrsquoposi-tionswithintheoverallsocialstructureofthegroup(iehowcentralanindividualisinstabilizingorfavoringaparticularsocialstructure)Combiningthisgreaterrealismwhenquantifyingsocialstructurethatisthepatternsofconnectionsinasocialnetworkwiththeabilitytomakeformalpredictionsaboutphenotypicevolutionhasthepotentialto significantly expandour understandingof the evolutionof socialtraits(FisherampMcAdam2017)
Inthisstudyweinvestigatehowsocialstructuresshapethe im-pactofsocialplasticityontheamountofphenotypicvarianceavailableforselectionandontheevolutionaryresponseoftraitstoselectionFirstweexpandmodelsofinteractingphenotypes(McGlothlinetal2010Mooreetal1997Wolfetal1999)todescribehowvaryingaspectsofsocialstructuresuchasstrengthsofconnectionsbetweengroupmembersandpreferentialassociationbasedonphenotypicsim-ilarityimpactphenotypicvariationandevolutionSecondwecreatereplicategroupsofindividualswithstructuredsocialinteractionsusingagent-based simulations to analyze how social structure influences
distributionsofphenotypesandtheabilitytorespondtonaturalselec-tionWefocusonthenumberofconnectionsobservedamonggroupmembers (ienetworkdensity thesumofallpresentedgeweightsdividedbythepossiblesumofedgeweightsifthenetworkwerefullyconnected)andthedegreetowhichindividualscanbiasthestrengthof their interactionswith others that have a similar phenotype (ienetworkhomophily)Althoughtheparametersofouranalyticalmodelarenotidenticaltothoseofoursimulationmodeltheyareanalogous(iemeanconnectionstrengthisrelatedtonetworkdensityandphe-notypicassortment isrelatedtohomophily)allowingustocomparetheconclusionsofthetwoapproaches
Wepredictthatsocialplasticityshouldhaveaminimaleffectonphenotypesandontheirvariationwhenconnectionsamongindividu-alsareweak(atlownetworkdensitiesFigure1leftpanels)becauseall individuals experience weaker effects of the same social envi-ronment (they are disconnected) Likewisewepredict therewill beminimalvariation in indirectgeneticeffectsamong individualswhenconnectionsarestrong(athighnetworkdensitiesFigure1rightpan-els)becauseall individuals interactequallyandwiththesamegroup(everyoneexcludingthemselves)Thusthesocialenvironmentexpe-riencedbyeachindividualshouldbeveryclosetotheaveragepheno-typeofthepopulationNetworkswithintermediatenetworkdensities(Figure1middle panel) have a greater scope to exhibitvariation inlocal social structure resulting invariation in thesocialenvironmentexperiencedbyindividualsNextwepredictthathomophilyandsocialplasticityshouldinteractinasimilarwayasdorelatednessandindirectgeneticeffectsindyadicmodels(McGlothlinetal2010)Specificallywhensocialplasticitycausesindividualstobecomemoresimilaradd-ingpreferentialassortmentshouldleadtoanincreaseinphenotypicvariation and anenhanced response to selectionConverselywhenindividualsexpressheterophily (disassortativeassociationbypheno-type)weexpectindirectgeneticeffectstodecreasetheabilityofthetraittoexhibitchangeinresponsetoselection
2emsp |emspMETHODS
21emsp|emspAn analytical model integrating connection strength and phenotypic assortment
Wedevelopananalyticalmodelofinteractingphenotypesinagen-eralized social network In our model the average social plasticityofagroupofindividualsisrepresentedbyaninteractioncoefficient(ψg)whichmeasurestheoverallphenotypiceffectofanindividualrsquossocial partnersrsquo phenotypes on its own phenotype The phenotypicchangesresultingfromsocialplasticityaremodulatedbytheoverallmeanstrengthoftheconnectionsamongindividuals(ieindividualsareembeddedwithinaweightednetworkwithconnectionstrengthsranging from0to1andthenetworkdensity is thesumofallpre-sentedgeweightsdividedbythepossiblesumofedgeweightsifthenetworkwerefullyconnected)Whiletheproductofsocialplasticityandconnectionstrengthcouldbemodeledasasingleparameterweprefertoretainthedistinctionbetweenconnectionstrengthandplas-ticitytokeepourmodelcompatiblewithempiricalstudiesofindirect
emspensp emsp | emsp1453MONTIGLIO eT aL
geneticeffects(egCappaampCantet2008)andallowextensionsofthismodel in the futureWeallowconnection strengths todependupon the nonplastic component of the phenotype (phenotypic as-sortment)Suchassortmentisanalogoustohomophilywhenassort-ment is positive (individuals seek similar partners) and heterophilywhenassortment isnegative(individualsavoidsimilarpartners)WefollowedtheapproachofMooreetal (1997) ignoringthepotentialfordirectsocialeffectsonfitness(socialselectionorgroupselectionWolf etal 1999)Althoughourmodel considers only a single traitforsimplicityitdoesnotconsiderthepossibilityforfeedbackeffectsonphenotypesmakingourmodelanalogoustothetwo-traitmodelwithnonreciprocaleffectsofMooreetal(1997)Wewilltreatphe-notypicfeedbackinafuturecontributionThemodelispresentedinitsentiretyintheAppendixbutwereportitsmainresultsbelow(seeResults)
22emsp|emspSimulation overview
Toinvestigatehowsocialplasticityandsocialstructurecanaffecttheextentofphenotypicvariationobservedwithinpopulationsandevo-lutionarychangewesimulategroupsofindividualswithafixedinter-actioncoefficient(ψg)butvaryingsocialstructures(networkdensityandhomophilyheterophily)EachgrouphasitsownuniquenetworkofinteractionsFromtheseinteractionswecalculatethephenotypethateachindividualinthegroupwouldexpressgivensocialplasticityWe then calculate thephenotypicmeanof the group the varianceinindirectgeneticeffectsexperiencedamongindividualgroupmem-bersthecorrelationbetweenindividualsrsquogenetictendenciesandtheindirectgeneticeffects theyexperienceandtheoverallphenotypicvarianceofthegroupWealsocalculatetheoverallgeneticvariance
WesimulatereplicatednetworksofvaryingdensityandhomophilyEachreplicatecanbeconsideredasa (small)populationorasadis-tinct group embeddedwithin a largermetapopulation To generatenetworksofinteractionwefirstgeneratepairsofcoordinatesfromauniformdistribution(range0ndash1)forindividualsToalloweachindivid-ualtointeractmorestronglywithsomeofitsconspecificsrelativetoothersweallowindividualstomovetowardtheirnearestneighborby15ofthedistancebetweenthemVaryingthispercentagedoesnotinfluenceourresults(resultsnotshown)Todeterminetheconnectionstrengthsbetweeneachpairof individuals inoursimulations(s)wecalculatetheEuclideandistancebetweenthemanduseanexponentialdecayfunctiongeneratingadecreasingconnectionstrengthasafunc-tionof thedistancebetweenany two individualsThusweassumethattheconnectionstrengthbetweentwoindividualsiss=eminusdistance
F IGURE 1emsp (a)Samplenetworksgeneratedusingthreevaluesofr(005015and09)creatingnetworksofvaryingdensitieslow(left)intermediate(center)andhighdensities(rightNgroup=12)(b)Foreachlevelofdensityindividualsalsovariedinthenumberofinteractionswithothergroupmembersshownatlow(left)intermediate(center)andhigh(right)networkdensities(Ngroup=500)
Becausetheresultingnetworkdensity(thesumofallpresentedgeweightsdividedby thepossible sumofedgeweights if thenetworkwerefullyconnected)foragivenvalueofrisstochasticnotdetermin-isticwereportourresultsasafunctionofnetworkdensitywhichwascalculatedusingtheRpackageassortnet(Farine2014)Statedanotherwaynetworkdensityisanemergentpropertyofvaryingrnotaparam-eterofoursimulationsOurapproachismostimmediatelyapplicabletosituationswhereindividualsareactuallydistributedintwo-dimensionalspaceandinteractmoreorlessintenselyasafunctionofthedistance(Farine 2015) Such an interaction structure applies directly to situ-ations such as competition amongneighboringplants (egCappaampCantet2008)orterritorialityinanimals(egRoyleHartleyOwensampParker1999)butisgeneralizableawidevarietyofothermorecomplexsituationsthatmaynotinvolveaspatiallyexplicitcomponent
Individualscanoftenchoosetoconnectmorestronglywithsomeindividuals than others In many species individuals preferentiallyinteractwithpartnersthataresimilar (ieunderassortativematingor during cooperative interactions) or dissimilar to them (ie underdisasortativemating or because of division of labor and social het-erosis seeNonacsampKapheim 2007)Hence networks can exhibitassortment (associations between individuals that are similar andor avoidance of dissimilar individuals Farine 2014) Firstwe studythe effect of randomly occurring network assortment in the sim-ulated groups To explicitly investigate the impact that interactionpreferencescanhaveonevolutionaryprocesseswethenallowindi-vidualstoreducethestrengthoftheirinteractionwithnonpreferredaffiliates (eg with dissimilar individuals in the case of homophilyorwithsimilar individuals inthecaseofheterophily)Wethusmod-ify the function used to calculate the strength of interaction (s) tos=eminusdistance
2∕rtimesH(
1
1+expminus20|xminusy| minus05)+05 which generates a sig-
moidalfunctionwithamagnitudeofH(thelevelofhomophilyrang-ingbetween0and02) as a functionof |xminusy| or thedifference inthephenotypesoftheindividualsIftwoindividualsareidenticalthestrengthoftheirinteractionismultipliedbyeither~0or~1ifmodelingheterophily or homophily respectivelyTheir connection strength ismultipliedby05iftheirphenotypicdifference(|xminusy|)isaverageAswithnetworkdensitywe report themeasurednetworkassortmentcalculatedusingtheRpackageassortnet(Farine2014)
strengthoftheirsocialinteractionssiIndividualswithnoconnectionstrengthdonotcontributetothephenotypeassi =0Inoursimula-tionsall individualshavethesameinteractioncoefficient(ψg)Wealsoinvestigatewhetherourresultsdependedonthedistributionofbreedingvaluesbyrunningadditionalsimulationswhereindividualbreedingvaluesare sampled fromanormaldistribution (mean=0andvariance=1)IntheresultswepointoutwheresuchachangeindistributionaffectsourresultsInpreviousmodels(McGlothlinampBrodie2009McGlothlinetal2010)ψghasbeenconstrainedtoliebetweenminus1and1fortworeasonsFirstvaluesofψggreaterthan1canleadtounreasonablephenotypicvalues(particularlyinmodelsthat include phenotypic feedback) Second phenotypic values areoftenstandardizedtoameanofzeroandunitvarianceforanalysiswhichshouldresult inψgvaluesbetweenminus1and1 Inoursimula-tionsthemeanandvarianceofindividualphenotypesvariedineachgroup because of samplingwhichmade such standardization dif-ficultWechose touseunstandardized traitvaluesanda largeψg value(4)inallsimulationsSuchavalueofψgwhichwouldyieldanaveragestandardizedvalueofψgof~030whichiscomparabletoempiricalψgvaluesreportedintheliterature(egBaileyampHoskins2014BaileyampZuk2012)Usingthislargevaluefacilitatesvisual-izing social effects anddoesnot lead tounreasonablephenotypicvalues due to the absence of phenotypic feedback in ourmodelAs noted in theAppendixψg ismultiplied by average connectionstrength (network density) when calculating phenotypes whichwillreducetheeffectofψgexceptinfullyconnectednetworksAspredictedbytheanalyticalmodel increasingthestrengthofsocialplasticity(iehowmuchanindividualchangedhisphenotypeinre-sponsetohissocialpartnerstheabsolutevalueofψg)amplifiesallthe patternswe report below (seeResults section)However be-causesuchincreasesareintuitiveandoflesserinterestwedonotreporttheresultsofanalysesvaryingψgUsingthecodeavailableasFigureS1 the reader cangenerate figures that are comparable totheoneswepresentbelowforanyvalueofψg
where G indicates additive genetic variance andE indicates envi-ronmental variance The third term above represents the among-individual variance due to social interactions This term shouldincreasesomewhatwithhomophilybutshoulddependmostheav-ily on network density The variance in social environment expe-rienced by individuals should be at amaximum at intermediate
becomemorehomogenous(ieeveryoneinteractswitheveryone)Thefourthtermwillbemost influencedbyhomophily (orhetero-phily)becauseassociatingwithsimilar(ordifferent)individualswillcause the covariance to increase (ordecrease)Themultiplicationbyψgwillcausephenotypicvariancewithinagrouptoincreasewithhomophilyunderpositivevaluesofψganddecreasewithhomophilywhenψg isnegativeThistermshouldalsobe influencedbyaver-ageconnectionstrength(
where R is a general measure of the strength of homophily (seeEquationA19 in Appendix) and β is the selection gradient (seeAppendix)Thisequationshowsthattheamountofgeneticvarianceavailableforresponsetoselectionatthepopulationlevelshouldde-pendon(1)thedegreeofsocialplasticity(2)theaverageconnectionstrength(whichshouldincreasewithmeanconnectionstrength)and(3)theamountofassociationbetweenindividualsthatisbasedonge-neticvaluesimilarity(homophilyorheterophily)Thismodelisnearlyidenticaltopreviousmodelswithsimplergroupstructure(McGlothlinetal 2010) except for the inclusion of the connection strength (
=s)
and the replacementof relatednesswithhomophilyheterophily (R)Theseanalyticalresultsprovidepredictionsthatwetestbelowusingindividual-basedsimulations
32emsp|emspNetwork density
Inoursimulationsincreasingnetworkdensitywhichisanalogoustoincreasing mean connection strength in the analytical model doesnot lead to an increase inphenotypicmeanonaverage (ie acrossallgroupsFigure2red line)Howeverathighernetworkdensitiesthere is much greater variation among groups in their phenotypicmean (Var[
=z ] Figure2 gray dots) This occurs because although
themeangeneticvalueacrossall simulations iszero thisvaluecandiffer across groups due to sampling As predicted by Equation2increasing network density (or
=s) increases the importance of the
group genotypic composition in determining the effects of indirectgeneticeffectsmagnifyingdifferencesamonggroupsingeneticvalue(=a) across replicate simulation runs This amplification effect is also
Thephenotypicvariance in indirecteffectswithineachgroup ismaximalatintermediatenetworkdensities(Figure3a)Whenindivid-ualshave fewconnections (and connection strength isweaker) thescopeforindirecteffectstodifferamongmembersofagivengroupisnarrowtherebydecreasingthecontributionofsocial interactionstophenotypicvariance(Figure3a)Likewiseingroupswhereindividualsarehighlyconnected (highnetworkdensity) thesocialenvironmentexperiencedbyeachindividualisclosertotheaveragebreedingandenvironmentalvalueofthepopulation(whichis0inoursimulations)In otherwordsVar[aprime] and consequentlyVar[saprime]within groups issmallathighdensities(seeEquation3)Howeveratintermediateden-sities indirecteffectshadthepotentialtomakealargecontributiontophenotypicvariancealthoughthiseffectwashighlyvariableacrosssimulations
Intheabsenceofhomophilyheterophilyhighnetworkdensityleadstoanegativecorrelationbetweendirectandindirectgeneticeffects(Figure3b)Atlownetworkdensitiesthiscorrelationisex-pectedtobezerobecauseindividualsassociateatrandom(althoughthiswouldnotbe thecase if therewasanyspatial assortmentbyphenotype) However at high densities this correlation becomesnegativeeventhoughindividualassociationisalsorandomThisef-fectarisesbecauseindividualsarenotcountedaspartoftheirownsocial environment andasnetworkdensities increase the impor-tanceofthisdifferencebecomesmagnifiedAtthehighestnetwork
(3)Var[z]=G+E+ψ2gVar
[sa + se
]+2ψgCov
[a +e sa + se
]
(4)Δ=zasymp
(1+ψg
=s)G(1+Rψg
)β
F IGURE 2emspThechangeinaveragephenotypeofindividualsinanetworkasafunctionofthenetworkdensity(redline)Thechangeinaveragephenotypeisexpressedrelativetothephenotypeexpectedinabsenceofinteractionsamongindividuals(ie0)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4Asdensityincreasedweobservedagreatervariationinmeanphenotypeamonggroups(graydots)
1456emsp |emsp emspensp MONTIGLIO eT aL
densitiessocialenvironmentsare indistinguishableexceptforthiseffect of excluding oneself thus leading to a directndashindirect cor-relationofminus1Smallergroupswillexhibitthispatterntoastrongerextent than larger groups (see FigureS5 also McDonald FarineFosterampBiernaskie2017)Thecombinedimpactoftheeffectsofnetworkdensityonthevariancein indirectgeneticeffectsandonthecovariancebetweendirectandindirectgeneticeffectsisarel-ativedecrease inphenotypicvariationwithingroups(comparedtothephenotypicvariationinabsenceofanyinteractions)asnetworkdensityincreases(Figure3c)Oppositepatternsareobservedwhenψg isnegative(FigureS6)Finallywenotethatalthoughthemeanphenotypic variationwithin each group decreaseswith increasingnetworkdensitywefindthatthevariationamonggroups(eachdotin each panel of Figure3c represents one group) ismaximized atintermediatenetworkdensities
Although the phenotypic variance typically decreases with in-creasednetworkdensitythevarianceintotalbreedingvalues(rela-tivetothegeneticvarianceinabsenceofanysocialinteraction)hasthe greatest increase at highest network densities (Figure3d redline)Thisisbecausetheexpectedvarianceintotalbreedingvaluesisequalto
(1+ψg
=s)2
G(seeEquationA12)Thatisthevarianceintotalbreedingvaluesdoesnotdependonthevarianceinindirectgeneticeffects noron the covariancebetweendirect and indirect geneticeffectswhich leadtothedecrease invarianceshowninFigure3cRatherthevarianceintotalbreedingvaluesisafunctionofdirectge-neticeffectsandeffectsofanindividualrsquosgenesonothersthelatter
ofwhichbecomesinflatedathigherdensitiesTheresponsetoselec-tiondependsonthecovariancebetweentotalbreedingvaluesandphenotypicvalueswhichisexpectedtoincreaselinearlywithdensity(EquationA15)Whenwesubjectgroupstoaselectiongradientof02networkswithincreasingdensitiesexhibitedanincreasedevolu-tionaryresponsetoselection(Figure4redline)Increasingnetworkdensityalso increases thevariance in responsetoselectionamonggroups (Figure4 gray dots) This likely happened because individ-ualsadjusttheirphenotypetotheaveragesocialenvironmentthattheyexperienceThusathighernetworkdensitiesindividualswithextreme phenotypicvalues have a disproportionate impact on theaveragesocialenvironmentexperiencedbyindividualsSmalldiffer-encesinthephenotypicvaluesofextremeindividualsfromgrouptogroupcreatedifferencesinthecovariancebetweenthephenotypicvarianceandthetotalbreedingvaluesamonggroupsandincreasingthevariance in response to selection amonggroups In agreementwiththisextremeindividualsalsogenerategreaterphenotypicvari-anceamonggroupsathighernetworkdensities(Figure2)andwhenindividualphenotypesfollowauniformdistribution(moreindividualswithextremephenotypes)thananormaldistribution(fewerindivid-ualswithextremephenotypesSeeFigureS3)
F IGURE 3emspEffectsofnetworkdensityon(a)thevarianceinindirecteffectsexperiencedbyindividuals(b)thecorrelationbetweendirectandindirectgeneticeffectsexperiencedbyindividuals(c)thechangeinphenotypicvariancewithingroupsrelativetothegeneticvariance(iethephenotypicvarianceinabsenceofinteractions)and(d)thechangeintotalgeneticvariationrelativetothegeneticvariance(ievarianceofindividualdirectgeneticeffectsandindirectgeneticeffectsimposedtoothers)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψg of4
emspensp emsp | emsp1457MONTIGLIO eT aL
hasnoeffectonthemeanphenotypeofeachgroup(Figure5)whichis consistent with our analytical model (Equation2) However in-creasednetworkassortmentisassociatedwithanincreaseinthevari-anceinindirectgeneticeffectsexperiencedbyindividualsinagivengroup(seethethirdterminEquation3Figure6a)Becauseindividu-alsinteractmorestronglywithconspecificsthathavesimilarbreedingvalues(highwithhighlowwithlow)thedirectandindirectgeneticcontributions to phenotypes act in concert and covary positively(fourthterm inEquation3Figure6b)Thesetwoeffectscontributetowardincreasingphenotypicvarianceobservedwithinagivengroup(Figure6c)Theseeffectsarereversedwhenψgisnegativedirectandindirect contributions to individual phenotypes act to oppose eachothertherebyreducingtheamountofphenotypicvarianceobservedin the population (see FigureS7) Increasing network assortmentalsoleadstoasmalldecreaseinthevarianceintotalbreedingvalues(Figure6dredline)Thisisattributabletotheslightdecreaseinden-sityassociatedwithhigherlevelsofnetworkassortment(ieindividu-alshavetheabilitytoreducetheconnectionstrengthwithparticulargroupmembers)aphenomenonnotcapturedbyouranalyticalmodel
Applying selection to groups with varying network assortmentshowsthatasynergybetweendirectandindirectgeneticeffectsleadstoanincreaseinevolutionarychangewithincreasingnetworkassort-ment(Figure7redline)Thisresultisinaccordwiththepredictionsofouranalyticalmodelwhichpredictsanincreasedresponsetoselec-tionwithincreasingR(Equation4)AlthoughEquation4suggestsden-sityandhomophilyshouldhavesymmetricaleffectstheincreaseseeninFigure7isnotasdramaticasthatinFigure4perhapsbecauseoftheconcomitantdecreaseindensitycausedbyallowinghomophilyinoursimulationsUnlikenetworkdensitynetworkassortmentdoesnotaffectthevariationofevolutionaryresponsesamonggroups(Figure7graydots)
4emsp |emspDISCUSSION
Inthisstudyweexploretheconsequencesofsocialplasticityandthestructureofinteractionsinshapingtheamountofphenotypicvariationwithingroupsof interactingindividualsandtheevolutionaryresponseofthesegroupstoselectionWeconsiderreplicategroupswithvary-ingstructuresofinteractionsSuchreplicatescouldbeseenasmultiplegroups of individualswithin a given population (eg tribes packs orcolonies)orasmultipleisolatedpopulationswithinanecologicalcom-munityThroughananalyticalmodelandagent-basedsimulationsweshowthatthestructureofsocialnetworksmodulatedtheimpactofin-directgeneticeffectsontheamountofphenotypicvarianceavailablefor selectionOur resultsemphasize that thenumberandstrengthofconnectionsamongindividuals(networkdensity)aswellaspreferentialassociations among individualswith a similar phenotype (network as-sortment)haveimportanteffectsonthecontributionofindirectgeneticeffectsNetworkdensityandassortmentalsomodulatetheabilityfortraitstoexhibitevolutionarychangeinresponsetoselectionIncreasingthenumberofinteractionsamonggroupmembers(networkdensity)in-creasestheaverageevolutionaryresponseofgroupstoselectionandin-creasesthevariationinresponsetoselectionamonggroupsBycontrastincreasednetworkassortmentleadstoanincreaseintheaverageevolu-tionaryresponseofgroupstoselectionbutdoesnotaffectthevariationinevolutionary responseamonggroupsOur resultshavewidespreadimplicationsforstudiesofsocialevolutionmultilevelselectionandtheemergenceofkeystoneindividuals(ModlmeierKeiserWattersSihampPruitt2014)andniche-constructingtraits(egSihampWatters2005)
41emsp|emspComparison with earlier interacting phenotype models
Our analytical results show that given some simplifying assump-tions (most importantly ignoring the potential for phenotypic
F IGURE 4emspEvolutionaryresponseofphenotypetoaselectiongradientvarieswithnetworkdensityTheaveragechangeinphenotypemeanresultingfromselectionincreasedwithnetworkdensity(redline)Groupswithdensernetworksofinteractionsexhibitedmorevariationinthechangeinphenotypicmean(graydots)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4
F IGURE 5emspTheaveragephenotypeofindividualsasafunctionofnetworkhomophily(redline)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4Networkscouldnotreachhomophilyvaluesof1becauseweusedacontinuoustraitvalueratherthandiscretevalues(seeFarine2014)
1458emsp |emsp emspensp MONTIGLIO eT aL
feedback) considering more general social structures does notgreatlyalter theconclusionsofearliermodelsof interactingphe-notypeevolution(egMcGlothlinetal2010Mooreetal1997)First indirect genetic effects still alter the response to selectionby increasing the amount of genetic variance exposed to selec-tionNote thatbecausewedonotmodel feedback thiseffect is
directional with positiveψg (ie becomingmore similar to onersquosneighbors)increasingtheresponsetoselectionandnegativevalues(iebecomingmoredifferentfromonersquosneighbors)decreasingitSecondhomophilyheterophilyplaysa rolesimilar to relatednessinpreviousmodelsinalteringtheresponsetoselection(McGlothlinetal2010)IndeedMcGlothlinetal(2010)noted(ashavemanyothers)thatrelatednessperseisjustaspecialcaseofphenotypicassortment
Themostnotabledifferencebetweenourmodelandearliermod-elsisthatindividualsareallowedtodifferintheirinfluenceonsocialplasticityduetovariation inconnectionstrength (s)Perhapsunsur-prisingly responsetoselection ismorestrongly influencedbysocialinteractions indensernetworkswhere interactionsarestrongerandmorecommonaneffect that isapparent inbothouranalyticalandsimulation results Inour simulation resultswealso find thatvaria-tioninresponsetoselectionamongincreaseswithgreaterconnectionstrengthThis could occur because in some groups themostwell-connectedindividualshappentohaverelativelyhighorlowbreedingvaluesThesewell-connected individualswould thenhaveadispro-portionateeffectonthephenotypeofothers (relativeto individualsclosertothepopulationrsquosaveragebreedingvalue)byexertingastrongeffectonthemeansocialenvironmentexperiencedbyindividualsIndoingsowell-connectedextremeindividualscangeneratevariabilityinthecovariancebetweenbreedingvaluesandphenotypeandthusintheresponsetoselectionFuturemodelsshouldallowconnectionstrength to display a heritable component which would allow thesocialnetworkstructureitselftoevolveinresponsetosucheffects
F IGURE 6emspEffectofnetworkhomophilyon(a)thevariationinindirecteffects(b)thecorrelationbetweendirectandindirectgeneticeffects(c)therelativechangeinphenotypicvariancewithingroupsand(d)therelativechangeintotalgeneticvariationEachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4HomophilysimultaneouslyincreasesvariationamongindividualsinindirectgeneticeffectswithingroupsandgeneratesastrongpositivecovariancebetweendirectandindirectgeneticeffectstherebysubstantiallyincreasingthephenotypicvarianceobservedwithingroupsHoweverthisincreaseinphenotypicvarianceisnotassociatedwithanychangeatthegeneticlevel
F IGURE 7emspEvolutionaryresponseofphenotypetoaselectiongradientincreaseswithnetworkhomophily(redlineandgraydots)Eachdotrepresentsthechangeinmeangenotypeacrossgenerationsinasinglesimulatednetworkorgroupof50individuals(Ngroup=50)TheredlinerepresentstheaverageevolutionaryresponseasafunctionofnetworkdensityIndirectgeneticeffectsweregeneratedusingaψgof4
emspensp emsp | emsp1459MONTIGLIO eT aL
Studiesinthewildhaveshownthatpositioninasocialnetworkmaybe repeatable and have fitness consequences suggesting that con-nectionstrengthmaybeanevolvabletrait (AplinFirthetal2015FormicaWoodCookampBrodie2017Formicaetal2012)
42emsp|emspGroups with denser connections exert a stronger ldquopull to the meanrdquo
Our simulations show that groupswhere individuals have an in-termediatenumberorstrengthofsocialconnections (iegroupswithintermediatenetworkdensities)allowforthegreatestwithin-groupvariationinsocialenvironmentsexperiencedamongindivid-ualsThispatternariseswithinagenerationduetosocialplasticityratherthanasaresponsetoanyselectivepressureBygeneratinga greater range of phenotypes and social environments groupswithan intermediatedensityof social interactionscouldprovidethe basis for the emergence and evolution of alternative socialphenotypes (Bergmuumlller amp Taborsky 2010 Sinervo amp Calsbeek2010) When social phenotypes are subject to indirect geneticeffects the maintenance of variation in social behavior shouldthus be observed more frequently in groups with intermediateconnectedness
Whilelowtointermediatedensitiesofsocialinteractionsofferthewidestscopeforpromotingindividualvariationinphenotypegroupswith high densities exhibit a very different patternAs the numberand strengths of interactions increases among group members in-direct genetic effects experienced by each individual becomemoresimilarbecauseallgroupmembersstarttobecomeconnectedtooneanotherand theseconnectionsareuniformlystrong Inadditionasnetworksbecomemoreconnectedindividualsattheextremesofthedistributionofgenetic tendencies in thegroups (ie the individualsfurthest from the averagebreedingvalue) tend to experience a so-cialenvironmentexertinganopposingeffectontheirphenotype(ieCov[a+esa +se] in Equation3 becomes more negative) This ldquopullto themeanrdquo is stronger in smaller groups than in larger ones (seeFigureS5) anddecreases thepopulationphenotypicvariancewhenψg ispositive (egwhen individuals increasetheiraggressiveness inresponse to the aggression they receive) and increases it whenψg is negative (egwhen individuals inhibit their aggressiveness in re-sponsetotheaggressiontheyreceive)Whenindividualsexhibit im-portantphenotypicplasticitysuchaneffectappearssimilartosocialconformity where individuals express more similar phenotypes asgroupsthan in isolation (egHerbert-Readetal2013MagnhagenampBunnefeld2009)Conformity isusually thought toemergewhendissimilarindividualsareatafitnessdisadvantageForexamplepred-ators tend topick individuals that standout amonggroupsofpreyselecting forhomogeneousgroups (LandeauampTerborgh1986)Weshowherethatconformist-likepatternsinbehaviorcanemergefromverysimpleformsofsocialplasticity Importantlyweshowthatbe-havioralconformitycanemergeevenwhenindividualsarenotactivelycopyingthemostabundantphenotypeoftheirgroup inabsenceofanyselectivepressureExamplesofhighlyconnectedgroupsinnatureincludechorusesofmalesinsomespeciesoffrogsproducingmating
calls or leks ofmales displaying to attract females and adjust theirsignalingeffortinresponsetothesignalingoftheirrivals(Boatright-HorowitzHorowitzampSimmons2000SimmonsSimmonsampBates2008)Whenmalesareclosetoeachotherandeachmalecanadjustits signaling intensity to that of all the othermaleswe expect thisldquopulltothemeanrdquotodecreasethevariationinmalesignals(althoughsocialplasticitycantakemorecomplexpatternsthenismodeledhereGreenfieldampRand2000)Thiscandecreasetheeffectivenessoffe-malematechoiceandtheintensityofsexualselection
43emsp|emspGroups with denser connections potentiated the effect of keystone individuals
Aninsightfromoursimulationsisthatwheneverindividualsadjusttheirphenotypetotheaveragesocialenvironmentthattheyexperi-enceindividualsattheextremesofthegenotypicorphenotypicdis-tributionhavethegreatestimpactonthephenotypeofothergroupmembers This phenomenon arises because these individuals havethestrongest impacton themeansocialenvironmentexperiencedbytheirconspecificsTheevolutionofniche-constructingtraitsal-lowingsomeindividualstomanipulatetheirgroupinawaythatfa-vorstheirownsuccess(SaltzGeigerAndersonJohnsonampMarren2016) or to have a disproportionate effect on their group (Keiseramp Pruitt 2014 Modlmeier etal 2014 Pruitt amp Pinter-Wollman2015)hasbeenthefocusofmuchinterestrecentlySurprisinglynostudyhasexplored the implicationsof theexactpatternsofsocialplasticity for the identity and impact of such ldquokeystone individu-alsrdquo (Modlmeier etal 2014) It is reasonable to assume thatmostanimalsexhibitingsocialplasticityshouldadjusttheirphenotypeinresponse to theaverage socialconditions that theyexperience (al-thoughinsomecasessomeindividualscanadjusttheirphenotypeto themaximumor to theminimumphenotypicvalueof the indi-vidualswithwhomtheyinteractseeDyerCroftMorrellampKrause2009 for a potential example) Thus our simulations suggest thattheemergenceofkeystoneindividualsmightbeaphenomenonfarmore common than previously envisioned Keystone individualscouldemergeinanygroupofinteractingindividualsexhibitingphe-notypicplasticityanddenseinteractionnetworks(asinthelekkingexampleabove)Hencetheemergenceofkeystoneindividualsmightnotrequireacomplexsocialsystemdivisionoflabor(PruittBolnickSihDiRienzoampPinter-Wollman2016) collectivebehavior (PruittampPinter-Wollman2015)orniche-constructingtraits (egaggres-sivenesspolicingorelseChangampSih2013)butshouldbemostcommon in specieswhere individuals respond to thebehaviors ofthemajorityofgroupmembers
Denserinteractionsamongindividualswithinagrouppotentiatetheimpactofindividualswithextremephenotypicvaluesbyallow-ing these to interact and affect themajority of their groupmem-bersHencetheconsequencesofindividualsocialplasticitytendtobecomemuchgreater ingroupsasnetworkdensity increasesThisldquoamplificationrdquoeffectisalsostrongerwhengenotypesfollowauni-formdistribution (iewhenextremegenotypesaremorefrequentwithin groups) thanwhen they followaGaussiandistribution (ie
1460emsp |emsp emspensp MONTIGLIO eT aL
whenextremegenotypesarerarewithingroups)Networkdensityincreases the evolutionary response of groups on average groupswith denser connections also exhibit increasedvariation in evolu-tionaryresponsetoagivenselectiongradientSuchan increase inthevariationinevolutionaryresponseobservedinourstudyisap-parentbecauseourapproachallowsustorelaxtheassumptionthatindividualswithingroupsinteractequallywithallothergroupmem-bersbyintroducinganewparameter(averageconnectionstrength=s)intoourmodelandinsteadtoexplicitlyexploretheeffectofcon-nectiondensity
44emsp|emspHomophily affects the amount of phenotypic variation within groups
Our simulations also investigate the consequencesof social struc-turewhenindividualscaninteractpreferentiallywithindividualsthathaveasimilar(iehomophily)ordissimilar(ieheterophily)pheno-typeNetworkassortment(thenetworkmeasureofhomophily)doesnot have any impact on groupsrsquomean phenotype but can gener-ateagreatervariationinsocialenvironmentswithingroupsHenceassuming that different immediate social environments can favordifferent (alternative) phenotypes within groups our simulationssuggest that homophily should be associatedwith the emergenceof phenotypic variation among individuals (or social specializationBergmuumlller amp Taborsky 2010 Montiglio Ferrari amp Reacuteale 2013)Homophilyalsohasdirectconsequencesfortheevolutionofalter-nativephenotypesbycreatingsynergyoroppositionbetweendirectand indirect genetic effectsWhen social plasticity (ψg) is positive(egwheninteractingwithanaggressiveindividualincreasesafocalindividualrsquosaggression)andindividualsshowatendencytointeractwithsimilarphenotypesthesocialenvironmentactstoshapetheirphenotypeinthesamedirectionastheirgenotypeAsaresultsocialinteractionsandsocialplasticityincreasethephenotypicvarianceofthetraitrelativetoasituationinwhichconnectionsarerandominterms of their traits It also tends to increase the strength of theevolutionaryresponsetoselectioninresponsetoagivenselectiongradientThisincreaseinevolutionaryresponsearisesfromthesyn-ergybetweendirectandindirecteffect(orbetweensocialplasticityandhomophily)ratherthanfromachangeintotalgeneticvariationwithingroups
45emsp|emspPossible applications and tests of the model and future directions
differentialandmatechoicebyfemalesThestrengthofconnectionsbetweenmales of known phenotype could be increased artificiallyusingplaybacks tosimulatemore frequent interactionsamong indi-viduals(DabelsteenampPedersen1990Otteretal2001)tomonitorhowsuchincreasesinconnectionstrengthaffecttheextentofpheno-typicandgeneticadditivevariationAlternativelyonecanmanipulatethedistributionofterritoriesavailableandthepatternsofinteractionsby controlling the locationof nest boxes foodpatches or refugesSuchapproachescouldbeparticularlysuitableforcavity-nestingbirds(Both1998)
Ourmodel also studied the consequences of homophily for theevolutionary responses of phenotypic traits Assuming individualshave some level of control on their interactions homophily can beobservedwhen individualsexhibitpreferences to interactwithcon-specificsthatare(dis)similartothemSuchpreferencescouldexplainthemaintenanceofaltruisticbehaviorbecauseoftheirpotentialroleinshapingtheselectionpressuresactingonaltruismSomeworkonfruitflieshavereportedthatindividualpreferencesforparticularsocialenvironmentsisassociatedwithgeneticvariationandcanthuspoten-tiallyevolve (egSaltzampFoley2011)Onecould testourmodel insuchstudysystemsbyeitherallowingorpreventingtheexpressionofsocialpreferences(throughmixingofindividualsormanipulatingtheirinteractions) Alternatively homophily can also be observed whenindividualssegregateintheenvironmentasafunctionoftheirphe-notype(HelfensteinDanchinampWagner2004Ward1993WardampPorter1993)Forexamplemoreandlessaggressiveindividualsseg-regateinpatcheswithdifferentdensitiesofconspecifics(Duckworth2006)Thusbymanipulatingtheheterogeneityandthescaleatwhichitisobserved(iethesizeofpatchesofdifferenthabitat)onecouldtestthepredictionsofourmodelFutureworkwillexpandthemodelwe presented here to analyze the consequences of such traits forthemaintenanceofphenotypicvariationandtheevolutionofsocialstructure
One limitationofourmodel is thatweassumebothphenotypicfeedback(Mooreetal1997)andsocialselection(Wolfetal1999)tobeabsentIncludingfeedbackmayaltertheconclusionswehavepre-sentedhereasfeedbackeffectsmaycausesocialplasticitytomovethroughnetworksincounterintuitivewaysItispossiblethatnetworkmetricsbeyondconnectionstrength (suchasclusteringcoefficientsbetweennessetc)may influencewhetherfeedbackcontributessig-nificantly to variation and response to selection Regarding socialselectionwehaveshownherethatconnectionstrengthcontributestoamong-groupvariancewhichshould intensifyresponsetohigherlevelsofselectionsuchassocialselectionWewilltreatbothfeedbackandsocialselectioninfuturecontributions
5emsp |emspCONCLUSION
Wepresentbothananalyticmodelandsimulationsextendingpre-vious work on social phenotypic plasticity to more general socialstructuresOurstudygeneratesafirstsetofverygeneralandtest-able predictions on the role of social structure in modulating the
emspensp emsp | emsp1461MONTIGLIO eT aL
consequencesofsocialplasticityWeshowthatthebasiccharacter-isticsofthestructureofinteractionsamongindividualsingroupsandpopulationscanhaveimpactsontheconsequencesofsocialplasticityforthemeanphenotypeexpressedbytheindividualstheextentofphenotypicvariationavailableforselectionandfortheabilityofthepopulation to respond to selectivepressuresWehope that futurestudieswillbeabletotestourpredictionsempiricallybyapplyingourapproachtothestudyofsocialbehavior(egaggressionandcoop-eration)socialinformationuseoralternativematingtacticsinpopu-lationswithvaryingpatternsofsocialormatinginteractionsFromatheoreticalperspectivefutureresearchwouldwarrantinvestigatingthelinkbetweenindividualpositioninsocialnetworksandtheindi-rect genetic effects it experiences and thuswhether factors otherthan individualsrsquo breeding values can lead to keystone individualsFurtherinourstudyweassumethatallindividualsexpressedplas-ticityidenticallyHoweverindividualshavealsobeenshowntovaryintheirplasticity(DingemanseKazemReacutealeampWright2010NusseyWilsonampBrommer2007WestneatHatchWetzelampEnsminger2011)andsuchvariationmayalterthepredictionsofinteractingphe-notypemodels(KazancıoğluKlugampAlonzo2012)Linkingindividualdifferencesinbothsocialpositionandplasticitycouldyieldnewin-sightsandagreaterunderstandingoftheevolutionarymechanismsthatunderpinphenotypicvariationwithinindividualsbetweenindi-vidualsandamongpopulations
ACKNOWLEDGMENTS
We thank the Reader Hendry and Barrett laboratories in McGillUniversity forconstructivecommentsonadraftof thismanuscriptPOMwas supported by aNSERCpostdoctoral fellowshipDRF re-ceived funding from a grant to theBBSRC (BBL0060811 toBCSheldon)andtheMaxPlanckSociety
CONFLICT OF INTEREST
Nonedeclared
AUTHOR CONTRIBUTIONS
POMandDRFbuiltthesimulationsandJWMdevelopedthemodelPOMdrafted themanuscript andproduced the figuresAll authorscontributedtorevisionsandapprovedthefinalversionofthearticle
AplinLMFarineDRMorand-FerronJCockburnAThorntonAamp SheldonBC (2015) Experimentally induced innovations lead topersistentcultureviaconformityinwildbirdsNature518538ndash541
Aplin LMFirthJAFarineDRVoelklBCratesRACulinaAhellipSheldonBC (2015)Consistent individual differences in the so-cialphenotypesofwildgreattits(Parusmajor)Animal Behaviour108117ndash127httpsdoiorg101016janbehav201507016
BaileyNWampHoskins J L (2014)Detecting cryptic indirect geneticeffectsEvolution681871ndash1882httpsdoiorg101111evo12401
Bailey N W amp Zuk M (2012) Socially flexible female choice differsamongpopulationsofthePacificfieldcricketGeographicalvariationin the interaction coefficient psi (Ψ)Proceedings of the Royal Society of London Series B Biological Sciences 279 3589ndash3596 httpsdoiorg101098rspb20120631
Bergmuumlller R amp Taborsky M (2010) Animal personality due to socialnichespecialisationTrends in Ecology amp Evolution25504ndash511httpsdoiorg101016jtree201006012
Bijma P ampWade M J (2008) The joint effects of kin multilevel se-lection and indirect genetic effects on response to genetic selec-tion Journal of Evolutionary Biology 21 1175ndash1188 httpsdoiorg101111j1420-9101200801550x
Boatright-HorowitzSLHorowitzSSampSimmonsAM(2000)Patternsof vocal interactions n a BullfrogRana catesbeiana chorus preferen-tial responding to farneighborsEthology106701ndash712httpsdoiorg101046j1439-0310200000580x
BothC(1998)Experimentalevidencefordensitydependenceofrepro-ductioningreattitsJournal of Animal Ecology67667ndash674httpsdoiorg101046j1365-2656199800228x
Cappa E P amp Cantet R J C (2008) Direct and competition additiveeffects in treebreedingBayesianestimation froman individual treemixedmodelSilvae Genetica5745ndash56
ChangAampSihA (2013)Multilevel selection andeffects of keystonehyperaggressivemalesonmatingsuccessandbehaviorinstreamwaterstridersBehavioral Ecology241166ndash1176httpsdoiorg101093behecoart044
Clutton-BrockTH(1989)MammalianmatingsystemsProceedings of the Royal Society B236339ndash372httpsdoiorg101098rspb19890027
Crowley P H amp Cox J J (2011) Intraguild mutualism Trends in Ecology amp Evolution 26 627ndash633 httpsdoiorg101016jtree201107011
Duckworth R A (2006) Aggressive behaviour affects selection onmorphology by influencing settlement patterns in a passerine birdProceedings of the Royal Society B 273 1789ndash1795 httpsdoiorg101098rspb20063517
Farine D R (2014) Measuring phenotypic assortment in animal so-cial networks Weighted associations are more robust than binaryedges Animal Behavior 89 141ndash153 httpsdoiorg101016janbehav201401001
FarineDRampWhiteheadH(2015)Constructingconductingandinter-preting animal social network analysis Journal of Animal Ecology841144ndash1163httpsdoiorg1011111365-265612418
Fawcett TW amp Johnstone RA (2010) Learning your own strengthWinner and loser effects should change with age and experienceProceedings of the Royal Society of London Series B Biological Sciences2771427ndash1434httpsdoiorg101098rspb20092088
Fisher D N amp McAdam A G (2017) Social traits social networksand evolutionary biology Journal of Evolutionary Biology httpsdoiorg101111jeb13195Inpress
FormicaVAWood CW LarsenW B Butterfield R EAugatMEHougenHYampBrodieIIIED(2012)Fitnessconsequencesofsocialnetworkpositioninawildpopulationofforkedfungusbeetles(Bolitotherus cornutus) Journal of Evolutionary Biology 25 130ndash137httpsdoiorg101111j1420-9101201102411x
Greenfield M D amp Rand S A (2000) Frogs have rules selective at-tention algorithms regulate chorusing in Physalaemus pustulosus (Leptodactylidae)Ethology106131ndash147
Helfenstein FDanchin E ampWagner RH (2004)Assortativematingand sexual size dimorphism in blacklegged kittiwakes Waterbirds27 350ndash354 httpsdoiorg1016751524-4695(2004)027[0350AMASSD]20CO2
Herbert-Read J E Krause S Morrell L J Schaerf T M Krause JampWardAJW (2013)The roleof individuality in collectivegroupmovementProceedings of the Royal Society B- Biological Sciences28020122564
KeiserCNampPruittJN (2014)Personality composition ismore im-portantthangroupsizeindeterminingcollectiveforagingbehaviourinthewildProceedings of the Royal Society of London Series B Biological Sciences28120141424httpsdoiorg101098rspb20141424
Krause J amp Ruxton GD (2002) Living in groups Oxford UKOxfordUniversityPress
Landeau L ampTerborgh J (1986)Oddity and the ldquoconfusion effectrdquo inpredationAnimal Behavior341372ndash1380httpsdoiorg101016S0003-3472(86)80208-1
Magnhagen C amp Bunnefeld N (2009) Express your personality or goalong with the group What determines the behaviour of shoalingperchProceedings of the Royal Society B- Biological Sciences2763369ndash3375httpsdoiorg101098rspb20090851
McDonaldG C FarineD R Foster K R ampBiernaskie JM (2017)Assortment and the analysis of natural selection on social traitsEvolution712693ndash2702httpsdoiorg101111evo13365
McGlothlin JW amp Brodie III E D (2009) How to measure individ-ual genetic effects The congruence of trait-based and variance-partitioning approaches Evolution 63 1785ndash1795 httpsdoiorg101111j1558-5646200900676x
McGlothlin J W Moore A J Wolf J B amp Brodie III E D(2010) Interacting phenotypes and the evolutionary pro-cess III Social evolution Evolution 64 2558ndash2574 httpsdoiorg101111j1558-5646201001012x
MillerJRBAmentJMampSchmitzOJ (2014)Fearon themovePredatorhuntingmodepredictsvariation inpreymortalityandplas-ticityinpreyspatialresponseJournal of Animal Ecology83214ndash222httpsdoiorg1011111365-265612111
ModlmeierAPKeiserCNWattersJVSihAampPruittJN(2014)The keystone individual concept An ecological and evolutionaryoverview Animal Behavior 89 53ndash62 httpsdoiorg101016janbehav201312020
MontiglioP-OFerrariCampReacutealeD(2013)Socialnichespecializationunder constraints Personality social interactions and environmentalheterogeneityPhilosophical Transactions of the Royal Society of London Series B Biological Sciences36820120343httpsdoiorg101098rstb20120343
Moore A J Brodie III E D ampWolf J B (1997) Interacting pheno-types and the evolutionary process I Direct and indirect geneticeffects of social interactions Evolution 51 1352ndash1362 httpsdoiorg101111j1558-56461997tb01458x
NonacsPampKapheimKM(2007)Socialheterosisandthemaintenanceof genetic diversity Journal of Evolutionary Biology 20 2253ndash2265httpsdoiorg101111j1420-9101200701418x
Nussey D H Wilson A J amp Brommer J E (2007) The evolution-ary ecology of individual phenotypic plasticity in wild popula-tions Journal of Evolutionary Biology 20 831ndash844 httpsdoiorg101111j1420-9101200701300x
OtterKAStewartIRKMcGregorPKTerryAMRDabelsteenTampBurkeT(2001)Extra-pairpaternityamonggreattitsParus major following manipulation of male signals Journal of Avian Biology 32338ndash344httpsdoiorg101111j0908-88572001320408x
Pruitt J N Bolnick D I Sih A DiRienzo N amp Pinter-Wollman N(2016)Behavioralhypervolumesofspidercoloniespredictscommu-nity performance and disbandmentProceedings of the Royal Society B- Biological Sciences 283 20161409 httpsdoiorg101098rspb20161409
PruittJNampPinter-WollmanN(2015)Thelegacyeffectsofkeystonein-dividualsoncollectivebehaviourscaletohowlongtheyremainwithina group Proceedings of the Royal Society B- Biological Sciences 28220151766httpsdoiorg101098rspb20151766
RoyleNJHartley IROwens I P FampParkerGA (1999) Siblingcompetition and the evolution of growth rates in birds Proceedings of the Royal Society B 266 923ndash932 httpsdoiorg101098rspb19990725
SaltzJBampFoleyBR(2011)Naturalgeneticvariationinsocialnicheconstruction Social effects of aggression drive disruptive sexual se-lectioninDrosophila melanogaster American Naturalist177645ndash654httpsdoiorg101086659631
ShusterSM LonsdorfEVWimpGMBaileyJKampWhithamTG (2006) Community heritabilitymeasures the evolutionary conse-quencesofindirectgeneticeffectsoncommunitystructureEvolution60991ndash1003httpsdoiorg101111j0014-38202006tb01177x
SimmonsAMSimmonsJAampBatesMA (2008)Analyzingacous-tic interactions in natural bullfrog (Rana catesbeiana) chorusesJournal of Comparative Psychology 122 274ndash282 httpsdoiorg1010370735-70361223274
Sinervo B R amp Calsbeek R (2010) Behavioral concepts of selectionExperiments and genetic causes of selection on the sexes In D FWestneatampCWFox(Eds)Evolutionary behavioral ecologyLondonUKOxfordUniversityPress
Thompson J N (1982) Interaction and coevolution Chicago USA TheUniversityofChicagoPress
emspensp emsp | emsp1463MONTIGLIO eT aL
VanderWaal K L ObandaV Omondi G P McCowan BWang HFushingHampIsbellLA (2016)Thestrengthofweaktiesandhel-minth parasitism in giraffe social networks Behavioral Ecology 271190ndash1197httpsdoiorg101093behecoarw035
Ward P I (1993) Micro-habitat segregation and the mating systemof Gammarus pulex Animal Behavior 45 191ndash192 httpsdoiorg101006anbe19931019
Ward P I amp PorterAH (1993)The relative role of habitat structureandmale-malecompetition in thematingsystemofGammarus pulex (CrustaceaAmphipoda)AsimulationstudyAnimal Behavior45119ndash133httpsdoiorg101006anbe19931011
West-EberhardMJ(1989)Phenotypicplasticityandtheoriginsofdiver-sityAnnual Review of Ecology and Systematics20249ndash278httpsdoiorg101146annureves20110189001341
Westneat D F Hatch M IWetzel D P amp Ensminger A L (2011)IndividualvariationinparentalcarereactionnormsIntegrationofper-sonalityandplasticityAmerican Naturalist178652ndash667httpsdoiorg101086662173
Wilson A J Gelin U Perron M-C amp Reacuteale D (2009) Indirect ge-neticeffectsandtheevolutionofaggression inavertebratesystemProceedings of the Royal Society of London Series B Biological Sciences276533ndash541httpsdoiorg101098rspb20081193
Additional Supporting Informationmay be found online in the sup-portinginformationtabforthisarticle
How to cite this articleMontiglioP-OMcGlothlinJWFarineDRSocialstructuremodulatestheevolutionaryconsequencesofsocialplasticityAsocialnetworkperspectiveoninteractingphenotypesEcol Evol 201881451ndash1464 httpsdoiorg101002ece33753
APPENDIX
PHENOTYPIC MEAN AND VARIANCE
FollowingMooreetal(1997)wemodelasinglephenotypeofanindi-vidual (z)asanadditivecombinationoftheeffectsof itsowngenes(iedirectgeneticeffectsa)thenonsocialenvironmentitexperiences(e)andaplasticcomponentthatissomefunctionofthephenotypesinitssocialgroupMooreetal(1997)originallymodeledthesocialeffectasafunctionofthephenotypeofoneinteractingindividualMcGlothlinandBrodie (2009)andMcGlothlinetal (2010)consideredsocialef-fectsinapopulationconsistingofgroupsofnindividualswhereinter-actionswereassumedtooccursimultaneouslywithinagroupwithallindividuals within a group having the same strength of interactionHereweconsideramoregeneralsocialstructurewhereindividualsinteractwithallpossiblesocialinteractantsingroupsizenwithvaria-bleconnectionstrengthsirangingfrom0to1giving
wherethesummationistakenacrossalln minus1possiblesocialinterac-tionsforeachindividualsandψrepresentstheinteractioncoefficientwhichdetermines thestrengthanddirectionof the indirectpheno-typic effect of individual social interactantsHere and elsewhere aprimeindicatesaparameterbelongingtoasocialpartnerAnysocialnetworkstructurecanbemodeledbychangingthedistributionofs High-densitysocialnetworkswithstrongconnectionswillhavemanylargevaluesofswhilesparsernetworkswithweakerconnectionswillhavemanyweaksvalueswithmanyequaltozeroConsideringphenotypicfeedback(asdoMooreetal1997)insuch
The value of the two covariance terms represents how stronglystrengthofinteractiondependsonthegenesandenvironmentofin-dividualsocialpartnersThiscovarianceisdeterminedforeachindi-vidualandmayvaryacrossindividualsTheseshouldbepositiveunderhomophilyandnegativeunderheterophilyTakingthemeanandas-suming
=e=0
where double overbars indicate global means and large overbarswithintheparenthesesindicatemeanstakenacrossindividualsbasedonsummarystatisticsoftheirsocialgroupsThiscanbeexpandedasaboveto
The remainingcovariance terms represent theaveragedegree towhichindividualconnectionstrengthsareadjustedbasedonthephe-notypeofpotentialinteractantsInthecaseofhomophilyorheteroph-ilyindividualswillmakethisadjustmentbasedontheirownphenotypewithlargeindividualshavingapositivecovarianceandsmallindividu-alshavinganegativecovariance(orviceversa)ThereforeweexpecttheseaveragecovariancetermstotendtowardzeroMakingthisas-sumptionandrearrangingprovidesEquation2inthetext
EXTENSION TO MULTIPLE GROUPS
EquationA8iswrittenassumingthatthepopulationconsistsofasin-gle social networkwhere individualsmay interact in anywayNowassumethatthepopulationisdividedintomultiplegroupswhereindi-vidualsmay interactwithanystrengthswithinagroupanddonotinteract at all between groups Assuming the covariance terms inEquationA8arezeroandthatenvironmentaldeviationsdonotvaryamonggroupsthemeanofeachgroupwillbe
where overbars now indicate within-groupmeans Assuming equalgroupsizethepopulationmeanisnow
(IfgroupsvaryinsizethenEquationA10canbemodifiedtogiveaweightedmean) Ifconnectionstrengthhasnoheritablebasis thenthe covariance term become zero and EquationA10 collapses toEquation2inthetextWemaycalculateamong-groupvariancemosteasilybymakingafewassumptionsthatarealsomadeinoursimula-tionsFirstasaboveweassumethatgroupsareofequalsizeSecondweassume thatmean interactiondoesnotvaryacrossgroups ands=
=sMakingtheseassumptions
Thisshowsthat indirectgeneticeffectswillmagnifyslightdiffer-ences in genetic values across groups regardless of sign Strongermeanconnectionstrengthswillintensifythiseffect
RESPONSE TO SELECTION
FollowingMoore etal (1997) andMcGlothlin etal (2010) and as-suming that thecovariance terms inEquationA8areeither zeroorpopulation parameters that do not have a heritable component anindividualrsquostotalbreedingvaluecanbewrittenasthegeneticcontri-butiontothepopulationmean
where Ristheregressionofsaprimeonaandisthusanalogoustorelated-ness This assumes thatCov[aseprime] is negligible Positive values ofR indicatehomophilyandnegativevaluesindicateheterophilyMakingthissubstitutiongivesEquation4inthetextEquation4canalsobeexpresseddifferentlybyrearrangingas
geneticeffects(egCappaampCantet2008)andallowextensionsofthismodel in the futureWeallowconnection strengths todependupon the nonplastic component of the phenotype (phenotypic as-sortment)Suchassortmentisanalogoustohomophilywhenassort-ment is positive (individuals seek similar partners) and heterophilywhenassortment isnegative(individualsavoidsimilarpartners)WefollowedtheapproachofMooreetal (1997) ignoringthepotentialfordirectsocialeffectsonfitness(socialselectionorgroupselectionWolf etal 1999)Althoughourmodel considers only a single traitforsimplicityitdoesnotconsiderthepossibilityforfeedbackeffectsonphenotypesmakingourmodelanalogoustothetwo-traitmodelwithnonreciprocaleffectsofMooreetal(1997)Wewilltreatphe-notypicfeedbackinafuturecontributionThemodelispresentedinitsentiretyintheAppendixbutwereportitsmainresultsbelow(seeResults)
22emsp|emspSimulation overview
Toinvestigatehowsocialplasticityandsocialstructurecanaffecttheextentofphenotypicvariationobservedwithinpopulationsandevo-lutionarychangewesimulategroupsofindividualswithafixedinter-actioncoefficient(ψg)butvaryingsocialstructures(networkdensityandhomophilyheterophily)EachgrouphasitsownuniquenetworkofinteractionsFromtheseinteractionswecalculatethephenotypethateachindividualinthegroupwouldexpressgivensocialplasticityWe then calculate thephenotypicmeanof the group the varianceinindirectgeneticeffectsexperiencedamongindividualgroupmem-bersthecorrelationbetweenindividualsrsquogenetictendenciesandtheindirectgeneticeffects theyexperienceandtheoverallphenotypicvarianceofthegroupWealsocalculatetheoverallgeneticvariance
WesimulatereplicatednetworksofvaryingdensityandhomophilyEachreplicatecanbeconsideredasa (small)populationorasadis-tinct group embeddedwithin a largermetapopulation To generatenetworksofinteractionwefirstgeneratepairsofcoordinatesfromauniformdistribution(range0ndash1)forindividualsToalloweachindivid-ualtointeractmorestronglywithsomeofitsconspecificsrelativetoothersweallowindividualstomovetowardtheirnearestneighborby15ofthedistancebetweenthemVaryingthispercentagedoesnotinfluenceourresults(resultsnotshown)Todeterminetheconnectionstrengthsbetweeneachpairof individuals inoursimulations(s)wecalculatetheEuclideandistancebetweenthemanduseanexponentialdecayfunctiongeneratingadecreasingconnectionstrengthasafunc-tionof thedistancebetweenany two individualsThusweassumethattheconnectionstrengthbetweentwoindividualsiss=eminusdistance
F IGURE 1emsp (a)Samplenetworksgeneratedusingthreevaluesofr(005015and09)creatingnetworksofvaryingdensitieslow(left)intermediate(center)andhighdensities(rightNgroup=12)(b)Foreachlevelofdensityindividualsalsovariedinthenumberofinteractionswithothergroupmembersshownatlow(left)intermediate(center)andhigh(right)networkdensities(Ngroup=500)
Becausetheresultingnetworkdensity(thesumofallpresentedgeweightsdividedby thepossible sumofedgeweights if thenetworkwerefullyconnected)foragivenvalueofrisstochasticnotdetermin-isticwereportourresultsasafunctionofnetworkdensitywhichwascalculatedusingtheRpackageassortnet(Farine2014)Statedanotherwaynetworkdensityisanemergentpropertyofvaryingrnotaparam-eterofoursimulationsOurapproachismostimmediatelyapplicabletosituationswhereindividualsareactuallydistributedintwo-dimensionalspaceandinteractmoreorlessintenselyasafunctionofthedistance(Farine 2015) Such an interaction structure applies directly to situ-ations such as competition amongneighboringplants (egCappaampCantet2008)orterritorialityinanimals(egRoyleHartleyOwensampParker1999)butisgeneralizableawidevarietyofothermorecomplexsituationsthatmaynotinvolveaspatiallyexplicitcomponent
Individualscanoftenchoosetoconnectmorestronglywithsomeindividuals than others In many species individuals preferentiallyinteractwithpartnersthataresimilar (ieunderassortativematingor during cooperative interactions) or dissimilar to them (ie underdisasortativemating or because of division of labor and social het-erosis seeNonacsampKapheim 2007)Hence networks can exhibitassortment (associations between individuals that are similar andor avoidance of dissimilar individuals Farine 2014) Firstwe studythe effect of randomly occurring network assortment in the sim-ulated groups To explicitly investigate the impact that interactionpreferencescanhaveonevolutionaryprocesseswethenallowindi-vidualstoreducethestrengthoftheirinteractionwithnonpreferredaffiliates (eg with dissimilar individuals in the case of homophilyorwithsimilar individuals inthecaseofheterophily)Wethusmod-ify the function used to calculate the strength of interaction (s) tos=eminusdistance
2∕rtimesH(
1
1+expminus20|xminusy| minus05)+05 which generates a sig-
moidalfunctionwithamagnitudeofH(thelevelofhomophilyrang-ingbetween0and02) as a functionof |xminusy| or thedifference inthephenotypesoftheindividualsIftwoindividualsareidenticalthestrengthoftheirinteractionismultipliedbyeither~0or~1ifmodelingheterophily or homophily respectivelyTheir connection strength ismultipliedby05iftheirphenotypicdifference(|xminusy|)isaverageAswithnetworkdensitywe report themeasurednetworkassortmentcalculatedusingtheRpackageassortnet(Farine2014)
strengthoftheirsocialinteractionssiIndividualswithnoconnectionstrengthdonotcontributetothephenotypeassi =0Inoursimula-tionsall individualshavethesameinteractioncoefficient(ψg)Wealsoinvestigatewhetherourresultsdependedonthedistributionofbreedingvaluesbyrunningadditionalsimulationswhereindividualbreedingvaluesare sampled fromanormaldistribution (mean=0andvariance=1)IntheresultswepointoutwheresuchachangeindistributionaffectsourresultsInpreviousmodels(McGlothlinampBrodie2009McGlothlinetal2010)ψghasbeenconstrainedtoliebetweenminus1and1fortworeasonsFirstvaluesofψggreaterthan1canleadtounreasonablephenotypicvalues(particularlyinmodelsthat include phenotypic feedback) Second phenotypic values areoftenstandardizedtoameanofzeroandunitvarianceforanalysiswhichshouldresult inψgvaluesbetweenminus1and1 Inoursimula-tionsthemeanandvarianceofindividualphenotypesvariedineachgroup because of samplingwhichmade such standardization dif-ficultWechose touseunstandardized traitvaluesanda largeψg value(4)inallsimulationsSuchavalueofψgwhichwouldyieldanaveragestandardizedvalueofψgof~030whichiscomparabletoempiricalψgvaluesreportedintheliterature(egBaileyampHoskins2014BaileyampZuk2012)Usingthislargevaluefacilitatesvisual-izing social effects anddoesnot lead tounreasonablephenotypicvalues due to the absence of phenotypic feedback in ourmodelAs noted in theAppendixψg ismultiplied by average connectionstrength (network density) when calculating phenotypes whichwillreducetheeffectofψgexceptinfullyconnectednetworksAspredictedbytheanalyticalmodel increasingthestrengthofsocialplasticity(iehowmuchanindividualchangedhisphenotypeinre-sponsetohissocialpartnerstheabsolutevalueofψg)amplifiesallthe patternswe report below (seeResults section)However be-causesuchincreasesareintuitiveandoflesserinterestwedonotreporttheresultsofanalysesvaryingψgUsingthecodeavailableasFigureS1 the reader cangenerate figures that are comparable totheoneswepresentbelowforanyvalueofψg
where G indicates additive genetic variance andE indicates envi-ronmental variance The third term above represents the among-individual variance due to social interactions This term shouldincreasesomewhatwithhomophilybutshoulddependmostheav-ily on network density The variance in social environment expe-rienced by individuals should be at amaximum at intermediate
becomemorehomogenous(ieeveryoneinteractswitheveryone)Thefourthtermwillbemost influencedbyhomophily (orhetero-phily)becauseassociatingwithsimilar(ordifferent)individualswillcause the covariance to increase (ordecrease)Themultiplicationbyψgwillcausephenotypicvariancewithinagrouptoincreasewithhomophilyunderpositivevaluesofψganddecreasewithhomophilywhenψg isnegativeThistermshouldalsobe influencedbyaver-ageconnectionstrength(
where R is a general measure of the strength of homophily (seeEquationA19 in Appendix) and β is the selection gradient (seeAppendix)Thisequationshowsthattheamountofgeneticvarianceavailableforresponsetoselectionatthepopulationlevelshouldde-pendon(1)thedegreeofsocialplasticity(2)theaverageconnectionstrength(whichshouldincreasewithmeanconnectionstrength)and(3)theamountofassociationbetweenindividualsthatisbasedonge-neticvaluesimilarity(homophilyorheterophily)Thismodelisnearlyidenticaltopreviousmodelswithsimplergroupstructure(McGlothlinetal 2010) except for the inclusion of the connection strength (
=s)
and the replacementof relatednesswithhomophilyheterophily (R)Theseanalyticalresultsprovidepredictionsthatwetestbelowusingindividual-basedsimulations
32emsp|emspNetwork density
Inoursimulationsincreasingnetworkdensitywhichisanalogoustoincreasing mean connection strength in the analytical model doesnot lead to an increase inphenotypicmeanonaverage (ie acrossallgroupsFigure2red line)Howeverathighernetworkdensitiesthere is much greater variation among groups in their phenotypicmean (Var[
=z ] Figure2 gray dots) This occurs because although
themeangeneticvalueacrossall simulations iszero thisvaluecandiffer across groups due to sampling As predicted by Equation2increasing network density (or
=s) increases the importance of the
group genotypic composition in determining the effects of indirectgeneticeffectsmagnifyingdifferencesamonggroupsingeneticvalue(=a) across replicate simulation runs This amplification effect is also
Thephenotypicvariance in indirecteffectswithineachgroup ismaximalatintermediatenetworkdensities(Figure3a)Whenindivid-ualshave fewconnections (and connection strength isweaker) thescopeforindirecteffectstodifferamongmembersofagivengroupisnarrowtherebydecreasingthecontributionofsocial interactionstophenotypicvariance(Figure3a)Likewiseingroupswhereindividualsarehighlyconnected (highnetworkdensity) thesocialenvironmentexperiencedbyeachindividualisclosertotheaveragebreedingandenvironmentalvalueofthepopulation(whichis0inoursimulations)In otherwordsVar[aprime] and consequentlyVar[saprime]within groups issmallathighdensities(seeEquation3)Howeveratintermediateden-sities indirecteffectshadthepotentialtomakealargecontributiontophenotypicvariancealthoughthiseffectwashighlyvariableacrosssimulations
Intheabsenceofhomophilyheterophilyhighnetworkdensityleadstoanegativecorrelationbetweendirectandindirectgeneticeffects(Figure3b)Atlownetworkdensitiesthiscorrelationisex-pectedtobezerobecauseindividualsassociateatrandom(althoughthiswouldnotbe thecase if therewasanyspatial assortmentbyphenotype) However at high densities this correlation becomesnegativeeventhoughindividualassociationisalsorandomThisef-fectarisesbecauseindividualsarenotcountedaspartoftheirownsocial environment andasnetworkdensities increase the impor-tanceofthisdifferencebecomesmagnifiedAtthehighestnetwork
(3)Var[z]=G+E+ψ2gVar
[sa + se
]+2ψgCov
[a +e sa + se
]
(4)Δ=zasymp
(1+ψg
=s)G(1+Rψg
)β
F IGURE 2emspThechangeinaveragephenotypeofindividualsinanetworkasafunctionofthenetworkdensity(redline)Thechangeinaveragephenotypeisexpressedrelativetothephenotypeexpectedinabsenceofinteractionsamongindividuals(ie0)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4Asdensityincreasedweobservedagreatervariationinmeanphenotypeamonggroups(graydots)
1456emsp |emsp emspensp MONTIGLIO eT aL
densitiessocialenvironmentsare indistinguishableexceptforthiseffect of excluding oneself thus leading to a directndashindirect cor-relationofminus1Smallergroupswillexhibitthispatterntoastrongerextent than larger groups (see FigureS5 also McDonald FarineFosterampBiernaskie2017)Thecombinedimpactoftheeffectsofnetworkdensityonthevariancein indirectgeneticeffectsandonthecovariancebetweendirectandindirectgeneticeffectsisarel-ativedecrease inphenotypicvariationwithingroups(comparedtothephenotypicvariationinabsenceofanyinteractions)asnetworkdensityincreases(Figure3c)Oppositepatternsareobservedwhenψg isnegative(FigureS6)Finallywenotethatalthoughthemeanphenotypic variationwithin each group decreaseswith increasingnetworkdensitywefindthatthevariationamonggroups(eachdotin each panel of Figure3c represents one group) ismaximized atintermediatenetworkdensities
Although the phenotypic variance typically decreases with in-creasednetworkdensitythevarianceintotalbreedingvalues(rela-tivetothegeneticvarianceinabsenceofanysocialinteraction)hasthe greatest increase at highest network densities (Figure3d redline)Thisisbecausetheexpectedvarianceintotalbreedingvaluesisequalto
(1+ψg
=s)2
G(seeEquationA12)Thatisthevarianceintotalbreedingvaluesdoesnotdependonthevarianceinindirectgeneticeffects noron the covariancebetweendirect and indirect geneticeffectswhich leadtothedecrease invarianceshowninFigure3cRatherthevarianceintotalbreedingvaluesisafunctionofdirectge-neticeffectsandeffectsofanindividualrsquosgenesonothersthelatter
ofwhichbecomesinflatedathigherdensitiesTheresponsetoselec-tiondependsonthecovariancebetweentotalbreedingvaluesandphenotypicvalueswhichisexpectedtoincreaselinearlywithdensity(EquationA15)Whenwesubjectgroupstoaselectiongradientof02networkswithincreasingdensitiesexhibitedanincreasedevolu-tionaryresponsetoselection(Figure4redline)Increasingnetworkdensityalso increases thevariance in responsetoselectionamonggroups (Figure4 gray dots) This likely happened because individ-ualsadjusttheirphenotypetotheaveragesocialenvironmentthattheyexperienceThusathighernetworkdensitiesindividualswithextreme phenotypicvalues have a disproportionate impact on theaveragesocialenvironmentexperiencedbyindividualsSmalldiffer-encesinthephenotypicvaluesofextremeindividualsfromgrouptogroupcreatedifferencesinthecovariancebetweenthephenotypicvarianceandthetotalbreedingvaluesamonggroupsandincreasingthevariance in response to selection amonggroups In agreementwiththisextremeindividualsalsogenerategreaterphenotypicvari-anceamonggroupsathighernetworkdensities(Figure2)andwhenindividualphenotypesfollowauniformdistribution(moreindividualswithextremephenotypes)thananormaldistribution(fewerindivid-ualswithextremephenotypesSeeFigureS3)
F IGURE 3emspEffectsofnetworkdensityon(a)thevarianceinindirecteffectsexperiencedbyindividuals(b)thecorrelationbetweendirectandindirectgeneticeffectsexperiencedbyindividuals(c)thechangeinphenotypicvariancewithingroupsrelativetothegeneticvariance(iethephenotypicvarianceinabsenceofinteractions)and(d)thechangeintotalgeneticvariationrelativetothegeneticvariance(ievarianceofindividualdirectgeneticeffectsandindirectgeneticeffectsimposedtoothers)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψg of4
emspensp emsp | emsp1457MONTIGLIO eT aL
hasnoeffectonthemeanphenotypeofeachgroup(Figure5)whichis consistent with our analytical model (Equation2) However in-creasednetworkassortmentisassociatedwithanincreaseinthevari-anceinindirectgeneticeffectsexperiencedbyindividualsinagivengroup(seethethirdterminEquation3Figure6a)Becauseindividu-alsinteractmorestronglywithconspecificsthathavesimilarbreedingvalues(highwithhighlowwithlow)thedirectandindirectgeneticcontributions to phenotypes act in concert and covary positively(fourthterm inEquation3Figure6b)Thesetwoeffectscontributetowardincreasingphenotypicvarianceobservedwithinagivengroup(Figure6c)Theseeffectsarereversedwhenψgisnegativedirectandindirect contributions to individual phenotypes act to oppose eachothertherebyreducingtheamountofphenotypicvarianceobservedin the population (see FigureS7) Increasing network assortmentalsoleadstoasmalldecreaseinthevarianceintotalbreedingvalues(Figure6dredline)Thisisattributabletotheslightdecreaseinden-sityassociatedwithhigherlevelsofnetworkassortment(ieindividu-alshavetheabilitytoreducetheconnectionstrengthwithparticulargroupmembers)aphenomenonnotcapturedbyouranalyticalmodel
Applying selection to groups with varying network assortmentshowsthatasynergybetweendirectandindirectgeneticeffectsleadstoanincreaseinevolutionarychangewithincreasingnetworkassort-ment(Figure7redline)Thisresultisinaccordwiththepredictionsofouranalyticalmodelwhichpredictsanincreasedresponsetoselec-tionwithincreasingR(Equation4)AlthoughEquation4suggestsden-sityandhomophilyshouldhavesymmetricaleffectstheincreaseseeninFigure7isnotasdramaticasthatinFigure4perhapsbecauseoftheconcomitantdecreaseindensitycausedbyallowinghomophilyinoursimulationsUnlikenetworkdensitynetworkassortmentdoesnotaffectthevariationofevolutionaryresponsesamonggroups(Figure7graydots)
4emsp |emspDISCUSSION
Inthisstudyweexploretheconsequencesofsocialplasticityandthestructureofinteractionsinshapingtheamountofphenotypicvariationwithingroupsof interactingindividualsandtheevolutionaryresponseofthesegroupstoselectionWeconsiderreplicategroupswithvary-ingstructuresofinteractionsSuchreplicatescouldbeseenasmultiplegroups of individualswithin a given population (eg tribes packs orcolonies)orasmultipleisolatedpopulationswithinanecologicalcom-munityThroughananalyticalmodelandagent-basedsimulationsweshowthatthestructureofsocialnetworksmodulatedtheimpactofin-directgeneticeffectsontheamountofphenotypicvarianceavailablefor selectionOur resultsemphasize that thenumberandstrengthofconnectionsamongindividuals(networkdensity)aswellaspreferentialassociations among individualswith a similar phenotype (network as-sortment)haveimportanteffectsonthecontributionofindirectgeneticeffectsNetworkdensityandassortmentalsomodulatetheabilityfortraitstoexhibitevolutionarychangeinresponsetoselectionIncreasingthenumberofinteractionsamonggroupmembers(networkdensity)in-creasestheaverageevolutionaryresponseofgroupstoselectionandin-creasesthevariationinresponsetoselectionamonggroupsBycontrastincreasednetworkassortmentleadstoanincreaseintheaverageevolu-tionaryresponseofgroupstoselectionbutdoesnotaffectthevariationinevolutionary responseamonggroupsOur resultshavewidespreadimplicationsforstudiesofsocialevolutionmultilevelselectionandtheemergenceofkeystoneindividuals(ModlmeierKeiserWattersSihampPruitt2014)andniche-constructingtraits(egSihampWatters2005)
41emsp|emspComparison with earlier interacting phenotype models
Our analytical results show that given some simplifying assump-tions (most importantly ignoring the potential for phenotypic
F IGURE 4emspEvolutionaryresponseofphenotypetoaselectiongradientvarieswithnetworkdensityTheaveragechangeinphenotypemeanresultingfromselectionincreasedwithnetworkdensity(redline)Groupswithdensernetworksofinteractionsexhibitedmorevariationinthechangeinphenotypicmean(graydots)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4
F IGURE 5emspTheaveragephenotypeofindividualsasafunctionofnetworkhomophily(redline)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4Networkscouldnotreachhomophilyvaluesof1becauseweusedacontinuoustraitvalueratherthandiscretevalues(seeFarine2014)
1458emsp |emsp emspensp MONTIGLIO eT aL
feedback) considering more general social structures does notgreatlyalter theconclusionsofearliermodelsof interactingphe-notypeevolution(egMcGlothlinetal2010Mooreetal1997)First indirect genetic effects still alter the response to selectionby increasing the amount of genetic variance exposed to selec-tionNote thatbecausewedonotmodel feedback thiseffect is
directional with positiveψg (ie becomingmore similar to onersquosneighbors)increasingtheresponsetoselectionandnegativevalues(iebecomingmoredifferentfromonersquosneighbors)decreasingitSecondhomophilyheterophilyplaysa rolesimilar to relatednessinpreviousmodelsinalteringtheresponsetoselection(McGlothlinetal2010)IndeedMcGlothlinetal(2010)noted(ashavemanyothers)thatrelatednessperseisjustaspecialcaseofphenotypicassortment
Themostnotabledifferencebetweenourmodelandearliermod-elsisthatindividualsareallowedtodifferintheirinfluenceonsocialplasticityduetovariation inconnectionstrength (s)Perhapsunsur-prisingly responsetoselection ismorestrongly influencedbysocialinteractions indensernetworkswhere interactionsarestrongerandmorecommonaneffect that isapparent inbothouranalyticalandsimulation results Inour simulation resultswealso find thatvaria-tioninresponsetoselectionamongincreaseswithgreaterconnectionstrengthThis could occur because in some groups themostwell-connectedindividualshappentohaverelativelyhighorlowbreedingvaluesThesewell-connected individualswould thenhaveadispro-portionateeffectonthephenotypeofothers (relativeto individualsclosertothepopulationrsquosaveragebreedingvalue)byexertingastrongeffectonthemeansocialenvironmentexperiencedbyindividualsIndoingsowell-connectedextremeindividualscangeneratevariabilityinthecovariancebetweenbreedingvaluesandphenotypeandthusintheresponsetoselectionFuturemodelsshouldallowconnectionstrength to display a heritable component which would allow thesocialnetworkstructureitselftoevolveinresponsetosucheffects
F IGURE 6emspEffectofnetworkhomophilyon(a)thevariationinindirecteffects(b)thecorrelationbetweendirectandindirectgeneticeffects(c)therelativechangeinphenotypicvariancewithingroupsand(d)therelativechangeintotalgeneticvariationEachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4HomophilysimultaneouslyincreasesvariationamongindividualsinindirectgeneticeffectswithingroupsandgeneratesastrongpositivecovariancebetweendirectandindirectgeneticeffectstherebysubstantiallyincreasingthephenotypicvarianceobservedwithingroupsHoweverthisincreaseinphenotypicvarianceisnotassociatedwithanychangeatthegeneticlevel
F IGURE 7emspEvolutionaryresponseofphenotypetoaselectiongradientincreaseswithnetworkhomophily(redlineandgraydots)Eachdotrepresentsthechangeinmeangenotypeacrossgenerationsinasinglesimulatednetworkorgroupof50individuals(Ngroup=50)TheredlinerepresentstheaverageevolutionaryresponseasafunctionofnetworkdensityIndirectgeneticeffectsweregeneratedusingaψgof4
emspensp emsp | emsp1459MONTIGLIO eT aL
Studiesinthewildhaveshownthatpositioninasocialnetworkmaybe repeatable and have fitness consequences suggesting that con-nectionstrengthmaybeanevolvabletrait (AplinFirthetal2015FormicaWoodCookampBrodie2017Formicaetal2012)
42emsp|emspGroups with denser connections exert a stronger ldquopull to the meanrdquo
Our simulations show that groupswhere individuals have an in-termediatenumberorstrengthofsocialconnections (iegroupswithintermediatenetworkdensities)allowforthegreatestwithin-groupvariationinsocialenvironmentsexperiencedamongindivid-ualsThispatternariseswithinagenerationduetosocialplasticityratherthanasaresponsetoanyselectivepressureBygeneratinga greater range of phenotypes and social environments groupswithan intermediatedensityof social interactionscouldprovidethe basis for the emergence and evolution of alternative socialphenotypes (Bergmuumlller amp Taborsky 2010 Sinervo amp Calsbeek2010) When social phenotypes are subject to indirect geneticeffects the maintenance of variation in social behavior shouldthus be observed more frequently in groups with intermediateconnectedness
Whilelowtointermediatedensitiesofsocialinteractionsofferthewidestscopeforpromotingindividualvariationinphenotypegroupswith high densities exhibit a very different patternAs the numberand strengths of interactions increases among group members in-direct genetic effects experienced by each individual becomemoresimilarbecauseallgroupmembersstarttobecomeconnectedtooneanotherand theseconnectionsareuniformlystrong Inadditionasnetworksbecomemoreconnectedindividualsattheextremesofthedistributionofgenetic tendencies in thegroups (ie the individualsfurthest from the averagebreedingvalue) tend to experience a so-cialenvironmentexertinganopposingeffectontheirphenotype(ieCov[a+esa +se] in Equation3 becomes more negative) This ldquopullto themeanrdquo is stronger in smaller groups than in larger ones (seeFigureS5) anddecreases thepopulationphenotypicvariancewhenψg ispositive (egwhen individuals increasetheiraggressiveness inresponse to the aggression they receive) and increases it whenψg is negative (egwhen individuals inhibit their aggressiveness in re-sponsetotheaggressiontheyreceive)Whenindividualsexhibit im-portantphenotypicplasticitysuchaneffectappearssimilartosocialconformity where individuals express more similar phenotypes asgroupsthan in isolation (egHerbert-Readetal2013MagnhagenampBunnefeld2009)Conformity isusually thought toemergewhendissimilarindividualsareatafitnessdisadvantageForexamplepred-ators tend topick individuals that standout amonggroupsofpreyselecting forhomogeneousgroups (LandeauampTerborgh1986)Weshowherethatconformist-likepatternsinbehaviorcanemergefromverysimpleformsofsocialplasticity Importantlyweshowthatbe-havioralconformitycanemergeevenwhenindividualsarenotactivelycopyingthemostabundantphenotypeoftheirgroup inabsenceofanyselectivepressureExamplesofhighlyconnectedgroupsinnatureincludechorusesofmalesinsomespeciesoffrogsproducingmating
calls or leks ofmales displaying to attract females and adjust theirsignalingeffortinresponsetothesignalingoftheirrivals(Boatright-HorowitzHorowitzampSimmons2000SimmonsSimmonsampBates2008)Whenmalesareclosetoeachotherandeachmalecanadjustits signaling intensity to that of all the othermaleswe expect thisldquopulltothemeanrdquotodecreasethevariationinmalesignals(althoughsocialplasticitycantakemorecomplexpatternsthenismodeledhereGreenfieldampRand2000)Thiscandecreasetheeffectivenessoffe-malematechoiceandtheintensityofsexualselection
43emsp|emspGroups with denser connections potentiated the effect of keystone individuals
Aninsightfromoursimulationsisthatwheneverindividualsadjusttheirphenotypetotheaveragesocialenvironmentthattheyexperi-enceindividualsattheextremesofthegenotypicorphenotypicdis-tributionhavethegreatestimpactonthephenotypeofothergroupmembers This phenomenon arises because these individuals havethestrongest impacton themeansocialenvironmentexperiencedbytheirconspecificsTheevolutionofniche-constructingtraitsal-lowingsomeindividualstomanipulatetheirgroupinawaythatfa-vorstheirownsuccess(SaltzGeigerAndersonJohnsonampMarren2016) or to have a disproportionate effect on their group (Keiseramp Pruitt 2014 Modlmeier etal 2014 Pruitt amp Pinter-Wollman2015)hasbeenthefocusofmuchinterestrecentlySurprisinglynostudyhasexplored the implicationsof theexactpatternsofsocialplasticity for the identity and impact of such ldquokeystone individu-alsrdquo (Modlmeier etal 2014) It is reasonable to assume thatmostanimalsexhibitingsocialplasticityshouldadjusttheirphenotypeinresponse to theaverage socialconditions that theyexperience (al-thoughinsomecasessomeindividualscanadjusttheirphenotypeto themaximumor to theminimumphenotypicvalueof the indi-vidualswithwhomtheyinteractseeDyerCroftMorrellampKrause2009 for a potential example) Thus our simulations suggest thattheemergenceofkeystoneindividualsmightbeaphenomenonfarmore common than previously envisioned Keystone individualscouldemergeinanygroupofinteractingindividualsexhibitingphe-notypicplasticityanddenseinteractionnetworks(asinthelekkingexampleabove)Hencetheemergenceofkeystoneindividualsmightnotrequireacomplexsocialsystemdivisionoflabor(PruittBolnickSihDiRienzoampPinter-Wollman2016) collectivebehavior (PruittampPinter-Wollman2015)orniche-constructingtraits (egaggres-sivenesspolicingorelseChangampSih2013)butshouldbemostcommon in specieswhere individuals respond to thebehaviors ofthemajorityofgroupmembers
Denserinteractionsamongindividualswithinagrouppotentiatetheimpactofindividualswithextremephenotypicvaluesbyallow-ing these to interact and affect themajority of their groupmem-bersHencetheconsequencesofindividualsocialplasticitytendtobecomemuchgreater ingroupsasnetworkdensity increasesThisldquoamplificationrdquoeffectisalsostrongerwhengenotypesfollowauni-formdistribution (iewhenextremegenotypesaremorefrequentwithin groups) thanwhen they followaGaussiandistribution (ie
1460emsp |emsp emspensp MONTIGLIO eT aL
whenextremegenotypesarerarewithingroups)Networkdensityincreases the evolutionary response of groups on average groupswith denser connections also exhibit increasedvariation in evolu-tionaryresponsetoagivenselectiongradientSuchan increase inthevariationinevolutionaryresponseobservedinourstudyisap-parentbecauseourapproachallowsustorelaxtheassumptionthatindividualswithingroupsinteractequallywithallothergroupmem-bersbyintroducinganewparameter(averageconnectionstrength=s)intoourmodelandinsteadtoexplicitlyexploretheeffectofcon-nectiondensity
44emsp|emspHomophily affects the amount of phenotypic variation within groups
Our simulations also investigate the consequencesof social struc-turewhenindividualscaninteractpreferentiallywithindividualsthathaveasimilar(iehomophily)ordissimilar(ieheterophily)pheno-typeNetworkassortment(thenetworkmeasureofhomophily)doesnot have any impact on groupsrsquomean phenotype but can gener-ateagreatervariationinsocialenvironmentswithingroupsHenceassuming that different immediate social environments can favordifferent (alternative) phenotypes within groups our simulationssuggest that homophily should be associatedwith the emergenceof phenotypic variation among individuals (or social specializationBergmuumlller amp Taborsky 2010 Montiglio Ferrari amp Reacuteale 2013)Homophilyalsohasdirectconsequencesfortheevolutionofalter-nativephenotypesbycreatingsynergyoroppositionbetweendirectand indirect genetic effectsWhen social plasticity (ψg) is positive(egwheninteractingwithanaggressiveindividualincreasesafocalindividualrsquosaggression)andindividualsshowatendencytointeractwithsimilarphenotypesthesocialenvironmentactstoshapetheirphenotypeinthesamedirectionastheirgenotypeAsaresultsocialinteractionsandsocialplasticityincreasethephenotypicvarianceofthetraitrelativetoasituationinwhichconnectionsarerandominterms of their traits It also tends to increase the strength of theevolutionaryresponsetoselectioninresponsetoagivenselectiongradientThisincreaseinevolutionaryresponsearisesfromthesyn-ergybetweendirectandindirecteffect(orbetweensocialplasticityandhomophily)ratherthanfromachangeintotalgeneticvariationwithingroups
45emsp|emspPossible applications and tests of the model and future directions
differentialandmatechoicebyfemalesThestrengthofconnectionsbetweenmales of known phenotype could be increased artificiallyusingplaybacks tosimulatemore frequent interactionsamong indi-viduals(DabelsteenampPedersen1990Otteretal2001)tomonitorhowsuchincreasesinconnectionstrengthaffecttheextentofpheno-typicandgeneticadditivevariationAlternativelyonecanmanipulatethedistributionofterritoriesavailableandthepatternsofinteractionsby controlling the locationof nest boxes foodpatches or refugesSuchapproachescouldbeparticularlysuitableforcavity-nestingbirds(Both1998)
Ourmodel also studied the consequences of homophily for theevolutionary responses of phenotypic traits Assuming individualshave some level of control on their interactions homophily can beobservedwhen individualsexhibitpreferences to interactwithcon-specificsthatare(dis)similartothemSuchpreferencescouldexplainthemaintenanceofaltruisticbehaviorbecauseoftheirpotentialroleinshapingtheselectionpressuresactingonaltruismSomeworkonfruitflieshavereportedthatindividualpreferencesforparticularsocialenvironmentsisassociatedwithgeneticvariationandcanthuspoten-tiallyevolve (egSaltzampFoley2011)Onecould testourmodel insuchstudysystemsbyeitherallowingorpreventingtheexpressionofsocialpreferences(throughmixingofindividualsormanipulatingtheirinteractions) Alternatively homophily can also be observed whenindividualssegregateintheenvironmentasafunctionoftheirphe-notype(HelfensteinDanchinampWagner2004Ward1993WardampPorter1993)Forexamplemoreandlessaggressiveindividualsseg-regateinpatcheswithdifferentdensitiesofconspecifics(Duckworth2006)Thusbymanipulatingtheheterogeneityandthescaleatwhichitisobserved(iethesizeofpatchesofdifferenthabitat)onecouldtestthepredictionsofourmodelFutureworkwillexpandthemodelwe presented here to analyze the consequences of such traits forthemaintenanceofphenotypicvariationandtheevolutionofsocialstructure
One limitationofourmodel is thatweassumebothphenotypicfeedback(Mooreetal1997)andsocialselection(Wolfetal1999)tobeabsentIncludingfeedbackmayaltertheconclusionswehavepre-sentedhereasfeedbackeffectsmaycausesocialplasticitytomovethroughnetworksincounterintuitivewaysItispossiblethatnetworkmetricsbeyondconnectionstrength (suchasclusteringcoefficientsbetweennessetc)may influencewhetherfeedbackcontributessig-nificantly to variation and response to selection Regarding socialselectionwehaveshownherethatconnectionstrengthcontributestoamong-groupvariancewhichshould intensifyresponsetohigherlevelsofselectionsuchassocialselectionWewilltreatbothfeedbackandsocialselectioninfuturecontributions
5emsp |emspCONCLUSION
Wepresentbothananalyticmodelandsimulationsextendingpre-vious work on social phenotypic plasticity to more general socialstructuresOurstudygeneratesafirstsetofverygeneralandtest-able predictions on the role of social structure in modulating the
emspensp emsp | emsp1461MONTIGLIO eT aL
consequencesofsocialplasticityWeshowthatthebasiccharacter-isticsofthestructureofinteractionsamongindividualsingroupsandpopulationscanhaveimpactsontheconsequencesofsocialplasticityforthemeanphenotypeexpressedbytheindividualstheextentofphenotypicvariationavailableforselectionandfortheabilityofthepopulation to respond to selectivepressuresWehope that futurestudieswillbeabletotestourpredictionsempiricallybyapplyingourapproachtothestudyofsocialbehavior(egaggressionandcoop-eration)socialinformationuseoralternativematingtacticsinpopu-lationswithvaryingpatternsofsocialormatinginteractionsFromatheoreticalperspectivefutureresearchwouldwarrantinvestigatingthelinkbetweenindividualpositioninsocialnetworksandtheindi-rect genetic effects it experiences and thuswhether factors otherthan individualsrsquo breeding values can lead to keystone individualsFurtherinourstudyweassumethatallindividualsexpressedplas-ticityidenticallyHoweverindividualshavealsobeenshowntovaryintheirplasticity(DingemanseKazemReacutealeampWright2010NusseyWilsonampBrommer2007WestneatHatchWetzelampEnsminger2011)andsuchvariationmayalterthepredictionsofinteractingphe-notypemodels(KazancıoğluKlugampAlonzo2012)Linkingindividualdifferencesinbothsocialpositionandplasticitycouldyieldnewin-sightsandagreaterunderstandingoftheevolutionarymechanismsthatunderpinphenotypicvariationwithinindividualsbetweenindi-vidualsandamongpopulations
ACKNOWLEDGMENTS
We thank the Reader Hendry and Barrett laboratories in McGillUniversity forconstructivecommentsonadraftof thismanuscriptPOMwas supported by aNSERCpostdoctoral fellowshipDRF re-ceived funding from a grant to theBBSRC (BBL0060811 toBCSheldon)andtheMaxPlanckSociety
CONFLICT OF INTEREST
Nonedeclared
AUTHOR CONTRIBUTIONS
POMandDRFbuiltthesimulationsandJWMdevelopedthemodelPOMdrafted themanuscript andproduced the figuresAll authorscontributedtorevisionsandapprovedthefinalversionofthearticle
AplinLMFarineDRMorand-FerronJCockburnAThorntonAamp SheldonBC (2015) Experimentally induced innovations lead topersistentcultureviaconformityinwildbirdsNature518538ndash541
Aplin LMFirthJAFarineDRVoelklBCratesRACulinaAhellipSheldonBC (2015)Consistent individual differences in the so-cialphenotypesofwildgreattits(Parusmajor)Animal Behaviour108117ndash127httpsdoiorg101016janbehav201507016
BaileyNWampHoskins J L (2014)Detecting cryptic indirect geneticeffectsEvolution681871ndash1882httpsdoiorg101111evo12401
Bailey N W amp Zuk M (2012) Socially flexible female choice differsamongpopulationsofthePacificfieldcricketGeographicalvariationin the interaction coefficient psi (Ψ)Proceedings of the Royal Society of London Series B Biological Sciences 279 3589ndash3596 httpsdoiorg101098rspb20120631
Bergmuumlller R amp Taborsky M (2010) Animal personality due to socialnichespecialisationTrends in Ecology amp Evolution25504ndash511httpsdoiorg101016jtree201006012
Bijma P ampWade M J (2008) The joint effects of kin multilevel se-lection and indirect genetic effects on response to genetic selec-tion Journal of Evolutionary Biology 21 1175ndash1188 httpsdoiorg101111j1420-9101200801550x
Boatright-HorowitzSLHorowitzSSampSimmonsAM(2000)Patternsof vocal interactions n a BullfrogRana catesbeiana chorus preferen-tial responding to farneighborsEthology106701ndash712httpsdoiorg101046j1439-0310200000580x
BothC(1998)Experimentalevidencefordensitydependenceofrepro-ductioningreattitsJournal of Animal Ecology67667ndash674httpsdoiorg101046j1365-2656199800228x
Cappa E P amp Cantet R J C (2008) Direct and competition additiveeffects in treebreedingBayesianestimation froman individual treemixedmodelSilvae Genetica5745ndash56
ChangAampSihA (2013)Multilevel selection andeffects of keystonehyperaggressivemalesonmatingsuccessandbehaviorinstreamwaterstridersBehavioral Ecology241166ndash1176httpsdoiorg101093behecoart044
Clutton-BrockTH(1989)MammalianmatingsystemsProceedings of the Royal Society B236339ndash372httpsdoiorg101098rspb19890027
Crowley P H amp Cox J J (2011) Intraguild mutualism Trends in Ecology amp Evolution 26 627ndash633 httpsdoiorg101016jtree201107011
Duckworth R A (2006) Aggressive behaviour affects selection onmorphology by influencing settlement patterns in a passerine birdProceedings of the Royal Society B 273 1789ndash1795 httpsdoiorg101098rspb20063517
Farine D R (2014) Measuring phenotypic assortment in animal so-cial networks Weighted associations are more robust than binaryedges Animal Behavior 89 141ndash153 httpsdoiorg101016janbehav201401001
FarineDRampWhiteheadH(2015)Constructingconductingandinter-preting animal social network analysis Journal of Animal Ecology841144ndash1163httpsdoiorg1011111365-265612418
Fawcett TW amp Johnstone RA (2010) Learning your own strengthWinner and loser effects should change with age and experienceProceedings of the Royal Society of London Series B Biological Sciences2771427ndash1434httpsdoiorg101098rspb20092088
Fisher D N amp McAdam A G (2017) Social traits social networksand evolutionary biology Journal of Evolutionary Biology httpsdoiorg101111jeb13195Inpress
FormicaVAWood CW LarsenW B Butterfield R EAugatMEHougenHYampBrodieIIIED(2012)Fitnessconsequencesofsocialnetworkpositioninawildpopulationofforkedfungusbeetles(Bolitotherus cornutus) Journal of Evolutionary Biology 25 130ndash137httpsdoiorg101111j1420-9101201102411x
Greenfield M D amp Rand S A (2000) Frogs have rules selective at-tention algorithms regulate chorusing in Physalaemus pustulosus (Leptodactylidae)Ethology106131ndash147
Helfenstein FDanchin E ampWagner RH (2004)Assortativematingand sexual size dimorphism in blacklegged kittiwakes Waterbirds27 350ndash354 httpsdoiorg1016751524-4695(2004)027[0350AMASSD]20CO2
Herbert-Read J E Krause S Morrell L J Schaerf T M Krause JampWardAJW (2013)The roleof individuality in collectivegroupmovementProceedings of the Royal Society B- Biological Sciences28020122564
KeiserCNampPruittJN (2014)Personality composition ismore im-portantthangroupsizeindeterminingcollectiveforagingbehaviourinthewildProceedings of the Royal Society of London Series B Biological Sciences28120141424httpsdoiorg101098rspb20141424
Krause J amp Ruxton GD (2002) Living in groups Oxford UKOxfordUniversityPress
Landeau L ampTerborgh J (1986)Oddity and the ldquoconfusion effectrdquo inpredationAnimal Behavior341372ndash1380httpsdoiorg101016S0003-3472(86)80208-1
Magnhagen C amp Bunnefeld N (2009) Express your personality or goalong with the group What determines the behaviour of shoalingperchProceedings of the Royal Society B- Biological Sciences2763369ndash3375httpsdoiorg101098rspb20090851
McDonaldG C FarineD R Foster K R ampBiernaskie JM (2017)Assortment and the analysis of natural selection on social traitsEvolution712693ndash2702httpsdoiorg101111evo13365
McGlothlin JW amp Brodie III E D (2009) How to measure individ-ual genetic effects The congruence of trait-based and variance-partitioning approaches Evolution 63 1785ndash1795 httpsdoiorg101111j1558-5646200900676x
McGlothlin J W Moore A J Wolf J B amp Brodie III E D(2010) Interacting phenotypes and the evolutionary pro-cess III Social evolution Evolution 64 2558ndash2574 httpsdoiorg101111j1558-5646201001012x
MillerJRBAmentJMampSchmitzOJ (2014)Fearon themovePredatorhuntingmodepredictsvariation inpreymortalityandplas-ticityinpreyspatialresponseJournal of Animal Ecology83214ndash222httpsdoiorg1011111365-265612111
ModlmeierAPKeiserCNWattersJVSihAampPruittJN(2014)The keystone individual concept An ecological and evolutionaryoverview Animal Behavior 89 53ndash62 httpsdoiorg101016janbehav201312020
MontiglioP-OFerrariCampReacutealeD(2013)Socialnichespecializationunder constraints Personality social interactions and environmentalheterogeneityPhilosophical Transactions of the Royal Society of London Series B Biological Sciences36820120343httpsdoiorg101098rstb20120343
Moore A J Brodie III E D ampWolf J B (1997) Interacting pheno-types and the evolutionary process I Direct and indirect geneticeffects of social interactions Evolution 51 1352ndash1362 httpsdoiorg101111j1558-56461997tb01458x
NonacsPampKapheimKM(2007)Socialheterosisandthemaintenanceof genetic diversity Journal of Evolutionary Biology 20 2253ndash2265httpsdoiorg101111j1420-9101200701418x
Nussey D H Wilson A J amp Brommer J E (2007) The evolution-ary ecology of individual phenotypic plasticity in wild popula-tions Journal of Evolutionary Biology 20 831ndash844 httpsdoiorg101111j1420-9101200701300x
OtterKAStewartIRKMcGregorPKTerryAMRDabelsteenTampBurkeT(2001)Extra-pairpaternityamonggreattitsParus major following manipulation of male signals Journal of Avian Biology 32338ndash344httpsdoiorg101111j0908-88572001320408x
Pruitt J N Bolnick D I Sih A DiRienzo N amp Pinter-Wollman N(2016)Behavioralhypervolumesofspidercoloniespredictscommu-nity performance and disbandmentProceedings of the Royal Society B- Biological Sciences 283 20161409 httpsdoiorg101098rspb20161409
PruittJNampPinter-WollmanN(2015)Thelegacyeffectsofkeystonein-dividualsoncollectivebehaviourscaletohowlongtheyremainwithina group Proceedings of the Royal Society B- Biological Sciences 28220151766httpsdoiorg101098rspb20151766
RoyleNJHartley IROwens I P FampParkerGA (1999) Siblingcompetition and the evolution of growth rates in birds Proceedings of the Royal Society B 266 923ndash932 httpsdoiorg101098rspb19990725
SaltzJBampFoleyBR(2011)Naturalgeneticvariationinsocialnicheconstruction Social effects of aggression drive disruptive sexual se-lectioninDrosophila melanogaster American Naturalist177645ndash654httpsdoiorg101086659631
ShusterSM LonsdorfEVWimpGMBaileyJKampWhithamTG (2006) Community heritabilitymeasures the evolutionary conse-quencesofindirectgeneticeffectsoncommunitystructureEvolution60991ndash1003httpsdoiorg101111j0014-38202006tb01177x
SimmonsAMSimmonsJAampBatesMA (2008)Analyzingacous-tic interactions in natural bullfrog (Rana catesbeiana) chorusesJournal of Comparative Psychology 122 274ndash282 httpsdoiorg1010370735-70361223274
Sinervo B R amp Calsbeek R (2010) Behavioral concepts of selectionExperiments and genetic causes of selection on the sexes In D FWestneatampCWFox(Eds)Evolutionary behavioral ecologyLondonUKOxfordUniversityPress
Thompson J N (1982) Interaction and coevolution Chicago USA TheUniversityofChicagoPress
emspensp emsp | emsp1463MONTIGLIO eT aL
VanderWaal K L ObandaV Omondi G P McCowan BWang HFushingHampIsbellLA (2016)Thestrengthofweaktiesandhel-minth parasitism in giraffe social networks Behavioral Ecology 271190ndash1197httpsdoiorg101093behecoarw035
Ward P I (1993) Micro-habitat segregation and the mating systemof Gammarus pulex Animal Behavior 45 191ndash192 httpsdoiorg101006anbe19931019
Ward P I amp PorterAH (1993)The relative role of habitat structureandmale-malecompetition in thematingsystemofGammarus pulex (CrustaceaAmphipoda)AsimulationstudyAnimal Behavior45119ndash133httpsdoiorg101006anbe19931011
West-EberhardMJ(1989)Phenotypicplasticityandtheoriginsofdiver-sityAnnual Review of Ecology and Systematics20249ndash278httpsdoiorg101146annureves20110189001341
Westneat D F Hatch M IWetzel D P amp Ensminger A L (2011)IndividualvariationinparentalcarereactionnormsIntegrationofper-sonalityandplasticityAmerican Naturalist178652ndash667httpsdoiorg101086662173
Wilson A J Gelin U Perron M-C amp Reacuteale D (2009) Indirect ge-neticeffectsandtheevolutionofaggression inavertebratesystemProceedings of the Royal Society of London Series B Biological Sciences276533ndash541httpsdoiorg101098rspb20081193
Additional Supporting Informationmay be found online in the sup-portinginformationtabforthisarticle
How to cite this articleMontiglioP-OMcGlothlinJWFarineDRSocialstructuremodulatestheevolutionaryconsequencesofsocialplasticityAsocialnetworkperspectiveoninteractingphenotypesEcol Evol 201881451ndash1464 httpsdoiorg101002ece33753
APPENDIX
PHENOTYPIC MEAN AND VARIANCE
FollowingMooreetal(1997)wemodelasinglephenotypeofanindi-vidual (z)asanadditivecombinationoftheeffectsof itsowngenes(iedirectgeneticeffectsa)thenonsocialenvironmentitexperiences(e)andaplasticcomponentthatissomefunctionofthephenotypesinitssocialgroupMooreetal(1997)originallymodeledthesocialeffectasafunctionofthephenotypeofoneinteractingindividualMcGlothlinandBrodie (2009)andMcGlothlinetal (2010)consideredsocialef-fectsinapopulationconsistingofgroupsofnindividualswhereinter-actionswereassumedtooccursimultaneouslywithinagroupwithallindividuals within a group having the same strength of interactionHereweconsideramoregeneralsocialstructurewhereindividualsinteractwithallpossiblesocialinteractantsingroupsizenwithvaria-bleconnectionstrengthsirangingfrom0to1giving
wherethesummationistakenacrossalln minus1possiblesocialinterac-tionsforeachindividualsandψrepresentstheinteractioncoefficientwhichdetermines thestrengthanddirectionof the indirectpheno-typic effect of individual social interactantsHere and elsewhere aprimeindicatesaparameterbelongingtoasocialpartnerAnysocialnetworkstructurecanbemodeledbychangingthedistributionofs High-densitysocialnetworkswithstrongconnectionswillhavemanylargevaluesofswhilesparsernetworkswithweakerconnectionswillhavemanyweaksvalueswithmanyequaltozeroConsideringphenotypicfeedback(asdoMooreetal1997)insuch
The value of the two covariance terms represents how stronglystrengthofinteractiondependsonthegenesandenvironmentofin-dividualsocialpartnersThiscovarianceisdeterminedforeachindi-vidualandmayvaryacrossindividualsTheseshouldbepositiveunderhomophilyandnegativeunderheterophilyTakingthemeanandas-suming
=e=0
where double overbars indicate global means and large overbarswithintheparenthesesindicatemeanstakenacrossindividualsbasedonsummarystatisticsoftheirsocialgroupsThiscanbeexpandedasaboveto
The remainingcovariance terms represent theaveragedegree towhichindividualconnectionstrengthsareadjustedbasedonthephe-notypeofpotentialinteractantsInthecaseofhomophilyorheteroph-ilyindividualswillmakethisadjustmentbasedontheirownphenotypewithlargeindividualshavingapositivecovarianceandsmallindividu-alshavinganegativecovariance(orviceversa)ThereforeweexpecttheseaveragecovariancetermstotendtowardzeroMakingthisas-sumptionandrearrangingprovidesEquation2inthetext
EXTENSION TO MULTIPLE GROUPS
EquationA8iswrittenassumingthatthepopulationconsistsofasin-gle social networkwhere individualsmay interact in anywayNowassumethatthepopulationisdividedintomultiplegroupswhereindi-vidualsmay interactwithanystrengthswithinagroupanddonotinteract at all between groups Assuming the covariance terms inEquationA8arezeroandthatenvironmentaldeviationsdonotvaryamonggroupsthemeanofeachgroupwillbe
where overbars now indicate within-groupmeans Assuming equalgroupsizethepopulationmeanisnow
(IfgroupsvaryinsizethenEquationA10canbemodifiedtogiveaweightedmean) Ifconnectionstrengthhasnoheritablebasis thenthe covariance term become zero and EquationA10 collapses toEquation2inthetextWemaycalculateamong-groupvariancemosteasilybymakingafewassumptionsthatarealsomadeinoursimula-tionsFirstasaboveweassumethatgroupsareofequalsizeSecondweassume thatmean interactiondoesnotvaryacrossgroups ands=
=sMakingtheseassumptions
Thisshowsthat indirectgeneticeffectswillmagnifyslightdiffer-ences in genetic values across groups regardless of sign Strongermeanconnectionstrengthswillintensifythiseffect
RESPONSE TO SELECTION
FollowingMoore etal (1997) andMcGlothlin etal (2010) and as-suming that thecovariance terms inEquationA8areeither zeroorpopulation parameters that do not have a heritable component anindividualrsquostotalbreedingvaluecanbewrittenasthegeneticcontri-butiontothepopulationmean
where Ristheregressionofsaprimeonaandisthusanalogoustorelated-ness This assumes thatCov[aseprime] is negligible Positive values ofR indicatehomophilyandnegativevaluesindicateheterophilyMakingthissubstitutiongivesEquation4inthetextEquation4canalsobeexpresseddifferentlybyrearrangingas
Becausetheresultingnetworkdensity(thesumofallpresentedgeweightsdividedby thepossible sumofedgeweights if thenetworkwerefullyconnected)foragivenvalueofrisstochasticnotdetermin-isticwereportourresultsasafunctionofnetworkdensitywhichwascalculatedusingtheRpackageassortnet(Farine2014)Statedanotherwaynetworkdensityisanemergentpropertyofvaryingrnotaparam-eterofoursimulationsOurapproachismostimmediatelyapplicabletosituationswhereindividualsareactuallydistributedintwo-dimensionalspaceandinteractmoreorlessintenselyasafunctionofthedistance(Farine 2015) Such an interaction structure applies directly to situ-ations such as competition amongneighboringplants (egCappaampCantet2008)orterritorialityinanimals(egRoyleHartleyOwensampParker1999)butisgeneralizableawidevarietyofothermorecomplexsituationsthatmaynotinvolveaspatiallyexplicitcomponent
Individualscanoftenchoosetoconnectmorestronglywithsomeindividuals than others In many species individuals preferentiallyinteractwithpartnersthataresimilar (ieunderassortativematingor during cooperative interactions) or dissimilar to them (ie underdisasortativemating or because of division of labor and social het-erosis seeNonacsampKapheim 2007)Hence networks can exhibitassortment (associations between individuals that are similar andor avoidance of dissimilar individuals Farine 2014) Firstwe studythe effect of randomly occurring network assortment in the sim-ulated groups To explicitly investigate the impact that interactionpreferencescanhaveonevolutionaryprocesseswethenallowindi-vidualstoreducethestrengthoftheirinteractionwithnonpreferredaffiliates (eg with dissimilar individuals in the case of homophilyorwithsimilar individuals inthecaseofheterophily)Wethusmod-ify the function used to calculate the strength of interaction (s) tos=eminusdistance
2∕rtimesH(
1
1+expminus20|xminusy| minus05)+05 which generates a sig-
moidalfunctionwithamagnitudeofH(thelevelofhomophilyrang-ingbetween0and02) as a functionof |xminusy| or thedifference inthephenotypesoftheindividualsIftwoindividualsareidenticalthestrengthoftheirinteractionismultipliedbyeither~0or~1ifmodelingheterophily or homophily respectivelyTheir connection strength ismultipliedby05iftheirphenotypicdifference(|xminusy|)isaverageAswithnetworkdensitywe report themeasurednetworkassortmentcalculatedusingtheRpackageassortnet(Farine2014)
strengthoftheirsocialinteractionssiIndividualswithnoconnectionstrengthdonotcontributetothephenotypeassi =0Inoursimula-tionsall individualshavethesameinteractioncoefficient(ψg)Wealsoinvestigatewhetherourresultsdependedonthedistributionofbreedingvaluesbyrunningadditionalsimulationswhereindividualbreedingvaluesare sampled fromanormaldistribution (mean=0andvariance=1)IntheresultswepointoutwheresuchachangeindistributionaffectsourresultsInpreviousmodels(McGlothlinampBrodie2009McGlothlinetal2010)ψghasbeenconstrainedtoliebetweenminus1and1fortworeasonsFirstvaluesofψggreaterthan1canleadtounreasonablephenotypicvalues(particularlyinmodelsthat include phenotypic feedback) Second phenotypic values areoftenstandardizedtoameanofzeroandunitvarianceforanalysiswhichshouldresult inψgvaluesbetweenminus1and1 Inoursimula-tionsthemeanandvarianceofindividualphenotypesvariedineachgroup because of samplingwhichmade such standardization dif-ficultWechose touseunstandardized traitvaluesanda largeψg value(4)inallsimulationsSuchavalueofψgwhichwouldyieldanaveragestandardizedvalueofψgof~030whichiscomparabletoempiricalψgvaluesreportedintheliterature(egBaileyampHoskins2014BaileyampZuk2012)Usingthislargevaluefacilitatesvisual-izing social effects anddoesnot lead tounreasonablephenotypicvalues due to the absence of phenotypic feedback in ourmodelAs noted in theAppendixψg ismultiplied by average connectionstrength (network density) when calculating phenotypes whichwillreducetheeffectofψgexceptinfullyconnectednetworksAspredictedbytheanalyticalmodel increasingthestrengthofsocialplasticity(iehowmuchanindividualchangedhisphenotypeinre-sponsetohissocialpartnerstheabsolutevalueofψg)amplifiesallthe patternswe report below (seeResults section)However be-causesuchincreasesareintuitiveandoflesserinterestwedonotreporttheresultsofanalysesvaryingψgUsingthecodeavailableasFigureS1 the reader cangenerate figures that are comparable totheoneswepresentbelowforanyvalueofψg
where G indicates additive genetic variance andE indicates envi-ronmental variance The third term above represents the among-individual variance due to social interactions This term shouldincreasesomewhatwithhomophilybutshoulddependmostheav-ily on network density The variance in social environment expe-rienced by individuals should be at amaximum at intermediate
becomemorehomogenous(ieeveryoneinteractswitheveryone)Thefourthtermwillbemost influencedbyhomophily (orhetero-phily)becauseassociatingwithsimilar(ordifferent)individualswillcause the covariance to increase (ordecrease)Themultiplicationbyψgwillcausephenotypicvariancewithinagrouptoincreasewithhomophilyunderpositivevaluesofψganddecreasewithhomophilywhenψg isnegativeThistermshouldalsobe influencedbyaver-ageconnectionstrength(
where R is a general measure of the strength of homophily (seeEquationA19 in Appendix) and β is the selection gradient (seeAppendix)Thisequationshowsthattheamountofgeneticvarianceavailableforresponsetoselectionatthepopulationlevelshouldde-pendon(1)thedegreeofsocialplasticity(2)theaverageconnectionstrength(whichshouldincreasewithmeanconnectionstrength)and(3)theamountofassociationbetweenindividualsthatisbasedonge-neticvaluesimilarity(homophilyorheterophily)Thismodelisnearlyidenticaltopreviousmodelswithsimplergroupstructure(McGlothlinetal 2010) except for the inclusion of the connection strength (
=s)
and the replacementof relatednesswithhomophilyheterophily (R)Theseanalyticalresultsprovidepredictionsthatwetestbelowusingindividual-basedsimulations
32emsp|emspNetwork density
Inoursimulationsincreasingnetworkdensitywhichisanalogoustoincreasing mean connection strength in the analytical model doesnot lead to an increase inphenotypicmeanonaverage (ie acrossallgroupsFigure2red line)Howeverathighernetworkdensitiesthere is much greater variation among groups in their phenotypicmean (Var[
=z ] Figure2 gray dots) This occurs because although
themeangeneticvalueacrossall simulations iszero thisvaluecandiffer across groups due to sampling As predicted by Equation2increasing network density (or
=s) increases the importance of the
group genotypic composition in determining the effects of indirectgeneticeffectsmagnifyingdifferencesamonggroupsingeneticvalue(=a) across replicate simulation runs This amplification effect is also
Thephenotypicvariance in indirecteffectswithineachgroup ismaximalatintermediatenetworkdensities(Figure3a)Whenindivid-ualshave fewconnections (and connection strength isweaker) thescopeforindirecteffectstodifferamongmembersofagivengroupisnarrowtherebydecreasingthecontributionofsocial interactionstophenotypicvariance(Figure3a)Likewiseingroupswhereindividualsarehighlyconnected (highnetworkdensity) thesocialenvironmentexperiencedbyeachindividualisclosertotheaveragebreedingandenvironmentalvalueofthepopulation(whichis0inoursimulations)In otherwordsVar[aprime] and consequentlyVar[saprime]within groups issmallathighdensities(seeEquation3)Howeveratintermediateden-sities indirecteffectshadthepotentialtomakealargecontributiontophenotypicvariancealthoughthiseffectwashighlyvariableacrosssimulations
Intheabsenceofhomophilyheterophilyhighnetworkdensityleadstoanegativecorrelationbetweendirectandindirectgeneticeffects(Figure3b)Atlownetworkdensitiesthiscorrelationisex-pectedtobezerobecauseindividualsassociateatrandom(althoughthiswouldnotbe thecase if therewasanyspatial assortmentbyphenotype) However at high densities this correlation becomesnegativeeventhoughindividualassociationisalsorandomThisef-fectarisesbecauseindividualsarenotcountedaspartoftheirownsocial environment andasnetworkdensities increase the impor-tanceofthisdifferencebecomesmagnifiedAtthehighestnetwork
(3)Var[z]=G+E+ψ2gVar
[sa + se
]+2ψgCov
[a +e sa + se
]
(4)Δ=zasymp
(1+ψg
=s)G(1+Rψg
)β
F IGURE 2emspThechangeinaveragephenotypeofindividualsinanetworkasafunctionofthenetworkdensity(redline)Thechangeinaveragephenotypeisexpressedrelativetothephenotypeexpectedinabsenceofinteractionsamongindividuals(ie0)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4Asdensityincreasedweobservedagreatervariationinmeanphenotypeamonggroups(graydots)
1456emsp |emsp emspensp MONTIGLIO eT aL
densitiessocialenvironmentsare indistinguishableexceptforthiseffect of excluding oneself thus leading to a directndashindirect cor-relationofminus1Smallergroupswillexhibitthispatterntoastrongerextent than larger groups (see FigureS5 also McDonald FarineFosterampBiernaskie2017)Thecombinedimpactoftheeffectsofnetworkdensityonthevariancein indirectgeneticeffectsandonthecovariancebetweendirectandindirectgeneticeffectsisarel-ativedecrease inphenotypicvariationwithingroups(comparedtothephenotypicvariationinabsenceofanyinteractions)asnetworkdensityincreases(Figure3c)Oppositepatternsareobservedwhenψg isnegative(FigureS6)Finallywenotethatalthoughthemeanphenotypic variationwithin each group decreaseswith increasingnetworkdensitywefindthatthevariationamonggroups(eachdotin each panel of Figure3c represents one group) ismaximized atintermediatenetworkdensities
Although the phenotypic variance typically decreases with in-creasednetworkdensitythevarianceintotalbreedingvalues(rela-tivetothegeneticvarianceinabsenceofanysocialinteraction)hasthe greatest increase at highest network densities (Figure3d redline)Thisisbecausetheexpectedvarianceintotalbreedingvaluesisequalto
(1+ψg
=s)2
G(seeEquationA12)Thatisthevarianceintotalbreedingvaluesdoesnotdependonthevarianceinindirectgeneticeffects noron the covariancebetweendirect and indirect geneticeffectswhich leadtothedecrease invarianceshowninFigure3cRatherthevarianceintotalbreedingvaluesisafunctionofdirectge-neticeffectsandeffectsofanindividualrsquosgenesonothersthelatter
ofwhichbecomesinflatedathigherdensitiesTheresponsetoselec-tiondependsonthecovariancebetweentotalbreedingvaluesandphenotypicvalueswhichisexpectedtoincreaselinearlywithdensity(EquationA15)Whenwesubjectgroupstoaselectiongradientof02networkswithincreasingdensitiesexhibitedanincreasedevolu-tionaryresponsetoselection(Figure4redline)Increasingnetworkdensityalso increases thevariance in responsetoselectionamonggroups (Figure4 gray dots) This likely happened because individ-ualsadjusttheirphenotypetotheaveragesocialenvironmentthattheyexperienceThusathighernetworkdensitiesindividualswithextreme phenotypicvalues have a disproportionate impact on theaveragesocialenvironmentexperiencedbyindividualsSmalldiffer-encesinthephenotypicvaluesofextremeindividualsfromgrouptogroupcreatedifferencesinthecovariancebetweenthephenotypicvarianceandthetotalbreedingvaluesamonggroupsandincreasingthevariance in response to selection amonggroups In agreementwiththisextremeindividualsalsogenerategreaterphenotypicvari-anceamonggroupsathighernetworkdensities(Figure2)andwhenindividualphenotypesfollowauniformdistribution(moreindividualswithextremephenotypes)thananormaldistribution(fewerindivid-ualswithextremephenotypesSeeFigureS3)
F IGURE 3emspEffectsofnetworkdensityon(a)thevarianceinindirecteffectsexperiencedbyindividuals(b)thecorrelationbetweendirectandindirectgeneticeffectsexperiencedbyindividuals(c)thechangeinphenotypicvariancewithingroupsrelativetothegeneticvariance(iethephenotypicvarianceinabsenceofinteractions)and(d)thechangeintotalgeneticvariationrelativetothegeneticvariance(ievarianceofindividualdirectgeneticeffectsandindirectgeneticeffectsimposedtoothers)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψg of4
emspensp emsp | emsp1457MONTIGLIO eT aL
hasnoeffectonthemeanphenotypeofeachgroup(Figure5)whichis consistent with our analytical model (Equation2) However in-creasednetworkassortmentisassociatedwithanincreaseinthevari-anceinindirectgeneticeffectsexperiencedbyindividualsinagivengroup(seethethirdterminEquation3Figure6a)Becauseindividu-alsinteractmorestronglywithconspecificsthathavesimilarbreedingvalues(highwithhighlowwithlow)thedirectandindirectgeneticcontributions to phenotypes act in concert and covary positively(fourthterm inEquation3Figure6b)Thesetwoeffectscontributetowardincreasingphenotypicvarianceobservedwithinagivengroup(Figure6c)Theseeffectsarereversedwhenψgisnegativedirectandindirect contributions to individual phenotypes act to oppose eachothertherebyreducingtheamountofphenotypicvarianceobservedin the population (see FigureS7) Increasing network assortmentalsoleadstoasmalldecreaseinthevarianceintotalbreedingvalues(Figure6dredline)Thisisattributabletotheslightdecreaseinden-sityassociatedwithhigherlevelsofnetworkassortment(ieindividu-alshavetheabilitytoreducetheconnectionstrengthwithparticulargroupmembers)aphenomenonnotcapturedbyouranalyticalmodel
Applying selection to groups with varying network assortmentshowsthatasynergybetweendirectandindirectgeneticeffectsleadstoanincreaseinevolutionarychangewithincreasingnetworkassort-ment(Figure7redline)Thisresultisinaccordwiththepredictionsofouranalyticalmodelwhichpredictsanincreasedresponsetoselec-tionwithincreasingR(Equation4)AlthoughEquation4suggestsden-sityandhomophilyshouldhavesymmetricaleffectstheincreaseseeninFigure7isnotasdramaticasthatinFigure4perhapsbecauseoftheconcomitantdecreaseindensitycausedbyallowinghomophilyinoursimulationsUnlikenetworkdensitynetworkassortmentdoesnotaffectthevariationofevolutionaryresponsesamonggroups(Figure7graydots)
4emsp |emspDISCUSSION
Inthisstudyweexploretheconsequencesofsocialplasticityandthestructureofinteractionsinshapingtheamountofphenotypicvariationwithingroupsof interactingindividualsandtheevolutionaryresponseofthesegroupstoselectionWeconsiderreplicategroupswithvary-ingstructuresofinteractionsSuchreplicatescouldbeseenasmultiplegroups of individualswithin a given population (eg tribes packs orcolonies)orasmultipleisolatedpopulationswithinanecologicalcom-munityThroughananalyticalmodelandagent-basedsimulationsweshowthatthestructureofsocialnetworksmodulatedtheimpactofin-directgeneticeffectsontheamountofphenotypicvarianceavailablefor selectionOur resultsemphasize that thenumberandstrengthofconnectionsamongindividuals(networkdensity)aswellaspreferentialassociations among individualswith a similar phenotype (network as-sortment)haveimportanteffectsonthecontributionofindirectgeneticeffectsNetworkdensityandassortmentalsomodulatetheabilityfortraitstoexhibitevolutionarychangeinresponsetoselectionIncreasingthenumberofinteractionsamonggroupmembers(networkdensity)in-creasestheaverageevolutionaryresponseofgroupstoselectionandin-creasesthevariationinresponsetoselectionamonggroupsBycontrastincreasednetworkassortmentleadstoanincreaseintheaverageevolu-tionaryresponseofgroupstoselectionbutdoesnotaffectthevariationinevolutionary responseamonggroupsOur resultshavewidespreadimplicationsforstudiesofsocialevolutionmultilevelselectionandtheemergenceofkeystoneindividuals(ModlmeierKeiserWattersSihampPruitt2014)andniche-constructingtraits(egSihampWatters2005)
41emsp|emspComparison with earlier interacting phenotype models
Our analytical results show that given some simplifying assump-tions (most importantly ignoring the potential for phenotypic
F IGURE 4emspEvolutionaryresponseofphenotypetoaselectiongradientvarieswithnetworkdensityTheaveragechangeinphenotypemeanresultingfromselectionincreasedwithnetworkdensity(redline)Groupswithdensernetworksofinteractionsexhibitedmorevariationinthechangeinphenotypicmean(graydots)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4
F IGURE 5emspTheaveragephenotypeofindividualsasafunctionofnetworkhomophily(redline)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4Networkscouldnotreachhomophilyvaluesof1becauseweusedacontinuoustraitvalueratherthandiscretevalues(seeFarine2014)
1458emsp |emsp emspensp MONTIGLIO eT aL
feedback) considering more general social structures does notgreatlyalter theconclusionsofearliermodelsof interactingphe-notypeevolution(egMcGlothlinetal2010Mooreetal1997)First indirect genetic effects still alter the response to selectionby increasing the amount of genetic variance exposed to selec-tionNote thatbecausewedonotmodel feedback thiseffect is
directional with positiveψg (ie becomingmore similar to onersquosneighbors)increasingtheresponsetoselectionandnegativevalues(iebecomingmoredifferentfromonersquosneighbors)decreasingitSecondhomophilyheterophilyplaysa rolesimilar to relatednessinpreviousmodelsinalteringtheresponsetoselection(McGlothlinetal2010)IndeedMcGlothlinetal(2010)noted(ashavemanyothers)thatrelatednessperseisjustaspecialcaseofphenotypicassortment
Themostnotabledifferencebetweenourmodelandearliermod-elsisthatindividualsareallowedtodifferintheirinfluenceonsocialplasticityduetovariation inconnectionstrength (s)Perhapsunsur-prisingly responsetoselection ismorestrongly influencedbysocialinteractions indensernetworkswhere interactionsarestrongerandmorecommonaneffect that isapparent inbothouranalyticalandsimulation results Inour simulation resultswealso find thatvaria-tioninresponsetoselectionamongincreaseswithgreaterconnectionstrengthThis could occur because in some groups themostwell-connectedindividualshappentohaverelativelyhighorlowbreedingvaluesThesewell-connected individualswould thenhaveadispro-portionateeffectonthephenotypeofothers (relativeto individualsclosertothepopulationrsquosaveragebreedingvalue)byexertingastrongeffectonthemeansocialenvironmentexperiencedbyindividualsIndoingsowell-connectedextremeindividualscangeneratevariabilityinthecovariancebetweenbreedingvaluesandphenotypeandthusintheresponsetoselectionFuturemodelsshouldallowconnectionstrength to display a heritable component which would allow thesocialnetworkstructureitselftoevolveinresponsetosucheffects
F IGURE 6emspEffectofnetworkhomophilyon(a)thevariationinindirecteffects(b)thecorrelationbetweendirectandindirectgeneticeffects(c)therelativechangeinphenotypicvariancewithingroupsand(d)therelativechangeintotalgeneticvariationEachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4HomophilysimultaneouslyincreasesvariationamongindividualsinindirectgeneticeffectswithingroupsandgeneratesastrongpositivecovariancebetweendirectandindirectgeneticeffectstherebysubstantiallyincreasingthephenotypicvarianceobservedwithingroupsHoweverthisincreaseinphenotypicvarianceisnotassociatedwithanychangeatthegeneticlevel
F IGURE 7emspEvolutionaryresponseofphenotypetoaselectiongradientincreaseswithnetworkhomophily(redlineandgraydots)Eachdotrepresentsthechangeinmeangenotypeacrossgenerationsinasinglesimulatednetworkorgroupof50individuals(Ngroup=50)TheredlinerepresentstheaverageevolutionaryresponseasafunctionofnetworkdensityIndirectgeneticeffectsweregeneratedusingaψgof4
emspensp emsp | emsp1459MONTIGLIO eT aL
Studiesinthewildhaveshownthatpositioninasocialnetworkmaybe repeatable and have fitness consequences suggesting that con-nectionstrengthmaybeanevolvabletrait (AplinFirthetal2015FormicaWoodCookampBrodie2017Formicaetal2012)
42emsp|emspGroups with denser connections exert a stronger ldquopull to the meanrdquo
Our simulations show that groupswhere individuals have an in-termediatenumberorstrengthofsocialconnections (iegroupswithintermediatenetworkdensities)allowforthegreatestwithin-groupvariationinsocialenvironmentsexperiencedamongindivid-ualsThispatternariseswithinagenerationduetosocialplasticityratherthanasaresponsetoanyselectivepressureBygeneratinga greater range of phenotypes and social environments groupswithan intermediatedensityof social interactionscouldprovidethe basis for the emergence and evolution of alternative socialphenotypes (Bergmuumlller amp Taborsky 2010 Sinervo amp Calsbeek2010) When social phenotypes are subject to indirect geneticeffects the maintenance of variation in social behavior shouldthus be observed more frequently in groups with intermediateconnectedness
Whilelowtointermediatedensitiesofsocialinteractionsofferthewidestscopeforpromotingindividualvariationinphenotypegroupswith high densities exhibit a very different patternAs the numberand strengths of interactions increases among group members in-direct genetic effects experienced by each individual becomemoresimilarbecauseallgroupmembersstarttobecomeconnectedtooneanotherand theseconnectionsareuniformlystrong Inadditionasnetworksbecomemoreconnectedindividualsattheextremesofthedistributionofgenetic tendencies in thegroups (ie the individualsfurthest from the averagebreedingvalue) tend to experience a so-cialenvironmentexertinganopposingeffectontheirphenotype(ieCov[a+esa +se] in Equation3 becomes more negative) This ldquopullto themeanrdquo is stronger in smaller groups than in larger ones (seeFigureS5) anddecreases thepopulationphenotypicvariancewhenψg ispositive (egwhen individuals increasetheiraggressiveness inresponse to the aggression they receive) and increases it whenψg is negative (egwhen individuals inhibit their aggressiveness in re-sponsetotheaggressiontheyreceive)Whenindividualsexhibit im-portantphenotypicplasticitysuchaneffectappearssimilartosocialconformity where individuals express more similar phenotypes asgroupsthan in isolation (egHerbert-Readetal2013MagnhagenampBunnefeld2009)Conformity isusually thought toemergewhendissimilarindividualsareatafitnessdisadvantageForexamplepred-ators tend topick individuals that standout amonggroupsofpreyselecting forhomogeneousgroups (LandeauampTerborgh1986)Weshowherethatconformist-likepatternsinbehaviorcanemergefromverysimpleformsofsocialplasticity Importantlyweshowthatbe-havioralconformitycanemergeevenwhenindividualsarenotactivelycopyingthemostabundantphenotypeoftheirgroup inabsenceofanyselectivepressureExamplesofhighlyconnectedgroupsinnatureincludechorusesofmalesinsomespeciesoffrogsproducingmating
calls or leks ofmales displaying to attract females and adjust theirsignalingeffortinresponsetothesignalingoftheirrivals(Boatright-HorowitzHorowitzampSimmons2000SimmonsSimmonsampBates2008)Whenmalesareclosetoeachotherandeachmalecanadjustits signaling intensity to that of all the othermaleswe expect thisldquopulltothemeanrdquotodecreasethevariationinmalesignals(althoughsocialplasticitycantakemorecomplexpatternsthenismodeledhereGreenfieldampRand2000)Thiscandecreasetheeffectivenessoffe-malematechoiceandtheintensityofsexualselection
43emsp|emspGroups with denser connections potentiated the effect of keystone individuals
Aninsightfromoursimulationsisthatwheneverindividualsadjusttheirphenotypetotheaveragesocialenvironmentthattheyexperi-enceindividualsattheextremesofthegenotypicorphenotypicdis-tributionhavethegreatestimpactonthephenotypeofothergroupmembers This phenomenon arises because these individuals havethestrongest impacton themeansocialenvironmentexperiencedbytheirconspecificsTheevolutionofniche-constructingtraitsal-lowingsomeindividualstomanipulatetheirgroupinawaythatfa-vorstheirownsuccess(SaltzGeigerAndersonJohnsonampMarren2016) or to have a disproportionate effect on their group (Keiseramp Pruitt 2014 Modlmeier etal 2014 Pruitt amp Pinter-Wollman2015)hasbeenthefocusofmuchinterestrecentlySurprisinglynostudyhasexplored the implicationsof theexactpatternsofsocialplasticity for the identity and impact of such ldquokeystone individu-alsrdquo (Modlmeier etal 2014) It is reasonable to assume thatmostanimalsexhibitingsocialplasticityshouldadjusttheirphenotypeinresponse to theaverage socialconditions that theyexperience (al-thoughinsomecasessomeindividualscanadjusttheirphenotypeto themaximumor to theminimumphenotypicvalueof the indi-vidualswithwhomtheyinteractseeDyerCroftMorrellampKrause2009 for a potential example) Thus our simulations suggest thattheemergenceofkeystoneindividualsmightbeaphenomenonfarmore common than previously envisioned Keystone individualscouldemergeinanygroupofinteractingindividualsexhibitingphe-notypicplasticityanddenseinteractionnetworks(asinthelekkingexampleabove)Hencetheemergenceofkeystoneindividualsmightnotrequireacomplexsocialsystemdivisionoflabor(PruittBolnickSihDiRienzoampPinter-Wollman2016) collectivebehavior (PruittampPinter-Wollman2015)orniche-constructingtraits (egaggres-sivenesspolicingorelseChangampSih2013)butshouldbemostcommon in specieswhere individuals respond to thebehaviors ofthemajorityofgroupmembers
Denserinteractionsamongindividualswithinagrouppotentiatetheimpactofindividualswithextremephenotypicvaluesbyallow-ing these to interact and affect themajority of their groupmem-bersHencetheconsequencesofindividualsocialplasticitytendtobecomemuchgreater ingroupsasnetworkdensity increasesThisldquoamplificationrdquoeffectisalsostrongerwhengenotypesfollowauni-formdistribution (iewhenextremegenotypesaremorefrequentwithin groups) thanwhen they followaGaussiandistribution (ie
1460emsp |emsp emspensp MONTIGLIO eT aL
whenextremegenotypesarerarewithingroups)Networkdensityincreases the evolutionary response of groups on average groupswith denser connections also exhibit increasedvariation in evolu-tionaryresponsetoagivenselectiongradientSuchan increase inthevariationinevolutionaryresponseobservedinourstudyisap-parentbecauseourapproachallowsustorelaxtheassumptionthatindividualswithingroupsinteractequallywithallothergroupmem-bersbyintroducinganewparameter(averageconnectionstrength=s)intoourmodelandinsteadtoexplicitlyexploretheeffectofcon-nectiondensity
44emsp|emspHomophily affects the amount of phenotypic variation within groups
Our simulations also investigate the consequencesof social struc-turewhenindividualscaninteractpreferentiallywithindividualsthathaveasimilar(iehomophily)ordissimilar(ieheterophily)pheno-typeNetworkassortment(thenetworkmeasureofhomophily)doesnot have any impact on groupsrsquomean phenotype but can gener-ateagreatervariationinsocialenvironmentswithingroupsHenceassuming that different immediate social environments can favordifferent (alternative) phenotypes within groups our simulationssuggest that homophily should be associatedwith the emergenceof phenotypic variation among individuals (or social specializationBergmuumlller amp Taborsky 2010 Montiglio Ferrari amp Reacuteale 2013)Homophilyalsohasdirectconsequencesfortheevolutionofalter-nativephenotypesbycreatingsynergyoroppositionbetweendirectand indirect genetic effectsWhen social plasticity (ψg) is positive(egwheninteractingwithanaggressiveindividualincreasesafocalindividualrsquosaggression)andindividualsshowatendencytointeractwithsimilarphenotypesthesocialenvironmentactstoshapetheirphenotypeinthesamedirectionastheirgenotypeAsaresultsocialinteractionsandsocialplasticityincreasethephenotypicvarianceofthetraitrelativetoasituationinwhichconnectionsarerandominterms of their traits It also tends to increase the strength of theevolutionaryresponsetoselectioninresponsetoagivenselectiongradientThisincreaseinevolutionaryresponsearisesfromthesyn-ergybetweendirectandindirecteffect(orbetweensocialplasticityandhomophily)ratherthanfromachangeintotalgeneticvariationwithingroups
45emsp|emspPossible applications and tests of the model and future directions
differentialandmatechoicebyfemalesThestrengthofconnectionsbetweenmales of known phenotype could be increased artificiallyusingplaybacks tosimulatemore frequent interactionsamong indi-viduals(DabelsteenampPedersen1990Otteretal2001)tomonitorhowsuchincreasesinconnectionstrengthaffecttheextentofpheno-typicandgeneticadditivevariationAlternativelyonecanmanipulatethedistributionofterritoriesavailableandthepatternsofinteractionsby controlling the locationof nest boxes foodpatches or refugesSuchapproachescouldbeparticularlysuitableforcavity-nestingbirds(Both1998)
Ourmodel also studied the consequences of homophily for theevolutionary responses of phenotypic traits Assuming individualshave some level of control on their interactions homophily can beobservedwhen individualsexhibitpreferences to interactwithcon-specificsthatare(dis)similartothemSuchpreferencescouldexplainthemaintenanceofaltruisticbehaviorbecauseoftheirpotentialroleinshapingtheselectionpressuresactingonaltruismSomeworkonfruitflieshavereportedthatindividualpreferencesforparticularsocialenvironmentsisassociatedwithgeneticvariationandcanthuspoten-tiallyevolve (egSaltzampFoley2011)Onecould testourmodel insuchstudysystemsbyeitherallowingorpreventingtheexpressionofsocialpreferences(throughmixingofindividualsormanipulatingtheirinteractions) Alternatively homophily can also be observed whenindividualssegregateintheenvironmentasafunctionoftheirphe-notype(HelfensteinDanchinampWagner2004Ward1993WardampPorter1993)Forexamplemoreandlessaggressiveindividualsseg-regateinpatcheswithdifferentdensitiesofconspecifics(Duckworth2006)Thusbymanipulatingtheheterogeneityandthescaleatwhichitisobserved(iethesizeofpatchesofdifferenthabitat)onecouldtestthepredictionsofourmodelFutureworkwillexpandthemodelwe presented here to analyze the consequences of such traits forthemaintenanceofphenotypicvariationandtheevolutionofsocialstructure
One limitationofourmodel is thatweassumebothphenotypicfeedback(Mooreetal1997)andsocialselection(Wolfetal1999)tobeabsentIncludingfeedbackmayaltertheconclusionswehavepre-sentedhereasfeedbackeffectsmaycausesocialplasticitytomovethroughnetworksincounterintuitivewaysItispossiblethatnetworkmetricsbeyondconnectionstrength (suchasclusteringcoefficientsbetweennessetc)may influencewhetherfeedbackcontributessig-nificantly to variation and response to selection Regarding socialselectionwehaveshownherethatconnectionstrengthcontributestoamong-groupvariancewhichshould intensifyresponsetohigherlevelsofselectionsuchassocialselectionWewilltreatbothfeedbackandsocialselectioninfuturecontributions
5emsp |emspCONCLUSION
Wepresentbothananalyticmodelandsimulationsextendingpre-vious work on social phenotypic plasticity to more general socialstructuresOurstudygeneratesafirstsetofverygeneralandtest-able predictions on the role of social structure in modulating the
emspensp emsp | emsp1461MONTIGLIO eT aL
consequencesofsocialplasticityWeshowthatthebasiccharacter-isticsofthestructureofinteractionsamongindividualsingroupsandpopulationscanhaveimpactsontheconsequencesofsocialplasticityforthemeanphenotypeexpressedbytheindividualstheextentofphenotypicvariationavailableforselectionandfortheabilityofthepopulation to respond to selectivepressuresWehope that futurestudieswillbeabletotestourpredictionsempiricallybyapplyingourapproachtothestudyofsocialbehavior(egaggressionandcoop-eration)socialinformationuseoralternativematingtacticsinpopu-lationswithvaryingpatternsofsocialormatinginteractionsFromatheoreticalperspectivefutureresearchwouldwarrantinvestigatingthelinkbetweenindividualpositioninsocialnetworksandtheindi-rect genetic effects it experiences and thuswhether factors otherthan individualsrsquo breeding values can lead to keystone individualsFurtherinourstudyweassumethatallindividualsexpressedplas-ticityidenticallyHoweverindividualshavealsobeenshowntovaryintheirplasticity(DingemanseKazemReacutealeampWright2010NusseyWilsonampBrommer2007WestneatHatchWetzelampEnsminger2011)andsuchvariationmayalterthepredictionsofinteractingphe-notypemodels(KazancıoğluKlugampAlonzo2012)Linkingindividualdifferencesinbothsocialpositionandplasticitycouldyieldnewin-sightsandagreaterunderstandingoftheevolutionarymechanismsthatunderpinphenotypicvariationwithinindividualsbetweenindi-vidualsandamongpopulations
ACKNOWLEDGMENTS
We thank the Reader Hendry and Barrett laboratories in McGillUniversity forconstructivecommentsonadraftof thismanuscriptPOMwas supported by aNSERCpostdoctoral fellowshipDRF re-ceived funding from a grant to theBBSRC (BBL0060811 toBCSheldon)andtheMaxPlanckSociety
CONFLICT OF INTEREST
Nonedeclared
AUTHOR CONTRIBUTIONS
POMandDRFbuiltthesimulationsandJWMdevelopedthemodelPOMdrafted themanuscript andproduced the figuresAll authorscontributedtorevisionsandapprovedthefinalversionofthearticle
AplinLMFarineDRMorand-FerronJCockburnAThorntonAamp SheldonBC (2015) Experimentally induced innovations lead topersistentcultureviaconformityinwildbirdsNature518538ndash541
Aplin LMFirthJAFarineDRVoelklBCratesRACulinaAhellipSheldonBC (2015)Consistent individual differences in the so-cialphenotypesofwildgreattits(Parusmajor)Animal Behaviour108117ndash127httpsdoiorg101016janbehav201507016
BaileyNWampHoskins J L (2014)Detecting cryptic indirect geneticeffectsEvolution681871ndash1882httpsdoiorg101111evo12401
Bailey N W amp Zuk M (2012) Socially flexible female choice differsamongpopulationsofthePacificfieldcricketGeographicalvariationin the interaction coefficient psi (Ψ)Proceedings of the Royal Society of London Series B Biological Sciences 279 3589ndash3596 httpsdoiorg101098rspb20120631
Bergmuumlller R amp Taborsky M (2010) Animal personality due to socialnichespecialisationTrends in Ecology amp Evolution25504ndash511httpsdoiorg101016jtree201006012
Bijma P ampWade M J (2008) The joint effects of kin multilevel se-lection and indirect genetic effects on response to genetic selec-tion Journal of Evolutionary Biology 21 1175ndash1188 httpsdoiorg101111j1420-9101200801550x
Boatright-HorowitzSLHorowitzSSampSimmonsAM(2000)Patternsof vocal interactions n a BullfrogRana catesbeiana chorus preferen-tial responding to farneighborsEthology106701ndash712httpsdoiorg101046j1439-0310200000580x
BothC(1998)Experimentalevidencefordensitydependenceofrepro-ductioningreattitsJournal of Animal Ecology67667ndash674httpsdoiorg101046j1365-2656199800228x
Cappa E P amp Cantet R J C (2008) Direct and competition additiveeffects in treebreedingBayesianestimation froman individual treemixedmodelSilvae Genetica5745ndash56
ChangAampSihA (2013)Multilevel selection andeffects of keystonehyperaggressivemalesonmatingsuccessandbehaviorinstreamwaterstridersBehavioral Ecology241166ndash1176httpsdoiorg101093behecoart044
Clutton-BrockTH(1989)MammalianmatingsystemsProceedings of the Royal Society B236339ndash372httpsdoiorg101098rspb19890027
Crowley P H amp Cox J J (2011) Intraguild mutualism Trends in Ecology amp Evolution 26 627ndash633 httpsdoiorg101016jtree201107011
Duckworth R A (2006) Aggressive behaviour affects selection onmorphology by influencing settlement patterns in a passerine birdProceedings of the Royal Society B 273 1789ndash1795 httpsdoiorg101098rspb20063517
Farine D R (2014) Measuring phenotypic assortment in animal so-cial networks Weighted associations are more robust than binaryedges Animal Behavior 89 141ndash153 httpsdoiorg101016janbehav201401001
FarineDRampWhiteheadH(2015)Constructingconductingandinter-preting animal social network analysis Journal of Animal Ecology841144ndash1163httpsdoiorg1011111365-265612418
Fawcett TW amp Johnstone RA (2010) Learning your own strengthWinner and loser effects should change with age and experienceProceedings of the Royal Society of London Series B Biological Sciences2771427ndash1434httpsdoiorg101098rspb20092088
Fisher D N amp McAdam A G (2017) Social traits social networksand evolutionary biology Journal of Evolutionary Biology httpsdoiorg101111jeb13195Inpress
FormicaVAWood CW LarsenW B Butterfield R EAugatMEHougenHYampBrodieIIIED(2012)Fitnessconsequencesofsocialnetworkpositioninawildpopulationofforkedfungusbeetles(Bolitotherus cornutus) Journal of Evolutionary Biology 25 130ndash137httpsdoiorg101111j1420-9101201102411x
Greenfield M D amp Rand S A (2000) Frogs have rules selective at-tention algorithms regulate chorusing in Physalaemus pustulosus (Leptodactylidae)Ethology106131ndash147
Helfenstein FDanchin E ampWagner RH (2004)Assortativematingand sexual size dimorphism in blacklegged kittiwakes Waterbirds27 350ndash354 httpsdoiorg1016751524-4695(2004)027[0350AMASSD]20CO2
Herbert-Read J E Krause S Morrell L J Schaerf T M Krause JampWardAJW (2013)The roleof individuality in collectivegroupmovementProceedings of the Royal Society B- Biological Sciences28020122564
KeiserCNampPruittJN (2014)Personality composition ismore im-portantthangroupsizeindeterminingcollectiveforagingbehaviourinthewildProceedings of the Royal Society of London Series B Biological Sciences28120141424httpsdoiorg101098rspb20141424
Krause J amp Ruxton GD (2002) Living in groups Oxford UKOxfordUniversityPress
Landeau L ampTerborgh J (1986)Oddity and the ldquoconfusion effectrdquo inpredationAnimal Behavior341372ndash1380httpsdoiorg101016S0003-3472(86)80208-1
Magnhagen C amp Bunnefeld N (2009) Express your personality or goalong with the group What determines the behaviour of shoalingperchProceedings of the Royal Society B- Biological Sciences2763369ndash3375httpsdoiorg101098rspb20090851
McDonaldG C FarineD R Foster K R ampBiernaskie JM (2017)Assortment and the analysis of natural selection on social traitsEvolution712693ndash2702httpsdoiorg101111evo13365
McGlothlin JW amp Brodie III E D (2009) How to measure individ-ual genetic effects The congruence of trait-based and variance-partitioning approaches Evolution 63 1785ndash1795 httpsdoiorg101111j1558-5646200900676x
McGlothlin J W Moore A J Wolf J B amp Brodie III E D(2010) Interacting phenotypes and the evolutionary pro-cess III Social evolution Evolution 64 2558ndash2574 httpsdoiorg101111j1558-5646201001012x
MillerJRBAmentJMampSchmitzOJ (2014)Fearon themovePredatorhuntingmodepredictsvariation inpreymortalityandplas-ticityinpreyspatialresponseJournal of Animal Ecology83214ndash222httpsdoiorg1011111365-265612111
ModlmeierAPKeiserCNWattersJVSihAampPruittJN(2014)The keystone individual concept An ecological and evolutionaryoverview Animal Behavior 89 53ndash62 httpsdoiorg101016janbehav201312020
MontiglioP-OFerrariCampReacutealeD(2013)Socialnichespecializationunder constraints Personality social interactions and environmentalheterogeneityPhilosophical Transactions of the Royal Society of London Series B Biological Sciences36820120343httpsdoiorg101098rstb20120343
Moore A J Brodie III E D ampWolf J B (1997) Interacting pheno-types and the evolutionary process I Direct and indirect geneticeffects of social interactions Evolution 51 1352ndash1362 httpsdoiorg101111j1558-56461997tb01458x
NonacsPampKapheimKM(2007)Socialheterosisandthemaintenanceof genetic diversity Journal of Evolutionary Biology 20 2253ndash2265httpsdoiorg101111j1420-9101200701418x
Nussey D H Wilson A J amp Brommer J E (2007) The evolution-ary ecology of individual phenotypic plasticity in wild popula-tions Journal of Evolutionary Biology 20 831ndash844 httpsdoiorg101111j1420-9101200701300x
OtterKAStewartIRKMcGregorPKTerryAMRDabelsteenTampBurkeT(2001)Extra-pairpaternityamonggreattitsParus major following manipulation of male signals Journal of Avian Biology 32338ndash344httpsdoiorg101111j0908-88572001320408x
Pruitt J N Bolnick D I Sih A DiRienzo N amp Pinter-Wollman N(2016)Behavioralhypervolumesofspidercoloniespredictscommu-nity performance and disbandmentProceedings of the Royal Society B- Biological Sciences 283 20161409 httpsdoiorg101098rspb20161409
PruittJNampPinter-WollmanN(2015)Thelegacyeffectsofkeystonein-dividualsoncollectivebehaviourscaletohowlongtheyremainwithina group Proceedings of the Royal Society B- Biological Sciences 28220151766httpsdoiorg101098rspb20151766
RoyleNJHartley IROwens I P FampParkerGA (1999) Siblingcompetition and the evolution of growth rates in birds Proceedings of the Royal Society B 266 923ndash932 httpsdoiorg101098rspb19990725
SaltzJBampFoleyBR(2011)Naturalgeneticvariationinsocialnicheconstruction Social effects of aggression drive disruptive sexual se-lectioninDrosophila melanogaster American Naturalist177645ndash654httpsdoiorg101086659631
ShusterSM LonsdorfEVWimpGMBaileyJKampWhithamTG (2006) Community heritabilitymeasures the evolutionary conse-quencesofindirectgeneticeffectsoncommunitystructureEvolution60991ndash1003httpsdoiorg101111j0014-38202006tb01177x
SimmonsAMSimmonsJAampBatesMA (2008)Analyzingacous-tic interactions in natural bullfrog (Rana catesbeiana) chorusesJournal of Comparative Psychology 122 274ndash282 httpsdoiorg1010370735-70361223274
Sinervo B R amp Calsbeek R (2010) Behavioral concepts of selectionExperiments and genetic causes of selection on the sexes In D FWestneatampCWFox(Eds)Evolutionary behavioral ecologyLondonUKOxfordUniversityPress
Thompson J N (1982) Interaction and coevolution Chicago USA TheUniversityofChicagoPress
emspensp emsp | emsp1463MONTIGLIO eT aL
VanderWaal K L ObandaV Omondi G P McCowan BWang HFushingHampIsbellLA (2016)Thestrengthofweaktiesandhel-minth parasitism in giraffe social networks Behavioral Ecology 271190ndash1197httpsdoiorg101093behecoarw035
Ward P I (1993) Micro-habitat segregation and the mating systemof Gammarus pulex Animal Behavior 45 191ndash192 httpsdoiorg101006anbe19931019
Ward P I amp PorterAH (1993)The relative role of habitat structureandmale-malecompetition in thematingsystemofGammarus pulex (CrustaceaAmphipoda)AsimulationstudyAnimal Behavior45119ndash133httpsdoiorg101006anbe19931011
West-EberhardMJ(1989)Phenotypicplasticityandtheoriginsofdiver-sityAnnual Review of Ecology and Systematics20249ndash278httpsdoiorg101146annureves20110189001341
Westneat D F Hatch M IWetzel D P amp Ensminger A L (2011)IndividualvariationinparentalcarereactionnormsIntegrationofper-sonalityandplasticityAmerican Naturalist178652ndash667httpsdoiorg101086662173
Wilson A J Gelin U Perron M-C amp Reacuteale D (2009) Indirect ge-neticeffectsandtheevolutionofaggression inavertebratesystemProceedings of the Royal Society of London Series B Biological Sciences276533ndash541httpsdoiorg101098rspb20081193
Additional Supporting Informationmay be found online in the sup-portinginformationtabforthisarticle
How to cite this articleMontiglioP-OMcGlothlinJWFarineDRSocialstructuremodulatestheevolutionaryconsequencesofsocialplasticityAsocialnetworkperspectiveoninteractingphenotypesEcol Evol 201881451ndash1464 httpsdoiorg101002ece33753
APPENDIX
PHENOTYPIC MEAN AND VARIANCE
FollowingMooreetal(1997)wemodelasinglephenotypeofanindi-vidual (z)asanadditivecombinationoftheeffectsof itsowngenes(iedirectgeneticeffectsa)thenonsocialenvironmentitexperiences(e)andaplasticcomponentthatissomefunctionofthephenotypesinitssocialgroupMooreetal(1997)originallymodeledthesocialeffectasafunctionofthephenotypeofoneinteractingindividualMcGlothlinandBrodie (2009)andMcGlothlinetal (2010)consideredsocialef-fectsinapopulationconsistingofgroupsofnindividualswhereinter-actionswereassumedtooccursimultaneouslywithinagroupwithallindividuals within a group having the same strength of interactionHereweconsideramoregeneralsocialstructurewhereindividualsinteractwithallpossiblesocialinteractantsingroupsizenwithvaria-bleconnectionstrengthsirangingfrom0to1giving
wherethesummationistakenacrossalln minus1possiblesocialinterac-tionsforeachindividualsandψrepresentstheinteractioncoefficientwhichdetermines thestrengthanddirectionof the indirectpheno-typic effect of individual social interactantsHere and elsewhere aprimeindicatesaparameterbelongingtoasocialpartnerAnysocialnetworkstructurecanbemodeledbychangingthedistributionofs High-densitysocialnetworkswithstrongconnectionswillhavemanylargevaluesofswhilesparsernetworkswithweakerconnectionswillhavemanyweaksvalueswithmanyequaltozeroConsideringphenotypicfeedback(asdoMooreetal1997)insuch
The value of the two covariance terms represents how stronglystrengthofinteractiondependsonthegenesandenvironmentofin-dividualsocialpartnersThiscovarianceisdeterminedforeachindi-vidualandmayvaryacrossindividualsTheseshouldbepositiveunderhomophilyandnegativeunderheterophilyTakingthemeanandas-suming
=e=0
where double overbars indicate global means and large overbarswithintheparenthesesindicatemeanstakenacrossindividualsbasedonsummarystatisticsoftheirsocialgroupsThiscanbeexpandedasaboveto
The remainingcovariance terms represent theaveragedegree towhichindividualconnectionstrengthsareadjustedbasedonthephe-notypeofpotentialinteractantsInthecaseofhomophilyorheteroph-ilyindividualswillmakethisadjustmentbasedontheirownphenotypewithlargeindividualshavingapositivecovarianceandsmallindividu-alshavinganegativecovariance(orviceversa)ThereforeweexpecttheseaveragecovariancetermstotendtowardzeroMakingthisas-sumptionandrearrangingprovidesEquation2inthetext
EXTENSION TO MULTIPLE GROUPS
EquationA8iswrittenassumingthatthepopulationconsistsofasin-gle social networkwhere individualsmay interact in anywayNowassumethatthepopulationisdividedintomultiplegroupswhereindi-vidualsmay interactwithanystrengthswithinagroupanddonotinteract at all between groups Assuming the covariance terms inEquationA8arezeroandthatenvironmentaldeviationsdonotvaryamonggroupsthemeanofeachgroupwillbe
where overbars now indicate within-groupmeans Assuming equalgroupsizethepopulationmeanisnow
(IfgroupsvaryinsizethenEquationA10canbemodifiedtogiveaweightedmean) Ifconnectionstrengthhasnoheritablebasis thenthe covariance term become zero and EquationA10 collapses toEquation2inthetextWemaycalculateamong-groupvariancemosteasilybymakingafewassumptionsthatarealsomadeinoursimula-tionsFirstasaboveweassumethatgroupsareofequalsizeSecondweassume thatmean interactiondoesnotvaryacrossgroups ands=
=sMakingtheseassumptions
Thisshowsthat indirectgeneticeffectswillmagnifyslightdiffer-ences in genetic values across groups regardless of sign Strongermeanconnectionstrengthswillintensifythiseffect
RESPONSE TO SELECTION
FollowingMoore etal (1997) andMcGlothlin etal (2010) and as-suming that thecovariance terms inEquationA8areeither zeroorpopulation parameters that do not have a heritable component anindividualrsquostotalbreedingvaluecanbewrittenasthegeneticcontri-butiontothepopulationmean
where Ristheregressionofsaprimeonaandisthusanalogoustorelated-ness This assumes thatCov[aseprime] is negligible Positive values ofR indicatehomophilyandnegativevaluesindicateheterophilyMakingthissubstitutiongivesEquation4inthetextEquation4canalsobeexpresseddifferentlybyrearrangingas
where G indicates additive genetic variance andE indicates envi-ronmental variance The third term above represents the among-individual variance due to social interactions This term shouldincreasesomewhatwithhomophilybutshoulddependmostheav-ily on network density The variance in social environment expe-rienced by individuals should be at amaximum at intermediate
becomemorehomogenous(ieeveryoneinteractswitheveryone)Thefourthtermwillbemost influencedbyhomophily (orhetero-phily)becauseassociatingwithsimilar(ordifferent)individualswillcause the covariance to increase (ordecrease)Themultiplicationbyψgwillcausephenotypicvariancewithinagrouptoincreasewithhomophilyunderpositivevaluesofψganddecreasewithhomophilywhenψg isnegativeThistermshouldalsobe influencedbyaver-ageconnectionstrength(
where R is a general measure of the strength of homophily (seeEquationA19 in Appendix) and β is the selection gradient (seeAppendix)Thisequationshowsthattheamountofgeneticvarianceavailableforresponsetoselectionatthepopulationlevelshouldde-pendon(1)thedegreeofsocialplasticity(2)theaverageconnectionstrength(whichshouldincreasewithmeanconnectionstrength)and(3)theamountofassociationbetweenindividualsthatisbasedonge-neticvaluesimilarity(homophilyorheterophily)Thismodelisnearlyidenticaltopreviousmodelswithsimplergroupstructure(McGlothlinetal 2010) except for the inclusion of the connection strength (
=s)
and the replacementof relatednesswithhomophilyheterophily (R)Theseanalyticalresultsprovidepredictionsthatwetestbelowusingindividual-basedsimulations
32emsp|emspNetwork density
Inoursimulationsincreasingnetworkdensitywhichisanalogoustoincreasing mean connection strength in the analytical model doesnot lead to an increase inphenotypicmeanonaverage (ie acrossallgroupsFigure2red line)Howeverathighernetworkdensitiesthere is much greater variation among groups in their phenotypicmean (Var[
=z ] Figure2 gray dots) This occurs because although
themeangeneticvalueacrossall simulations iszero thisvaluecandiffer across groups due to sampling As predicted by Equation2increasing network density (or
=s) increases the importance of the
group genotypic composition in determining the effects of indirectgeneticeffectsmagnifyingdifferencesamonggroupsingeneticvalue(=a) across replicate simulation runs This amplification effect is also
Thephenotypicvariance in indirecteffectswithineachgroup ismaximalatintermediatenetworkdensities(Figure3a)Whenindivid-ualshave fewconnections (and connection strength isweaker) thescopeforindirecteffectstodifferamongmembersofagivengroupisnarrowtherebydecreasingthecontributionofsocial interactionstophenotypicvariance(Figure3a)Likewiseingroupswhereindividualsarehighlyconnected (highnetworkdensity) thesocialenvironmentexperiencedbyeachindividualisclosertotheaveragebreedingandenvironmentalvalueofthepopulation(whichis0inoursimulations)In otherwordsVar[aprime] and consequentlyVar[saprime]within groups issmallathighdensities(seeEquation3)Howeveratintermediateden-sities indirecteffectshadthepotentialtomakealargecontributiontophenotypicvariancealthoughthiseffectwashighlyvariableacrosssimulations
Intheabsenceofhomophilyheterophilyhighnetworkdensityleadstoanegativecorrelationbetweendirectandindirectgeneticeffects(Figure3b)Atlownetworkdensitiesthiscorrelationisex-pectedtobezerobecauseindividualsassociateatrandom(althoughthiswouldnotbe thecase if therewasanyspatial assortmentbyphenotype) However at high densities this correlation becomesnegativeeventhoughindividualassociationisalsorandomThisef-fectarisesbecauseindividualsarenotcountedaspartoftheirownsocial environment andasnetworkdensities increase the impor-tanceofthisdifferencebecomesmagnifiedAtthehighestnetwork
(3)Var[z]=G+E+ψ2gVar
[sa + se
]+2ψgCov
[a +e sa + se
]
(4)Δ=zasymp
(1+ψg
=s)G(1+Rψg
)β
F IGURE 2emspThechangeinaveragephenotypeofindividualsinanetworkasafunctionofthenetworkdensity(redline)Thechangeinaveragephenotypeisexpressedrelativetothephenotypeexpectedinabsenceofinteractionsamongindividuals(ie0)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4Asdensityincreasedweobservedagreatervariationinmeanphenotypeamonggroups(graydots)
1456emsp |emsp emspensp MONTIGLIO eT aL
densitiessocialenvironmentsare indistinguishableexceptforthiseffect of excluding oneself thus leading to a directndashindirect cor-relationofminus1Smallergroupswillexhibitthispatterntoastrongerextent than larger groups (see FigureS5 also McDonald FarineFosterampBiernaskie2017)Thecombinedimpactoftheeffectsofnetworkdensityonthevariancein indirectgeneticeffectsandonthecovariancebetweendirectandindirectgeneticeffectsisarel-ativedecrease inphenotypicvariationwithingroups(comparedtothephenotypicvariationinabsenceofanyinteractions)asnetworkdensityincreases(Figure3c)Oppositepatternsareobservedwhenψg isnegative(FigureS6)Finallywenotethatalthoughthemeanphenotypic variationwithin each group decreaseswith increasingnetworkdensitywefindthatthevariationamonggroups(eachdotin each panel of Figure3c represents one group) ismaximized atintermediatenetworkdensities
Although the phenotypic variance typically decreases with in-creasednetworkdensitythevarianceintotalbreedingvalues(rela-tivetothegeneticvarianceinabsenceofanysocialinteraction)hasthe greatest increase at highest network densities (Figure3d redline)Thisisbecausetheexpectedvarianceintotalbreedingvaluesisequalto
(1+ψg
=s)2
G(seeEquationA12)Thatisthevarianceintotalbreedingvaluesdoesnotdependonthevarianceinindirectgeneticeffects noron the covariancebetweendirect and indirect geneticeffectswhich leadtothedecrease invarianceshowninFigure3cRatherthevarianceintotalbreedingvaluesisafunctionofdirectge-neticeffectsandeffectsofanindividualrsquosgenesonothersthelatter
ofwhichbecomesinflatedathigherdensitiesTheresponsetoselec-tiondependsonthecovariancebetweentotalbreedingvaluesandphenotypicvalueswhichisexpectedtoincreaselinearlywithdensity(EquationA15)Whenwesubjectgroupstoaselectiongradientof02networkswithincreasingdensitiesexhibitedanincreasedevolu-tionaryresponsetoselection(Figure4redline)Increasingnetworkdensityalso increases thevariance in responsetoselectionamonggroups (Figure4 gray dots) This likely happened because individ-ualsadjusttheirphenotypetotheaveragesocialenvironmentthattheyexperienceThusathighernetworkdensitiesindividualswithextreme phenotypicvalues have a disproportionate impact on theaveragesocialenvironmentexperiencedbyindividualsSmalldiffer-encesinthephenotypicvaluesofextremeindividualsfromgrouptogroupcreatedifferencesinthecovariancebetweenthephenotypicvarianceandthetotalbreedingvaluesamonggroupsandincreasingthevariance in response to selection amonggroups In agreementwiththisextremeindividualsalsogenerategreaterphenotypicvari-anceamonggroupsathighernetworkdensities(Figure2)andwhenindividualphenotypesfollowauniformdistribution(moreindividualswithextremephenotypes)thananormaldistribution(fewerindivid-ualswithextremephenotypesSeeFigureS3)
F IGURE 3emspEffectsofnetworkdensityon(a)thevarianceinindirecteffectsexperiencedbyindividuals(b)thecorrelationbetweendirectandindirectgeneticeffectsexperiencedbyindividuals(c)thechangeinphenotypicvariancewithingroupsrelativetothegeneticvariance(iethephenotypicvarianceinabsenceofinteractions)and(d)thechangeintotalgeneticvariationrelativetothegeneticvariance(ievarianceofindividualdirectgeneticeffectsandindirectgeneticeffectsimposedtoothers)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψg of4
emspensp emsp | emsp1457MONTIGLIO eT aL
hasnoeffectonthemeanphenotypeofeachgroup(Figure5)whichis consistent with our analytical model (Equation2) However in-creasednetworkassortmentisassociatedwithanincreaseinthevari-anceinindirectgeneticeffectsexperiencedbyindividualsinagivengroup(seethethirdterminEquation3Figure6a)Becauseindividu-alsinteractmorestronglywithconspecificsthathavesimilarbreedingvalues(highwithhighlowwithlow)thedirectandindirectgeneticcontributions to phenotypes act in concert and covary positively(fourthterm inEquation3Figure6b)Thesetwoeffectscontributetowardincreasingphenotypicvarianceobservedwithinagivengroup(Figure6c)Theseeffectsarereversedwhenψgisnegativedirectandindirect contributions to individual phenotypes act to oppose eachothertherebyreducingtheamountofphenotypicvarianceobservedin the population (see FigureS7) Increasing network assortmentalsoleadstoasmalldecreaseinthevarianceintotalbreedingvalues(Figure6dredline)Thisisattributabletotheslightdecreaseinden-sityassociatedwithhigherlevelsofnetworkassortment(ieindividu-alshavetheabilitytoreducetheconnectionstrengthwithparticulargroupmembers)aphenomenonnotcapturedbyouranalyticalmodel
Applying selection to groups with varying network assortmentshowsthatasynergybetweendirectandindirectgeneticeffectsleadstoanincreaseinevolutionarychangewithincreasingnetworkassort-ment(Figure7redline)Thisresultisinaccordwiththepredictionsofouranalyticalmodelwhichpredictsanincreasedresponsetoselec-tionwithincreasingR(Equation4)AlthoughEquation4suggestsden-sityandhomophilyshouldhavesymmetricaleffectstheincreaseseeninFigure7isnotasdramaticasthatinFigure4perhapsbecauseoftheconcomitantdecreaseindensitycausedbyallowinghomophilyinoursimulationsUnlikenetworkdensitynetworkassortmentdoesnotaffectthevariationofevolutionaryresponsesamonggroups(Figure7graydots)
4emsp |emspDISCUSSION
Inthisstudyweexploretheconsequencesofsocialplasticityandthestructureofinteractionsinshapingtheamountofphenotypicvariationwithingroupsof interactingindividualsandtheevolutionaryresponseofthesegroupstoselectionWeconsiderreplicategroupswithvary-ingstructuresofinteractionsSuchreplicatescouldbeseenasmultiplegroups of individualswithin a given population (eg tribes packs orcolonies)orasmultipleisolatedpopulationswithinanecologicalcom-munityThroughananalyticalmodelandagent-basedsimulationsweshowthatthestructureofsocialnetworksmodulatedtheimpactofin-directgeneticeffectsontheamountofphenotypicvarianceavailablefor selectionOur resultsemphasize that thenumberandstrengthofconnectionsamongindividuals(networkdensity)aswellaspreferentialassociations among individualswith a similar phenotype (network as-sortment)haveimportanteffectsonthecontributionofindirectgeneticeffectsNetworkdensityandassortmentalsomodulatetheabilityfortraitstoexhibitevolutionarychangeinresponsetoselectionIncreasingthenumberofinteractionsamonggroupmembers(networkdensity)in-creasestheaverageevolutionaryresponseofgroupstoselectionandin-creasesthevariationinresponsetoselectionamonggroupsBycontrastincreasednetworkassortmentleadstoanincreaseintheaverageevolu-tionaryresponseofgroupstoselectionbutdoesnotaffectthevariationinevolutionary responseamonggroupsOur resultshavewidespreadimplicationsforstudiesofsocialevolutionmultilevelselectionandtheemergenceofkeystoneindividuals(ModlmeierKeiserWattersSihampPruitt2014)andniche-constructingtraits(egSihampWatters2005)
41emsp|emspComparison with earlier interacting phenotype models
Our analytical results show that given some simplifying assump-tions (most importantly ignoring the potential for phenotypic
F IGURE 4emspEvolutionaryresponseofphenotypetoaselectiongradientvarieswithnetworkdensityTheaveragechangeinphenotypemeanresultingfromselectionincreasedwithnetworkdensity(redline)Groupswithdensernetworksofinteractionsexhibitedmorevariationinthechangeinphenotypicmean(graydots)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4
F IGURE 5emspTheaveragephenotypeofindividualsasafunctionofnetworkhomophily(redline)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4Networkscouldnotreachhomophilyvaluesof1becauseweusedacontinuoustraitvalueratherthandiscretevalues(seeFarine2014)
1458emsp |emsp emspensp MONTIGLIO eT aL
feedback) considering more general social structures does notgreatlyalter theconclusionsofearliermodelsof interactingphe-notypeevolution(egMcGlothlinetal2010Mooreetal1997)First indirect genetic effects still alter the response to selectionby increasing the amount of genetic variance exposed to selec-tionNote thatbecausewedonotmodel feedback thiseffect is
directional with positiveψg (ie becomingmore similar to onersquosneighbors)increasingtheresponsetoselectionandnegativevalues(iebecomingmoredifferentfromonersquosneighbors)decreasingitSecondhomophilyheterophilyplaysa rolesimilar to relatednessinpreviousmodelsinalteringtheresponsetoselection(McGlothlinetal2010)IndeedMcGlothlinetal(2010)noted(ashavemanyothers)thatrelatednessperseisjustaspecialcaseofphenotypicassortment
Themostnotabledifferencebetweenourmodelandearliermod-elsisthatindividualsareallowedtodifferintheirinfluenceonsocialplasticityduetovariation inconnectionstrength (s)Perhapsunsur-prisingly responsetoselection ismorestrongly influencedbysocialinteractions indensernetworkswhere interactionsarestrongerandmorecommonaneffect that isapparent inbothouranalyticalandsimulation results Inour simulation resultswealso find thatvaria-tioninresponsetoselectionamongincreaseswithgreaterconnectionstrengthThis could occur because in some groups themostwell-connectedindividualshappentohaverelativelyhighorlowbreedingvaluesThesewell-connected individualswould thenhaveadispro-portionateeffectonthephenotypeofothers (relativeto individualsclosertothepopulationrsquosaveragebreedingvalue)byexertingastrongeffectonthemeansocialenvironmentexperiencedbyindividualsIndoingsowell-connectedextremeindividualscangeneratevariabilityinthecovariancebetweenbreedingvaluesandphenotypeandthusintheresponsetoselectionFuturemodelsshouldallowconnectionstrength to display a heritable component which would allow thesocialnetworkstructureitselftoevolveinresponsetosucheffects
F IGURE 6emspEffectofnetworkhomophilyon(a)thevariationinindirecteffects(b)thecorrelationbetweendirectandindirectgeneticeffects(c)therelativechangeinphenotypicvariancewithingroupsand(d)therelativechangeintotalgeneticvariationEachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4HomophilysimultaneouslyincreasesvariationamongindividualsinindirectgeneticeffectswithingroupsandgeneratesastrongpositivecovariancebetweendirectandindirectgeneticeffectstherebysubstantiallyincreasingthephenotypicvarianceobservedwithingroupsHoweverthisincreaseinphenotypicvarianceisnotassociatedwithanychangeatthegeneticlevel
F IGURE 7emspEvolutionaryresponseofphenotypetoaselectiongradientincreaseswithnetworkhomophily(redlineandgraydots)Eachdotrepresentsthechangeinmeangenotypeacrossgenerationsinasinglesimulatednetworkorgroupof50individuals(Ngroup=50)TheredlinerepresentstheaverageevolutionaryresponseasafunctionofnetworkdensityIndirectgeneticeffectsweregeneratedusingaψgof4
emspensp emsp | emsp1459MONTIGLIO eT aL
Studiesinthewildhaveshownthatpositioninasocialnetworkmaybe repeatable and have fitness consequences suggesting that con-nectionstrengthmaybeanevolvabletrait (AplinFirthetal2015FormicaWoodCookampBrodie2017Formicaetal2012)
42emsp|emspGroups with denser connections exert a stronger ldquopull to the meanrdquo
Our simulations show that groupswhere individuals have an in-termediatenumberorstrengthofsocialconnections (iegroupswithintermediatenetworkdensities)allowforthegreatestwithin-groupvariationinsocialenvironmentsexperiencedamongindivid-ualsThispatternariseswithinagenerationduetosocialplasticityratherthanasaresponsetoanyselectivepressureBygeneratinga greater range of phenotypes and social environments groupswithan intermediatedensityof social interactionscouldprovidethe basis for the emergence and evolution of alternative socialphenotypes (Bergmuumlller amp Taborsky 2010 Sinervo amp Calsbeek2010) When social phenotypes are subject to indirect geneticeffects the maintenance of variation in social behavior shouldthus be observed more frequently in groups with intermediateconnectedness
Whilelowtointermediatedensitiesofsocialinteractionsofferthewidestscopeforpromotingindividualvariationinphenotypegroupswith high densities exhibit a very different patternAs the numberand strengths of interactions increases among group members in-direct genetic effects experienced by each individual becomemoresimilarbecauseallgroupmembersstarttobecomeconnectedtooneanotherand theseconnectionsareuniformlystrong Inadditionasnetworksbecomemoreconnectedindividualsattheextremesofthedistributionofgenetic tendencies in thegroups (ie the individualsfurthest from the averagebreedingvalue) tend to experience a so-cialenvironmentexertinganopposingeffectontheirphenotype(ieCov[a+esa +se] in Equation3 becomes more negative) This ldquopullto themeanrdquo is stronger in smaller groups than in larger ones (seeFigureS5) anddecreases thepopulationphenotypicvariancewhenψg ispositive (egwhen individuals increasetheiraggressiveness inresponse to the aggression they receive) and increases it whenψg is negative (egwhen individuals inhibit their aggressiveness in re-sponsetotheaggressiontheyreceive)Whenindividualsexhibit im-portantphenotypicplasticitysuchaneffectappearssimilartosocialconformity where individuals express more similar phenotypes asgroupsthan in isolation (egHerbert-Readetal2013MagnhagenampBunnefeld2009)Conformity isusually thought toemergewhendissimilarindividualsareatafitnessdisadvantageForexamplepred-ators tend topick individuals that standout amonggroupsofpreyselecting forhomogeneousgroups (LandeauampTerborgh1986)Weshowherethatconformist-likepatternsinbehaviorcanemergefromverysimpleformsofsocialplasticity Importantlyweshowthatbe-havioralconformitycanemergeevenwhenindividualsarenotactivelycopyingthemostabundantphenotypeoftheirgroup inabsenceofanyselectivepressureExamplesofhighlyconnectedgroupsinnatureincludechorusesofmalesinsomespeciesoffrogsproducingmating
calls or leks ofmales displaying to attract females and adjust theirsignalingeffortinresponsetothesignalingoftheirrivals(Boatright-HorowitzHorowitzampSimmons2000SimmonsSimmonsampBates2008)Whenmalesareclosetoeachotherandeachmalecanadjustits signaling intensity to that of all the othermaleswe expect thisldquopulltothemeanrdquotodecreasethevariationinmalesignals(althoughsocialplasticitycantakemorecomplexpatternsthenismodeledhereGreenfieldampRand2000)Thiscandecreasetheeffectivenessoffe-malematechoiceandtheintensityofsexualselection
43emsp|emspGroups with denser connections potentiated the effect of keystone individuals
Aninsightfromoursimulationsisthatwheneverindividualsadjusttheirphenotypetotheaveragesocialenvironmentthattheyexperi-enceindividualsattheextremesofthegenotypicorphenotypicdis-tributionhavethegreatestimpactonthephenotypeofothergroupmembers This phenomenon arises because these individuals havethestrongest impacton themeansocialenvironmentexperiencedbytheirconspecificsTheevolutionofniche-constructingtraitsal-lowingsomeindividualstomanipulatetheirgroupinawaythatfa-vorstheirownsuccess(SaltzGeigerAndersonJohnsonampMarren2016) or to have a disproportionate effect on their group (Keiseramp Pruitt 2014 Modlmeier etal 2014 Pruitt amp Pinter-Wollman2015)hasbeenthefocusofmuchinterestrecentlySurprisinglynostudyhasexplored the implicationsof theexactpatternsofsocialplasticity for the identity and impact of such ldquokeystone individu-alsrdquo (Modlmeier etal 2014) It is reasonable to assume thatmostanimalsexhibitingsocialplasticityshouldadjusttheirphenotypeinresponse to theaverage socialconditions that theyexperience (al-thoughinsomecasessomeindividualscanadjusttheirphenotypeto themaximumor to theminimumphenotypicvalueof the indi-vidualswithwhomtheyinteractseeDyerCroftMorrellampKrause2009 for a potential example) Thus our simulations suggest thattheemergenceofkeystoneindividualsmightbeaphenomenonfarmore common than previously envisioned Keystone individualscouldemergeinanygroupofinteractingindividualsexhibitingphe-notypicplasticityanddenseinteractionnetworks(asinthelekkingexampleabove)Hencetheemergenceofkeystoneindividualsmightnotrequireacomplexsocialsystemdivisionoflabor(PruittBolnickSihDiRienzoampPinter-Wollman2016) collectivebehavior (PruittampPinter-Wollman2015)orniche-constructingtraits (egaggres-sivenesspolicingorelseChangampSih2013)butshouldbemostcommon in specieswhere individuals respond to thebehaviors ofthemajorityofgroupmembers
Denserinteractionsamongindividualswithinagrouppotentiatetheimpactofindividualswithextremephenotypicvaluesbyallow-ing these to interact and affect themajority of their groupmem-bersHencetheconsequencesofindividualsocialplasticitytendtobecomemuchgreater ingroupsasnetworkdensity increasesThisldquoamplificationrdquoeffectisalsostrongerwhengenotypesfollowauni-formdistribution (iewhenextremegenotypesaremorefrequentwithin groups) thanwhen they followaGaussiandistribution (ie
1460emsp |emsp emspensp MONTIGLIO eT aL
whenextremegenotypesarerarewithingroups)Networkdensityincreases the evolutionary response of groups on average groupswith denser connections also exhibit increasedvariation in evolu-tionaryresponsetoagivenselectiongradientSuchan increase inthevariationinevolutionaryresponseobservedinourstudyisap-parentbecauseourapproachallowsustorelaxtheassumptionthatindividualswithingroupsinteractequallywithallothergroupmem-bersbyintroducinganewparameter(averageconnectionstrength=s)intoourmodelandinsteadtoexplicitlyexploretheeffectofcon-nectiondensity
44emsp|emspHomophily affects the amount of phenotypic variation within groups
Our simulations also investigate the consequencesof social struc-turewhenindividualscaninteractpreferentiallywithindividualsthathaveasimilar(iehomophily)ordissimilar(ieheterophily)pheno-typeNetworkassortment(thenetworkmeasureofhomophily)doesnot have any impact on groupsrsquomean phenotype but can gener-ateagreatervariationinsocialenvironmentswithingroupsHenceassuming that different immediate social environments can favordifferent (alternative) phenotypes within groups our simulationssuggest that homophily should be associatedwith the emergenceof phenotypic variation among individuals (or social specializationBergmuumlller amp Taborsky 2010 Montiglio Ferrari amp Reacuteale 2013)Homophilyalsohasdirectconsequencesfortheevolutionofalter-nativephenotypesbycreatingsynergyoroppositionbetweendirectand indirect genetic effectsWhen social plasticity (ψg) is positive(egwheninteractingwithanaggressiveindividualincreasesafocalindividualrsquosaggression)andindividualsshowatendencytointeractwithsimilarphenotypesthesocialenvironmentactstoshapetheirphenotypeinthesamedirectionastheirgenotypeAsaresultsocialinteractionsandsocialplasticityincreasethephenotypicvarianceofthetraitrelativetoasituationinwhichconnectionsarerandominterms of their traits It also tends to increase the strength of theevolutionaryresponsetoselectioninresponsetoagivenselectiongradientThisincreaseinevolutionaryresponsearisesfromthesyn-ergybetweendirectandindirecteffect(orbetweensocialplasticityandhomophily)ratherthanfromachangeintotalgeneticvariationwithingroups
45emsp|emspPossible applications and tests of the model and future directions
differentialandmatechoicebyfemalesThestrengthofconnectionsbetweenmales of known phenotype could be increased artificiallyusingplaybacks tosimulatemore frequent interactionsamong indi-viduals(DabelsteenampPedersen1990Otteretal2001)tomonitorhowsuchincreasesinconnectionstrengthaffecttheextentofpheno-typicandgeneticadditivevariationAlternativelyonecanmanipulatethedistributionofterritoriesavailableandthepatternsofinteractionsby controlling the locationof nest boxes foodpatches or refugesSuchapproachescouldbeparticularlysuitableforcavity-nestingbirds(Both1998)
Ourmodel also studied the consequences of homophily for theevolutionary responses of phenotypic traits Assuming individualshave some level of control on their interactions homophily can beobservedwhen individualsexhibitpreferences to interactwithcon-specificsthatare(dis)similartothemSuchpreferencescouldexplainthemaintenanceofaltruisticbehaviorbecauseoftheirpotentialroleinshapingtheselectionpressuresactingonaltruismSomeworkonfruitflieshavereportedthatindividualpreferencesforparticularsocialenvironmentsisassociatedwithgeneticvariationandcanthuspoten-tiallyevolve (egSaltzampFoley2011)Onecould testourmodel insuchstudysystemsbyeitherallowingorpreventingtheexpressionofsocialpreferences(throughmixingofindividualsormanipulatingtheirinteractions) Alternatively homophily can also be observed whenindividualssegregateintheenvironmentasafunctionoftheirphe-notype(HelfensteinDanchinampWagner2004Ward1993WardampPorter1993)Forexamplemoreandlessaggressiveindividualsseg-regateinpatcheswithdifferentdensitiesofconspecifics(Duckworth2006)Thusbymanipulatingtheheterogeneityandthescaleatwhichitisobserved(iethesizeofpatchesofdifferenthabitat)onecouldtestthepredictionsofourmodelFutureworkwillexpandthemodelwe presented here to analyze the consequences of such traits forthemaintenanceofphenotypicvariationandtheevolutionofsocialstructure
One limitationofourmodel is thatweassumebothphenotypicfeedback(Mooreetal1997)andsocialselection(Wolfetal1999)tobeabsentIncludingfeedbackmayaltertheconclusionswehavepre-sentedhereasfeedbackeffectsmaycausesocialplasticitytomovethroughnetworksincounterintuitivewaysItispossiblethatnetworkmetricsbeyondconnectionstrength (suchasclusteringcoefficientsbetweennessetc)may influencewhetherfeedbackcontributessig-nificantly to variation and response to selection Regarding socialselectionwehaveshownherethatconnectionstrengthcontributestoamong-groupvariancewhichshould intensifyresponsetohigherlevelsofselectionsuchassocialselectionWewilltreatbothfeedbackandsocialselectioninfuturecontributions
5emsp |emspCONCLUSION
Wepresentbothananalyticmodelandsimulationsextendingpre-vious work on social phenotypic plasticity to more general socialstructuresOurstudygeneratesafirstsetofverygeneralandtest-able predictions on the role of social structure in modulating the
emspensp emsp | emsp1461MONTIGLIO eT aL
consequencesofsocialplasticityWeshowthatthebasiccharacter-isticsofthestructureofinteractionsamongindividualsingroupsandpopulationscanhaveimpactsontheconsequencesofsocialplasticityforthemeanphenotypeexpressedbytheindividualstheextentofphenotypicvariationavailableforselectionandfortheabilityofthepopulation to respond to selectivepressuresWehope that futurestudieswillbeabletotestourpredictionsempiricallybyapplyingourapproachtothestudyofsocialbehavior(egaggressionandcoop-eration)socialinformationuseoralternativematingtacticsinpopu-lationswithvaryingpatternsofsocialormatinginteractionsFromatheoreticalperspectivefutureresearchwouldwarrantinvestigatingthelinkbetweenindividualpositioninsocialnetworksandtheindi-rect genetic effects it experiences and thuswhether factors otherthan individualsrsquo breeding values can lead to keystone individualsFurtherinourstudyweassumethatallindividualsexpressedplas-ticityidenticallyHoweverindividualshavealsobeenshowntovaryintheirplasticity(DingemanseKazemReacutealeampWright2010NusseyWilsonampBrommer2007WestneatHatchWetzelampEnsminger2011)andsuchvariationmayalterthepredictionsofinteractingphe-notypemodels(KazancıoğluKlugampAlonzo2012)Linkingindividualdifferencesinbothsocialpositionandplasticitycouldyieldnewin-sightsandagreaterunderstandingoftheevolutionarymechanismsthatunderpinphenotypicvariationwithinindividualsbetweenindi-vidualsandamongpopulations
ACKNOWLEDGMENTS
We thank the Reader Hendry and Barrett laboratories in McGillUniversity forconstructivecommentsonadraftof thismanuscriptPOMwas supported by aNSERCpostdoctoral fellowshipDRF re-ceived funding from a grant to theBBSRC (BBL0060811 toBCSheldon)andtheMaxPlanckSociety
CONFLICT OF INTEREST
Nonedeclared
AUTHOR CONTRIBUTIONS
POMandDRFbuiltthesimulationsandJWMdevelopedthemodelPOMdrafted themanuscript andproduced the figuresAll authorscontributedtorevisionsandapprovedthefinalversionofthearticle
AplinLMFarineDRMorand-FerronJCockburnAThorntonAamp SheldonBC (2015) Experimentally induced innovations lead topersistentcultureviaconformityinwildbirdsNature518538ndash541
Aplin LMFirthJAFarineDRVoelklBCratesRACulinaAhellipSheldonBC (2015)Consistent individual differences in the so-cialphenotypesofwildgreattits(Parusmajor)Animal Behaviour108117ndash127httpsdoiorg101016janbehav201507016
BaileyNWampHoskins J L (2014)Detecting cryptic indirect geneticeffectsEvolution681871ndash1882httpsdoiorg101111evo12401
Bailey N W amp Zuk M (2012) Socially flexible female choice differsamongpopulationsofthePacificfieldcricketGeographicalvariationin the interaction coefficient psi (Ψ)Proceedings of the Royal Society of London Series B Biological Sciences 279 3589ndash3596 httpsdoiorg101098rspb20120631
Bergmuumlller R amp Taborsky M (2010) Animal personality due to socialnichespecialisationTrends in Ecology amp Evolution25504ndash511httpsdoiorg101016jtree201006012
Bijma P ampWade M J (2008) The joint effects of kin multilevel se-lection and indirect genetic effects on response to genetic selec-tion Journal of Evolutionary Biology 21 1175ndash1188 httpsdoiorg101111j1420-9101200801550x
Boatright-HorowitzSLHorowitzSSampSimmonsAM(2000)Patternsof vocal interactions n a BullfrogRana catesbeiana chorus preferen-tial responding to farneighborsEthology106701ndash712httpsdoiorg101046j1439-0310200000580x
BothC(1998)Experimentalevidencefordensitydependenceofrepro-ductioningreattitsJournal of Animal Ecology67667ndash674httpsdoiorg101046j1365-2656199800228x
Cappa E P amp Cantet R J C (2008) Direct and competition additiveeffects in treebreedingBayesianestimation froman individual treemixedmodelSilvae Genetica5745ndash56
ChangAampSihA (2013)Multilevel selection andeffects of keystonehyperaggressivemalesonmatingsuccessandbehaviorinstreamwaterstridersBehavioral Ecology241166ndash1176httpsdoiorg101093behecoart044
Clutton-BrockTH(1989)MammalianmatingsystemsProceedings of the Royal Society B236339ndash372httpsdoiorg101098rspb19890027
Crowley P H amp Cox J J (2011) Intraguild mutualism Trends in Ecology amp Evolution 26 627ndash633 httpsdoiorg101016jtree201107011
Duckworth R A (2006) Aggressive behaviour affects selection onmorphology by influencing settlement patterns in a passerine birdProceedings of the Royal Society B 273 1789ndash1795 httpsdoiorg101098rspb20063517
Farine D R (2014) Measuring phenotypic assortment in animal so-cial networks Weighted associations are more robust than binaryedges Animal Behavior 89 141ndash153 httpsdoiorg101016janbehav201401001
FarineDRampWhiteheadH(2015)Constructingconductingandinter-preting animal social network analysis Journal of Animal Ecology841144ndash1163httpsdoiorg1011111365-265612418
Fawcett TW amp Johnstone RA (2010) Learning your own strengthWinner and loser effects should change with age and experienceProceedings of the Royal Society of London Series B Biological Sciences2771427ndash1434httpsdoiorg101098rspb20092088
Fisher D N amp McAdam A G (2017) Social traits social networksand evolutionary biology Journal of Evolutionary Biology httpsdoiorg101111jeb13195Inpress
FormicaVAWood CW LarsenW B Butterfield R EAugatMEHougenHYampBrodieIIIED(2012)Fitnessconsequencesofsocialnetworkpositioninawildpopulationofforkedfungusbeetles(Bolitotherus cornutus) Journal of Evolutionary Biology 25 130ndash137httpsdoiorg101111j1420-9101201102411x
Greenfield M D amp Rand S A (2000) Frogs have rules selective at-tention algorithms regulate chorusing in Physalaemus pustulosus (Leptodactylidae)Ethology106131ndash147
Helfenstein FDanchin E ampWagner RH (2004)Assortativematingand sexual size dimorphism in blacklegged kittiwakes Waterbirds27 350ndash354 httpsdoiorg1016751524-4695(2004)027[0350AMASSD]20CO2
Herbert-Read J E Krause S Morrell L J Schaerf T M Krause JampWardAJW (2013)The roleof individuality in collectivegroupmovementProceedings of the Royal Society B- Biological Sciences28020122564
KeiserCNampPruittJN (2014)Personality composition ismore im-portantthangroupsizeindeterminingcollectiveforagingbehaviourinthewildProceedings of the Royal Society of London Series B Biological Sciences28120141424httpsdoiorg101098rspb20141424
Krause J amp Ruxton GD (2002) Living in groups Oxford UKOxfordUniversityPress
Landeau L ampTerborgh J (1986)Oddity and the ldquoconfusion effectrdquo inpredationAnimal Behavior341372ndash1380httpsdoiorg101016S0003-3472(86)80208-1
Magnhagen C amp Bunnefeld N (2009) Express your personality or goalong with the group What determines the behaviour of shoalingperchProceedings of the Royal Society B- Biological Sciences2763369ndash3375httpsdoiorg101098rspb20090851
McDonaldG C FarineD R Foster K R ampBiernaskie JM (2017)Assortment and the analysis of natural selection on social traitsEvolution712693ndash2702httpsdoiorg101111evo13365
McGlothlin JW amp Brodie III E D (2009) How to measure individ-ual genetic effects The congruence of trait-based and variance-partitioning approaches Evolution 63 1785ndash1795 httpsdoiorg101111j1558-5646200900676x
McGlothlin J W Moore A J Wolf J B amp Brodie III E D(2010) Interacting phenotypes and the evolutionary pro-cess III Social evolution Evolution 64 2558ndash2574 httpsdoiorg101111j1558-5646201001012x
MillerJRBAmentJMampSchmitzOJ (2014)Fearon themovePredatorhuntingmodepredictsvariation inpreymortalityandplas-ticityinpreyspatialresponseJournal of Animal Ecology83214ndash222httpsdoiorg1011111365-265612111
ModlmeierAPKeiserCNWattersJVSihAampPruittJN(2014)The keystone individual concept An ecological and evolutionaryoverview Animal Behavior 89 53ndash62 httpsdoiorg101016janbehav201312020
MontiglioP-OFerrariCampReacutealeD(2013)Socialnichespecializationunder constraints Personality social interactions and environmentalheterogeneityPhilosophical Transactions of the Royal Society of London Series B Biological Sciences36820120343httpsdoiorg101098rstb20120343
Moore A J Brodie III E D ampWolf J B (1997) Interacting pheno-types and the evolutionary process I Direct and indirect geneticeffects of social interactions Evolution 51 1352ndash1362 httpsdoiorg101111j1558-56461997tb01458x
NonacsPampKapheimKM(2007)Socialheterosisandthemaintenanceof genetic diversity Journal of Evolutionary Biology 20 2253ndash2265httpsdoiorg101111j1420-9101200701418x
Nussey D H Wilson A J amp Brommer J E (2007) The evolution-ary ecology of individual phenotypic plasticity in wild popula-tions Journal of Evolutionary Biology 20 831ndash844 httpsdoiorg101111j1420-9101200701300x
OtterKAStewartIRKMcGregorPKTerryAMRDabelsteenTampBurkeT(2001)Extra-pairpaternityamonggreattitsParus major following manipulation of male signals Journal of Avian Biology 32338ndash344httpsdoiorg101111j0908-88572001320408x
Pruitt J N Bolnick D I Sih A DiRienzo N amp Pinter-Wollman N(2016)Behavioralhypervolumesofspidercoloniespredictscommu-nity performance and disbandmentProceedings of the Royal Society B- Biological Sciences 283 20161409 httpsdoiorg101098rspb20161409
PruittJNampPinter-WollmanN(2015)Thelegacyeffectsofkeystonein-dividualsoncollectivebehaviourscaletohowlongtheyremainwithina group Proceedings of the Royal Society B- Biological Sciences 28220151766httpsdoiorg101098rspb20151766
RoyleNJHartley IROwens I P FampParkerGA (1999) Siblingcompetition and the evolution of growth rates in birds Proceedings of the Royal Society B 266 923ndash932 httpsdoiorg101098rspb19990725
SaltzJBampFoleyBR(2011)Naturalgeneticvariationinsocialnicheconstruction Social effects of aggression drive disruptive sexual se-lectioninDrosophila melanogaster American Naturalist177645ndash654httpsdoiorg101086659631
ShusterSM LonsdorfEVWimpGMBaileyJKampWhithamTG (2006) Community heritabilitymeasures the evolutionary conse-quencesofindirectgeneticeffectsoncommunitystructureEvolution60991ndash1003httpsdoiorg101111j0014-38202006tb01177x
SimmonsAMSimmonsJAampBatesMA (2008)Analyzingacous-tic interactions in natural bullfrog (Rana catesbeiana) chorusesJournal of Comparative Psychology 122 274ndash282 httpsdoiorg1010370735-70361223274
Sinervo B R amp Calsbeek R (2010) Behavioral concepts of selectionExperiments and genetic causes of selection on the sexes In D FWestneatampCWFox(Eds)Evolutionary behavioral ecologyLondonUKOxfordUniversityPress
Thompson J N (1982) Interaction and coevolution Chicago USA TheUniversityofChicagoPress
emspensp emsp | emsp1463MONTIGLIO eT aL
VanderWaal K L ObandaV Omondi G P McCowan BWang HFushingHampIsbellLA (2016)Thestrengthofweaktiesandhel-minth parasitism in giraffe social networks Behavioral Ecology 271190ndash1197httpsdoiorg101093behecoarw035
Ward P I (1993) Micro-habitat segregation and the mating systemof Gammarus pulex Animal Behavior 45 191ndash192 httpsdoiorg101006anbe19931019
Ward P I amp PorterAH (1993)The relative role of habitat structureandmale-malecompetition in thematingsystemofGammarus pulex (CrustaceaAmphipoda)AsimulationstudyAnimal Behavior45119ndash133httpsdoiorg101006anbe19931011
West-EberhardMJ(1989)Phenotypicplasticityandtheoriginsofdiver-sityAnnual Review of Ecology and Systematics20249ndash278httpsdoiorg101146annureves20110189001341
Westneat D F Hatch M IWetzel D P amp Ensminger A L (2011)IndividualvariationinparentalcarereactionnormsIntegrationofper-sonalityandplasticityAmerican Naturalist178652ndash667httpsdoiorg101086662173
Wilson A J Gelin U Perron M-C amp Reacuteale D (2009) Indirect ge-neticeffectsandtheevolutionofaggression inavertebratesystemProceedings of the Royal Society of London Series B Biological Sciences276533ndash541httpsdoiorg101098rspb20081193
Additional Supporting Informationmay be found online in the sup-portinginformationtabforthisarticle
How to cite this articleMontiglioP-OMcGlothlinJWFarineDRSocialstructuremodulatestheevolutionaryconsequencesofsocialplasticityAsocialnetworkperspectiveoninteractingphenotypesEcol Evol 201881451ndash1464 httpsdoiorg101002ece33753
APPENDIX
PHENOTYPIC MEAN AND VARIANCE
FollowingMooreetal(1997)wemodelasinglephenotypeofanindi-vidual (z)asanadditivecombinationoftheeffectsof itsowngenes(iedirectgeneticeffectsa)thenonsocialenvironmentitexperiences(e)andaplasticcomponentthatissomefunctionofthephenotypesinitssocialgroupMooreetal(1997)originallymodeledthesocialeffectasafunctionofthephenotypeofoneinteractingindividualMcGlothlinandBrodie (2009)andMcGlothlinetal (2010)consideredsocialef-fectsinapopulationconsistingofgroupsofnindividualswhereinter-actionswereassumedtooccursimultaneouslywithinagroupwithallindividuals within a group having the same strength of interactionHereweconsideramoregeneralsocialstructurewhereindividualsinteractwithallpossiblesocialinteractantsingroupsizenwithvaria-bleconnectionstrengthsirangingfrom0to1giving
wherethesummationistakenacrossalln minus1possiblesocialinterac-tionsforeachindividualsandψrepresentstheinteractioncoefficientwhichdetermines thestrengthanddirectionof the indirectpheno-typic effect of individual social interactantsHere and elsewhere aprimeindicatesaparameterbelongingtoasocialpartnerAnysocialnetworkstructurecanbemodeledbychangingthedistributionofs High-densitysocialnetworkswithstrongconnectionswillhavemanylargevaluesofswhilesparsernetworkswithweakerconnectionswillhavemanyweaksvalueswithmanyequaltozeroConsideringphenotypicfeedback(asdoMooreetal1997)insuch
The value of the two covariance terms represents how stronglystrengthofinteractiondependsonthegenesandenvironmentofin-dividualsocialpartnersThiscovarianceisdeterminedforeachindi-vidualandmayvaryacrossindividualsTheseshouldbepositiveunderhomophilyandnegativeunderheterophilyTakingthemeanandas-suming
=e=0
where double overbars indicate global means and large overbarswithintheparenthesesindicatemeanstakenacrossindividualsbasedonsummarystatisticsoftheirsocialgroupsThiscanbeexpandedasaboveto
The remainingcovariance terms represent theaveragedegree towhichindividualconnectionstrengthsareadjustedbasedonthephe-notypeofpotentialinteractantsInthecaseofhomophilyorheteroph-ilyindividualswillmakethisadjustmentbasedontheirownphenotypewithlargeindividualshavingapositivecovarianceandsmallindividu-alshavinganegativecovariance(orviceversa)ThereforeweexpecttheseaveragecovariancetermstotendtowardzeroMakingthisas-sumptionandrearrangingprovidesEquation2inthetext
EXTENSION TO MULTIPLE GROUPS
EquationA8iswrittenassumingthatthepopulationconsistsofasin-gle social networkwhere individualsmay interact in anywayNowassumethatthepopulationisdividedintomultiplegroupswhereindi-vidualsmay interactwithanystrengthswithinagroupanddonotinteract at all between groups Assuming the covariance terms inEquationA8arezeroandthatenvironmentaldeviationsdonotvaryamonggroupsthemeanofeachgroupwillbe
where overbars now indicate within-groupmeans Assuming equalgroupsizethepopulationmeanisnow
(IfgroupsvaryinsizethenEquationA10canbemodifiedtogiveaweightedmean) Ifconnectionstrengthhasnoheritablebasis thenthe covariance term become zero and EquationA10 collapses toEquation2inthetextWemaycalculateamong-groupvariancemosteasilybymakingafewassumptionsthatarealsomadeinoursimula-tionsFirstasaboveweassumethatgroupsareofequalsizeSecondweassume thatmean interactiondoesnotvaryacrossgroups ands=
=sMakingtheseassumptions
Thisshowsthat indirectgeneticeffectswillmagnifyslightdiffer-ences in genetic values across groups regardless of sign Strongermeanconnectionstrengthswillintensifythiseffect
RESPONSE TO SELECTION
FollowingMoore etal (1997) andMcGlothlin etal (2010) and as-suming that thecovariance terms inEquationA8areeither zeroorpopulation parameters that do not have a heritable component anindividualrsquostotalbreedingvaluecanbewrittenasthegeneticcontri-butiontothepopulationmean
where Ristheregressionofsaprimeonaandisthusanalogoustorelated-ness This assumes thatCov[aseprime] is negligible Positive values ofR indicatehomophilyandnegativevaluesindicateheterophilyMakingthissubstitutiongivesEquation4inthetextEquation4canalsobeexpresseddifferentlybyrearrangingas
densitiessocialenvironmentsare indistinguishableexceptforthiseffect of excluding oneself thus leading to a directndashindirect cor-relationofminus1Smallergroupswillexhibitthispatterntoastrongerextent than larger groups (see FigureS5 also McDonald FarineFosterampBiernaskie2017)Thecombinedimpactoftheeffectsofnetworkdensityonthevariancein indirectgeneticeffectsandonthecovariancebetweendirectandindirectgeneticeffectsisarel-ativedecrease inphenotypicvariationwithingroups(comparedtothephenotypicvariationinabsenceofanyinteractions)asnetworkdensityincreases(Figure3c)Oppositepatternsareobservedwhenψg isnegative(FigureS6)Finallywenotethatalthoughthemeanphenotypic variationwithin each group decreaseswith increasingnetworkdensitywefindthatthevariationamonggroups(eachdotin each panel of Figure3c represents one group) ismaximized atintermediatenetworkdensities
Although the phenotypic variance typically decreases with in-creasednetworkdensitythevarianceintotalbreedingvalues(rela-tivetothegeneticvarianceinabsenceofanysocialinteraction)hasthe greatest increase at highest network densities (Figure3d redline)Thisisbecausetheexpectedvarianceintotalbreedingvaluesisequalto
(1+ψg
=s)2
G(seeEquationA12)Thatisthevarianceintotalbreedingvaluesdoesnotdependonthevarianceinindirectgeneticeffects noron the covariancebetweendirect and indirect geneticeffectswhich leadtothedecrease invarianceshowninFigure3cRatherthevarianceintotalbreedingvaluesisafunctionofdirectge-neticeffectsandeffectsofanindividualrsquosgenesonothersthelatter
ofwhichbecomesinflatedathigherdensitiesTheresponsetoselec-tiondependsonthecovariancebetweentotalbreedingvaluesandphenotypicvalueswhichisexpectedtoincreaselinearlywithdensity(EquationA15)Whenwesubjectgroupstoaselectiongradientof02networkswithincreasingdensitiesexhibitedanincreasedevolu-tionaryresponsetoselection(Figure4redline)Increasingnetworkdensityalso increases thevariance in responsetoselectionamonggroups (Figure4 gray dots) This likely happened because individ-ualsadjusttheirphenotypetotheaveragesocialenvironmentthattheyexperienceThusathighernetworkdensitiesindividualswithextreme phenotypicvalues have a disproportionate impact on theaveragesocialenvironmentexperiencedbyindividualsSmalldiffer-encesinthephenotypicvaluesofextremeindividualsfromgrouptogroupcreatedifferencesinthecovariancebetweenthephenotypicvarianceandthetotalbreedingvaluesamonggroupsandincreasingthevariance in response to selection amonggroups In agreementwiththisextremeindividualsalsogenerategreaterphenotypicvari-anceamonggroupsathighernetworkdensities(Figure2)andwhenindividualphenotypesfollowauniformdistribution(moreindividualswithextremephenotypes)thananormaldistribution(fewerindivid-ualswithextremephenotypesSeeFigureS3)
F IGURE 3emspEffectsofnetworkdensityon(a)thevarianceinindirecteffectsexperiencedbyindividuals(b)thecorrelationbetweendirectandindirectgeneticeffectsexperiencedbyindividuals(c)thechangeinphenotypicvariancewithingroupsrelativetothegeneticvariance(iethephenotypicvarianceinabsenceofinteractions)and(d)thechangeintotalgeneticvariationrelativetothegeneticvariance(ievarianceofindividualdirectgeneticeffectsandindirectgeneticeffectsimposedtoothers)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψg of4
emspensp emsp | emsp1457MONTIGLIO eT aL
hasnoeffectonthemeanphenotypeofeachgroup(Figure5)whichis consistent with our analytical model (Equation2) However in-creasednetworkassortmentisassociatedwithanincreaseinthevari-anceinindirectgeneticeffectsexperiencedbyindividualsinagivengroup(seethethirdterminEquation3Figure6a)Becauseindividu-alsinteractmorestronglywithconspecificsthathavesimilarbreedingvalues(highwithhighlowwithlow)thedirectandindirectgeneticcontributions to phenotypes act in concert and covary positively(fourthterm inEquation3Figure6b)Thesetwoeffectscontributetowardincreasingphenotypicvarianceobservedwithinagivengroup(Figure6c)Theseeffectsarereversedwhenψgisnegativedirectandindirect contributions to individual phenotypes act to oppose eachothertherebyreducingtheamountofphenotypicvarianceobservedin the population (see FigureS7) Increasing network assortmentalsoleadstoasmalldecreaseinthevarianceintotalbreedingvalues(Figure6dredline)Thisisattributabletotheslightdecreaseinden-sityassociatedwithhigherlevelsofnetworkassortment(ieindividu-alshavetheabilitytoreducetheconnectionstrengthwithparticulargroupmembers)aphenomenonnotcapturedbyouranalyticalmodel
Applying selection to groups with varying network assortmentshowsthatasynergybetweendirectandindirectgeneticeffectsleadstoanincreaseinevolutionarychangewithincreasingnetworkassort-ment(Figure7redline)Thisresultisinaccordwiththepredictionsofouranalyticalmodelwhichpredictsanincreasedresponsetoselec-tionwithincreasingR(Equation4)AlthoughEquation4suggestsden-sityandhomophilyshouldhavesymmetricaleffectstheincreaseseeninFigure7isnotasdramaticasthatinFigure4perhapsbecauseoftheconcomitantdecreaseindensitycausedbyallowinghomophilyinoursimulationsUnlikenetworkdensitynetworkassortmentdoesnotaffectthevariationofevolutionaryresponsesamonggroups(Figure7graydots)
4emsp |emspDISCUSSION
Inthisstudyweexploretheconsequencesofsocialplasticityandthestructureofinteractionsinshapingtheamountofphenotypicvariationwithingroupsof interactingindividualsandtheevolutionaryresponseofthesegroupstoselectionWeconsiderreplicategroupswithvary-ingstructuresofinteractionsSuchreplicatescouldbeseenasmultiplegroups of individualswithin a given population (eg tribes packs orcolonies)orasmultipleisolatedpopulationswithinanecologicalcom-munityThroughananalyticalmodelandagent-basedsimulationsweshowthatthestructureofsocialnetworksmodulatedtheimpactofin-directgeneticeffectsontheamountofphenotypicvarianceavailablefor selectionOur resultsemphasize that thenumberandstrengthofconnectionsamongindividuals(networkdensity)aswellaspreferentialassociations among individualswith a similar phenotype (network as-sortment)haveimportanteffectsonthecontributionofindirectgeneticeffectsNetworkdensityandassortmentalsomodulatetheabilityfortraitstoexhibitevolutionarychangeinresponsetoselectionIncreasingthenumberofinteractionsamonggroupmembers(networkdensity)in-creasestheaverageevolutionaryresponseofgroupstoselectionandin-creasesthevariationinresponsetoselectionamonggroupsBycontrastincreasednetworkassortmentleadstoanincreaseintheaverageevolu-tionaryresponseofgroupstoselectionbutdoesnotaffectthevariationinevolutionary responseamonggroupsOur resultshavewidespreadimplicationsforstudiesofsocialevolutionmultilevelselectionandtheemergenceofkeystoneindividuals(ModlmeierKeiserWattersSihampPruitt2014)andniche-constructingtraits(egSihampWatters2005)
41emsp|emspComparison with earlier interacting phenotype models
Our analytical results show that given some simplifying assump-tions (most importantly ignoring the potential for phenotypic
F IGURE 4emspEvolutionaryresponseofphenotypetoaselectiongradientvarieswithnetworkdensityTheaveragechangeinphenotypemeanresultingfromselectionincreasedwithnetworkdensity(redline)Groupswithdensernetworksofinteractionsexhibitedmorevariationinthechangeinphenotypicmean(graydots)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4
F IGURE 5emspTheaveragephenotypeofindividualsasafunctionofnetworkhomophily(redline)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4Networkscouldnotreachhomophilyvaluesof1becauseweusedacontinuoustraitvalueratherthandiscretevalues(seeFarine2014)
1458emsp |emsp emspensp MONTIGLIO eT aL
feedback) considering more general social structures does notgreatlyalter theconclusionsofearliermodelsof interactingphe-notypeevolution(egMcGlothlinetal2010Mooreetal1997)First indirect genetic effects still alter the response to selectionby increasing the amount of genetic variance exposed to selec-tionNote thatbecausewedonotmodel feedback thiseffect is
directional with positiveψg (ie becomingmore similar to onersquosneighbors)increasingtheresponsetoselectionandnegativevalues(iebecomingmoredifferentfromonersquosneighbors)decreasingitSecondhomophilyheterophilyplaysa rolesimilar to relatednessinpreviousmodelsinalteringtheresponsetoselection(McGlothlinetal2010)IndeedMcGlothlinetal(2010)noted(ashavemanyothers)thatrelatednessperseisjustaspecialcaseofphenotypicassortment
Themostnotabledifferencebetweenourmodelandearliermod-elsisthatindividualsareallowedtodifferintheirinfluenceonsocialplasticityduetovariation inconnectionstrength (s)Perhapsunsur-prisingly responsetoselection ismorestrongly influencedbysocialinteractions indensernetworkswhere interactionsarestrongerandmorecommonaneffect that isapparent inbothouranalyticalandsimulation results Inour simulation resultswealso find thatvaria-tioninresponsetoselectionamongincreaseswithgreaterconnectionstrengthThis could occur because in some groups themostwell-connectedindividualshappentohaverelativelyhighorlowbreedingvaluesThesewell-connected individualswould thenhaveadispro-portionateeffectonthephenotypeofothers (relativeto individualsclosertothepopulationrsquosaveragebreedingvalue)byexertingastrongeffectonthemeansocialenvironmentexperiencedbyindividualsIndoingsowell-connectedextremeindividualscangeneratevariabilityinthecovariancebetweenbreedingvaluesandphenotypeandthusintheresponsetoselectionFuturemodelsshouldallowconnectionstrength to display a heritable component which would allow thesocialnetworkstructureitselftoevolveinresponsetosucheffects
F IGURE 6emspEffectofnetworkhomophilyon(a)thevariationinindirecteffects(b)thecorrelationbetweendirectandindirectgeneticeffects(c)therelativechangeinphenotypicvariancewithingroupsand(d)therelativechangeintotalgeneticvariationEachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4HomophilysimultaneouslyincreasesvariationamongindividualsinindirectgeneticeffectswithingroupsandgeneratesastrongpositivecovariancebetweendirectandindirectgeneticeffectstherebysubstantiallyincreasingthephenotypicvarianceobservedwithingroupsHoweverthisincreaseinphenotypicvarianceisnotassociatedwithanychangeatthegeneticlevel
F IGURE 7emspEvolutionaryresponseofphenotypetoaselectiongradientincreaseswithnetworkhomophily(redlineandgraydots)Eachdotrepresentsthechangeinmeangenotypeacrossgenerationsinasinglesimulatednetworkorgroupof50individuals(Ngroup=50)TheredlinerepresentstheaverageevolutionaryresponseasafunctionofnetworkdensityIndirectgeneticeffectsweregeneratedusingaψgof4
emspensp emsp | emsp1459MONTIGLIO eT aL
Studiesinthewildhaveshownthatpositioninasocialnetworkmaybe repeatable and have fitness consequences suggesting that con-nectionstrengthmaybeanevolvabletrait (AplinFirthetal2015FormicaWoodCookampBrodie2017Formicaetal2012)
42emsp|emspGroups with denser connections exert a stronger ldquopull to the meanrdquo
Our simulations show that groupswhere individuals have an in-termediatenumberorstrengthofsocialconnections (iegroupswithintermediatenetworkdensities)allowforthegreatestwithin-groupvariationinsocialenvironmentsexperiencedamongindivid-ualsThispatternariseswithinagenerationduetosocialplasticityratherthanasaresponsetoanyselectivepressureBygeneratinga greater range of phenotypes and social environments groupswithan intermediatedensityof social interactionscouldprovidethe basis for the emergence and evolution of alternative socialphenotypes (Bergmuumlller amp Taborsky 2010 Sinervo amp Calsbeek2010) When social phenotypes are subject to indirect geneticeffects the maintenance of variation in social behavior shouldthus be observed more frequently in groups with intermediateconnectedness
Whilelowtointermediatedensitiesofsocialinteractionsofferthewidestscopeforpromotingindividualvariationinphenotypegroupswith high densities exhibit a very different patternAs the numberand strengths of interactions increases among group members in-direct genetic effects experienced by each individual becomemoresimilarbecauseallgroupmembersstarttobecomeconnectedtooneanotherand theseconnectionsareuniformlystrong Inadditionasnetworksbecomemoreconnectedindividualsattheextremesofthedistributionofgenetic tendencies in thegroups (ie the individualsfurthest from the averagebreedingvalue) tend to experience a so-cialenvironmentexertinganopposingeffectontheirphenotype(ieCov[a+esa +se] in Equation3 becomes more negative) This ldquopullto themeanrdquo is stronger in smaller groups than in larger ones (seeFigureS5) anddecreases thepopulationphenotypicvariancewhenψg ispositive (egwhen individuals increasetheiraggressiveness inresponse to the aggression they receive) and increases it whenψg is negative (egwhen individuals inhibit their aggressiveness in re-sponsetotheaggressiontheyreceive)Whenindividualsexhibit im-portantphenotypicplasticitysuchaneffectappearssimilartosocialconformity where individuals express more similar phenotypes asgroupsthan in isolation (egHerbert-Readetal2013MagnhagenampBunnefeld2009)Conformity isusually thought toemergewhendissimilarindividualsareatafitnessdisadvantageForexamplepred-ators tend topick individuals that standout amonggroupsofpreyselecting forhomogeneousgroups (LandeauampTerborgh1986)Weshowherethatconformist-likepatternsinbehaviorcanemergefromverysimpleformsofsocialplasticity Importantlyweshowthatbe-havioralconformitycanemergeevenwhenindividualsarenotactivelycopyingthemostabundantphenotypeoftheirgroup inabsenceofanyselectivepressureExamplesofhighlyconnectedgroupsinnatureincludechorusesofmalesinsomespeciesoffrogsproducingmating
calls or leks ofmales displaying to attract females and adjust theirsignalingeffortinresponsetothesignalingoftheirrivals(Boatright-HorowitzHorowitzampSimmons2000SimmonsSimmonsampBates2008)Whenmalesareclosetoeachotherandeachmalecanadjustits signaling intensity to that of all the othermaleswe expect thisldquopulltothemeanrdquotodecreasethevariationinmalesignals(althoughsocialplasticitycantakemorecomplexpatternsthenismodeledhereGreenfieldampRand2000)Thiscandecreasetheeffectivenessoffe-malematechoiceandtheintensityofsexualselection
43emsp|emspGroups with denser connections potentiated the effect of keystone individuals
Aninsightfromoursimulationsisthatwheneverindividualsadjusttheirphenotypetotheaveragesocialenvironmentthattheyexperi-enceindividualsattheextremesofthegenotypicorphenotypicdis-tributionhavethegreatestimpactonthephenotypeofothergroupmembers This phenomenon arises because these individuals havethestrongest impacton themeansocialenvironmentexperiencedbytheirconspecificsTheevolutionofniche-constructingtraitsal-lowingsomeindividualstomanipulatetheirgroupinawaythatfa-vorstheirownsuccess(SaltzGeigerAndersonJohnsonampMarren2016) or to have a disproportionate effect on their group (Keiseramp Pruitt 2014 Modlmeier etal 2014 Pruitt amp Pinter-Wollman2015)hasbeenthefocusofmuchinterestrecentlySurprisinglynostudyhasexplored the implicationsof theexactpatternsofsocialplasticity for the identity and impact of such ldquokeystone individu-alsrdquo (Modlmeier etal 2014) It is reasonable to assume thatmostanimalsexhibitingsocialplasticityshouldadjusttheirphenotypeinresponse to theaverage socialconditions that theyexperience (al-thoughinsomecasessomeindividualscanadjusttheirphenotypeto themaximumor to theminimumphenotypicvalueof the indi-vidualswithwhomtheyinteractseeDyerCroftMorrellampKrause2009 for a potential example) Thus our simulations suggest thattheemergenceofkeystoneindividualsmightbeaphenomenonfarmore common than previously envisioned Keystone individualscouldemergeinanygroupofinteractingindividualsexhibitingphe-notypicplasticityanddenseinteractionnetworks(asinthelekkingexampleabove)Hencetheemergenceofkeystoneindividualsmightnotrequireacomplexsocialsystemdivisionoflabor(PruittBolnickSihDiRienzoampPinter-Wollman2016) collectivebehavior (PruittampPinter-Wollman2015)orniche-constructingtraits (egaggres-sivenesspolicingorelseChangampSih2013)butshouldbemostcommon in specieswhere individuals respond to thebehaviors ofthemajorityofgroupmembers
Denserinteractionsamongindividualswithinagrouppotentiatetheimpactofindividualswithextremephenotypicvaluesbyallow-ing these to interact and affect themajority of their groupmem-bersHencetheconsequencesofindividualsocialplasticitytendtobecomemuchgreater ingroupsasnetworkdensity increasesThisldquoamplificationrdquoeffectisalsostrongerwhengenotypesfollowauni-formdistribution (iewhenextremegenotypesaremorefrequentwithin groups) thanwhen they followaGaussiandistribution (ie
1460emsp |emsp emspensp MONTIGLIO eT aL
whenextremegenotypesarerarewithingroups)Networkdensityincreases the evolutionary response of groups on average groupswith denser connections also exhibit increasedvariation in evolu-tionaryresponsetoagivenselectiongradientSuchan increase inthevariationinevolutionaryresponseobservedinourstudyisap-parentbecauseourapproachallowsustorelaxtheassumptionthatindividualswithingroupsinteractequallywithallothergroupmem-bersbyintroducinganewparameter(averageconnectionstrength=s)intoourmodelandinsteadtoexplicitlyexploretheeffectofcon-nectiondensity
44emsp|emspHomophily affects the amount of phenotypic variation within groups
Our simulations also investigate the consequencesof social struc-turewhenindividualscaninteractpreferentiallywithindividualsthathaveasimilar(iehomophily)ordissimilar(ieheterophily)pheno-typeNetworkassortment(thenetworkmeasureofhomophily)doesnot have any impact on groupsrsquomean phenotype but can gener-ateagreatervariationinsocialenvironmentswithingroupsHenceassuming that different immediate social environments can favordifferent (alternative) phenotypes within groups our simulationssuggest that homophily should be associatedwith the emergenceof phenotypic variation among individuals (or social specializationBergmuumlller amp Taborsky 2010 Montiglio Ferrari amp Reacuteale 2013)Homophilyalsohasdirectconsequencesfortheevolutionofalter-nativephenotypesbycreatingsynergyoroppositionbetweendirectand indirect genetic effectsWhen social plasticity (ψg) is positive(egwheninteractingwithanaggressiveindividualincreasesafocalindividualrsquosaggression)andindividualsshowatendencytointeractwithsimilarphenotypesthesocialenvironmentactstoshapetheirphenotypeinthesamedirectionastheirgenotypeAsaresultsocialinteractionsandsocialplasticityincreasethephenotypicvarianceofthetraitrelativetoasituationinwhichconnectionsarerandominterms of their traits It also tends to increase the strength of theevolutionaryresponsetoselectioninresponsetoagivenselectiongradientThisincreaseinevolutionaryresponsearisesfromthesyn-ergybetweendirectandindirecteffect(orbetweensocialplasticityandhomophily)ratherthanfromachangeintotalgeneticvariationwithingroups
45emsp|emspPossible applications and tests of the model and future directions
differentialandmatechoicebyfemalesThestrengthofconnectionsbetweenmales of known phenotype could be increased artificiallyusingplaybacks tosimulatemore frequent interactionsamong indi-viduals(DabelsteenampPedersen1990Otteretal2001)tomonitorhowsuchincreasesinconnectionstrengthaffecttheextentofpheno-typicandgeneticadditivevariationAlternativelyonecanmanipulatethedistributionofterritoriesavailableandthepatternsofinteractionsby controlling the locationof nest boxes foodpatches or refugesSuchapproachescouldbeparticularlysuitableforcavity-nestingbirds(Both1998)
Ourmodel also studied the consequences of homophily for theevolutionary responses of phenotypic traits Assuming individualshave some level of control on their interactions homophily can beobservedwhen individualsexhibitpreferences to interactwithcon-specificsthatare(dis)similartothemSuchpreferencescouldexplainthemaintenanceofaltruisticbehaviorbecauseoftheirpotentialroleinshapingtheselectionpressuresactingonaltruismSomeworkonfruitflieshavereportedthatindividualpreferencesforparticularsocialenvironmentsisassociatedwithgeneticvariationandcanthuspoten-tiallyevolve (egSaltzampFoley2011)Onecould testourmodel insuchstudysystemsbyeitherallowingorpreventingtheexpressionofsocialpreferences(throughmixingofindividualsormanipulatingtheirinteractions) Alternatively homophily can also be observed whenindividualssegregateintheenvironmentasafunctionoftheirphe-notype(HelfensteinDanchinampWagner2004Ward1993WardampPorter1993)Forexamplemoreandlessaggressiveindividualsseg-regateinpatcheswithdifferentdensitiesofconspecifics(Duckworth2006)Thusbymanipulatingtheheterogeneityandthescaleatwhichitisobserved(iethesizeofpatchesofdifferenthabitat)onecouldtestthepredictionsofourmodelFutureworkwillexpandthemodelwe presented here to analyze the consequences of such traits forthemaintenanceofphenotypicvariationandtheevolutionofsocialstructure
One limitationofourmodel is thatweassumebothphenotypicfeedback(Mooreetal1997)andsocialselection(Wolfetal1999)tobeabsentIncludingfeedbackmayaltertheconclusionswehavepre-sentedhereasfeedbackeffectsmaycausesocialplasticitytomovethroughnetworksincounterintuitivewaysItispossiblethatnetworkmetricsbeyondconnectionstrength (suchasclusteringcoefficientsbetweennessetc)may influencewhetherfeedbackcontributessig-nificantly to variation and response to selection Regarding socialselectionwehaveshownherethatconnectionstrengthcontributestoamong-groupvariancewhichshould intensifyresponsetohigherlevelsofselectionsuchassocialselectionWewilltreatbothfeedbackandsocialselectioninfuturecontributions
5emsp |emspCONCLUSION
Wepresentbothananalyticmodelandsimulationsextendingpre-vious work on social phenotypic plasticity to more general socialstructuresOurstudygeneratesafirstsetofverygeneralandtest-able predictions on the role of social structure in modulating the
emspensp emsp | emsp1461MONTIGLIO eT aL
consequencesofsocialplasticityWeshowthatthebasiccharacter-isticsofthestructureofinteractionsamongindividualsingroupsandpopulationscanhaveimpactsontheconsequencesofsocialplasticityforthemeanphenotypeexpressedbytheindividualstheextentofphenotypicvariationavailableforselectionandfortheabilityofthepopulation to respond to selectivepressuresWehope that futurestudieswillbeabletotestourpredictionsempiricallybyapplyingourapproachtothestudyofsocialbehavior(egaggressionandcoop-eration)socialinformationuseoralternativematingtacticsinpopu-lationswithvaryingpatternsofsocialormatinginteractionsFromatheoreticalperspectivefutureresearchwouldwarrantinvestigatingthelinkbetweenindividualpositioninsocialnetworksandtheindi-rect genetic effects it experiences and thuswhether factors otherthan individualsrsquo breeding values can lead to keystone individualsFurtherinourstudyweassumethatallindividualsexpressedplas-ticityidenticallyHoweverindividualshavealsobeenshowntovaryintheirplasticity(DingemanseKazemReacutealeampWright2010NusseyWilsonampBrommer2007WestneatHatchWetzelampEnsminger2011)andsuchvariationmayalterthepredictionsofinteractingphe-notypemodels(KazancıoğluKlugampAlonzo2012)Linkingindividualdifferencesinbothsocialpositionandplasticitycouldyieldnewin-sightsandagreaterunderstandingoftheevolutionarymechanismsthatunderpinphenotypicvariationwithinindividualsbetweenindi-vidualsandamongpopulations
ACKNOWLEDGMENTS
We thank the Reader Hendry and Barrett laboratories in McGillUniversity forconstructivecommentsonadraftof thismanuscriptPOMwas supported by aNSERCpostdoctoral fellowshipDRF re-ceived funding from a grant to theBBSRC (BBL0060811 toBCSheldon)andtheMaxPlanckSociety
CONFLICT OF INTEREST
Nonedeclared
AUTHOR CONTRIBUTIONS
POMandDRFbuiltthesimulationsandJWMdevelopedthemodelPOMdrafted themanuscript andproduced the figuresAll authorscontributedtorevisionsandapprovedthefinalversionofthearticle
AplinLMFarineDRMorand-FerronJCockburnAThorntonAamp SheldonBC (2015) Experimentally induced innovations lead topersistentcultureviaconformityinwildbirdsNature518538ndash541
Aplin LMFirthJAFarineDRVoelklBCratesRACulinaAhellipSheldonBC (2015)Consistent individual differences in the so-cialphenotypesofwildgreattits(Parusmajor)Animal Behaviour108117ndash127httpsdoiorg101016janbehav201507016
BaileyNWampHoskins J L (2014)Detecting cryptic indirect geneticeffectsEvolution681871ndash1882httpsdoiorg101111evo12401
Bailey N W amp Zuk M (2012) Socially flexible female choice differsamongpopulationsofthePacificfieldcricketGeographicalvariationin the interaction coefficient psi (Ψ)Proceedings of the Royal Society of London Series B Biological Sciences 279 3589ndash3596 httpsdoiorg101098rspb20120631
Bergmuumlller R amp Taborsky M (2010) Animal personality due to socialnichespecialisationTrends in Ecology amp Evolution25504ndash511httpsdoiorg101016jtree201006012
Bijma P ampWade M J (2008) The joint effects of kin multilevel se-lection and indirect genetic effects on response to genetic selec-tion Journal of Evolutionary Biology 21 1175ndash1188 httpsdoiorg101111j1420-9101200801550x
Boatright-HorowitzSLHorowitzSSampSimmonsAM(2000)Patternsof vocal interactions n a BullfrogRana catesbeiana chorus preferen-tial responding to farneighborsEthology106701ndash712httpsdoiorg101046j1439-0310200000580x
BothC(1998)Experimentalevidencefordensitydependenceofrepro-ductioningreattitsJournal of Animal Ecology67667ndash674httpsdoiorg101046j1365-2656199800228x
Cappa E P amp Cantet R J C (2008) Direct and competition additiveeffects in treebreedingBayesianestimation froman individual treemixedmodelSilvae Genetica5745ndash56
ChangAampSihA (2013)Multilevel selection andeffects of keystonehyperaggressivemalesonmatingsuccessandbehaviorinstreamwaterstridersBehavioral Ecology241166ndash1176httpsdoiorg101093behecoart044
Clutton-BrockTH(1989)MammalianmatingsystemsProceedings of the Royal Society B236339ndash372httpsdoiorg101098rspb19890027
Crowley P H amp Cox J J (2011) Intraguild mutualism Trends in Ecology amp Evolution 26 627ndash633 httpsdoiorg101016jtree201107011
Duckworth R A (2006) Aggressive behaviour affects selection onmorphology by influencing settlement patterns in a passerine birdProceedings of the Royal Society B 273 1789ndash1795 httpsdoiorg101098rspb20063517
Farine D R (2014) Measuring phenotypic assortment in animal so-cial networks Weighted associations are more robust than binaryedges Animal Behavior 89 141ndash153 httpsdoiorg101016janbehav201401001
FarineDRampWhiteheadH(2015)Constructingconductingandinter-preting animal social network analysis Journal of Animal Ecology841144ndash1163httpsdoiorg1011111365-265612418
Fawcett TW amp Johnstone RA (2010) Learning your own strengthWinner and loser effects should change with age and experienceProceedings of the Royal Society of London Series B Biological Sciences2771427ndash1434httpsdoiorg101098rspb20092088
Fisher D N amp McAdam A G (2017) Social traits social networksand evolutionary biology Journal of Evolutionary Biology httpsdoiorg101111jeb13195Inpress
FormicaVAWood CW LarsenW B Butterfield R EAugatMEHougenHYampBrodieIIIED(2012)Fitnessconsequencesofsocialnetworkpositioninawildpopulationofforkedfungusbeetles(Bolitotherus cornutus) Journal of Evolutionary Biology 25 130ndash137httpsdoiorg101111j1420-9101201102411x
Greenfield M D amp Rand S A (2000) Frogs have rules selective at-tention algorithms regulate chorusing in Physalaemus pustulosus (Leptodactylidae)Ethology106131ndash147
Helfenstein FDanchin E ampWagner RH (2004)Assortativematingand sexual size dimorphism in blacklegged kittiwakes Waterbirds27 350ndash354 httpsdoiorg1016751524-4695(2004)027[0350AMASSD]20CO2
Herbert-Read J E Krause S Morrell L J Schaerf T M Krause JampWardAJW (2013)The roleof individuality in collectivegroupmovementProceedings of the Royal Society B- Biological Sciences28020122564
KeiserCNampPruittJN (2014)Personality composition ismore im-portantthangroupsizeindeterminingcollectiveforagingbehaviourinthewildProceedings of the Royal Society of London Series B Biological Sciences28120141424httpsdoiorg101098rspb20141424
Krause J amp Ruxton GD (2002) Living in groups Oxford UKOxfordUniversityPress
Landeau L ampTerborgh J (1986)Oddity and the ldquoconfusion effectrdquo inpredationAnimal Behavior341372ndash1380httpsdoiorg101016S0003-3472(86)80208-1
Magnhagen C amp Bunnefeld N (2009) Express your personality or goalong with the group What determines the behaviour of shoalingperchProceedings of the Royal Society B- Biological Sciences2763369ndash3375httpsdoiorg101098rspb20090851
McDonaldG C FarineD R Foster K R ampBiernaskie JM (2017)Assortment and the analysis of natural selection on social traitsEvolution712693ndash2702httpsdoiorg101111evo13365
McGlothlin JW amp Brodie III E D (2009) How to measure individ-ual genetic effects The congruence of trait-based and variance-partitioning approaches Evolution 63 1785ndash1795 httpsdoiorg101111j1558-5646200900676x
McGlothlin J W Moore A J Wolf J B amp Brodie III E D(2010) Interacting phenotypes and the evolutionary pro-cess III Social evolution Evolution 64 2558ndash2574 httpsdoiorg101111j1558-5646201001012x
MillerJRBAmentJMampSchmitzOJ (2014)Fearon themovePredatorhuntingmodepredictsvariation inpreymortalityandplas-ticityinpreyspatialresponseJournal of Animal Ecology83214ndash222httpsdoiorg1011111365-265612111
ModlmeierAPKeiserCNWattersJVSihAampPruittJN(2014)The keystone individual concept An ecological and evolutionaryoverview Animal Behavior 89 53ndash62 httpsdoiorg101016janbehav201312020
MontiglioP-OFerrariCampReacutealeD(2013)Socialnichespecializationunder constraints Personality social interactions and environmentalheterogeneityPhilosophical Transactions of the Royal Society of London Series B Biological Sciences36820120343httpsdoiorg101098rstb20120343
Moore A J Brodie III E D ampWolf J B (1997) Interacting pheno-types and the evolutionary process I Direct and indirect geneticeffects of social interactions Evolution 51 1352ndash1362 httpsdoiorg101111j1558-56461997tb01458x
NonacsPampKapheimKM(2007)Socialheterosisandthemaintenanceof genetic diversity Journal of Evolutionary Biology 20 2253ndash2265httpsdoiorg101111j1420-9101200701418x
Nussey D H Wilson A J amp Brommer J E (2007) The evolution-ary ecology of individual phenotypic plasticity in wild popula-tions Journal of Evolutionary Biology 20 831ndash844 httpsdoiorg101111j1420-9101200701300x
OtterKAStewartIRKMcGregorPKTerryAMRDabelsteenTampBurkeT(2001)Extra-pairpaternityamonggreattitsParus major following manipulation of male signals Journal of Avian Biology 32338ndash344httpsdoiorg101111j0908-88572001320408x
Pruitt J N Bolnick D I Sih A DiRienzo N amp Pinter-Wollman N(2016)Behavioralhypervolumesofspidercoloniespredictscommu-nity performance and disbandmentProceedings of the Royal Society B- Biological Sciences 283 20161409 httpsdoiorg101098rspb20161409
PruittJNampPinter-WollmanN(2015)Thelegacyeffectsofkeystonein-dividualsoncollectivebehaviourscaletohowlongtheyremainwithina group Proceedings of the Royal Society B- Biological Sciences 28220151766httpsdoiorg101098rspb20151766
RoyleNJHartley IROwens I P FampParkerGA (1999) Siblingcompetition and the evolution of growth rates in birds Proceedings of the Royal Society B 266 923ndash932 httpsdoiorg101098rspb19990725
SaltzJBampFoleyBR(2011)Naturalgeneticvariationinsocialnicheconstruction Social effects of aggression drive disruptive sexual se-lectioninDrosophila melanogaster American Naturalist177645ndash654httpsdoiorg101086659631
ShusterSM LonsdorfEVWimpGMBaileyJKampWhithamTG (2006) Community heritabilitymeasures the evolutionary conse-quencesofindirectgeneticeffectsoncommunitystructureEvolution60991ndash1003httpsdoiorg101111j0014-38202006tb01177x
SimmonsAMSimmonsJAampBatesMA (2008)Analyzingacous-tic interactions in natural bullfrog (Rana catesbeiana) chorusesJournal of Comparative Psychology 122 274ndash282 httpsdoiorg1010370735-70361223274
Sinervo B R amp Calsbeek R (2010) Behavioral concepts of selectionExperiments and genetic causes of selection on the sexes In D FWestneatampCWFox(Eds)Evolutionary behavioral ecologyLondonUKOxfordUniversityPress
Thompson J N (1982) Interaction and coevolution Chicago USA TheUniversityofChicagoPress
emspensp emsp | emsp1463MONTIGLIO eT aL
VanderWaal K L ObandaV Omondi G P McCowan BWang HFushingHampIsbellLA (2016)Thestrengthofweaktiesandhel-minth parasitism in giraffe social networks Behavioral Ecology 271190ndash1197httpsdoiorg101093behecoarw035
Ward P I (1993) Micro-habitat segregation and the mating systemof Gammarus pulex Animal Behavior 45 191ndash192 httpsdoiorg101006anbe19931019
Ward P I amp PorterAH (1993)The relative role of habitat structureandmale-malecompetition in thematingsystemofGammarus pulex (CrustaceaAmphipoda)AsimulationstudyAnimal Behavior45119ndash133httpsdoiorg101006anbe19931011
West-EberhardMJ(1989)Phenotypicplasticityandtheoriginsofdiver-sityAnnual Review of Ecology and Systematics20249ndash278httpsdoiorg101146annureves20110189001341
Westneat D F Hatch M IWetzel D P amp Ensminger A L (2011)IndividualvariationinparentalcarereactionnormsIntegrationofper-sonalityandplasticityAmerican Naturalist178652ndash667httpsdoiorg101086662173
Wilson A J Gelin U Perron M-C amp Reacuteale D (2009) Indirect ge-neticeffectsandtheevolutionofaggression inavertebratesystemProceedings of the Royal Society of London Series B Biological Sciences276533ndash541httpsdoiorg101098rspb20081193
Additional Supporting Informationmay be found online in the sup-portinginformationtabforthisarticle
How to cite this articleMontiglioP-OMcGlothlinJWFarineDRSocialstructuremodulatestheevolutionaryconsequencesofsocialplasticityAsocialnetworkperspectiveoninteractingphenotypesEcol Evol 201881451ndash1464 httpsdoiorg101002ece33753
APPENDIX
PHENOTYPIC MEAN AND VARIANCE
FollowingMooreetal(1997)wemodelasinglephenotypeofanindi-vidual (z)asanadditivecombinationoftheeffectsof itsowngenes(iedirectgeneticeffectsa)thenonsocialenvironmentitexperiences(e)andaplasticcomponentthatissomefunctionofthephenotypesinitssocialgroupMooreetal(1997)originallymodeledthesocialeffectasafunctionofthephenotypeofoneinteractingindividualMcGlothlinandBrodie (2009)andMcGlothlinetal (2010)consideredsocialef-fectsinapopulationconsistingofgroupsofnindividualswhereinter-actionswereassumedtooccursimultaneouslywithinagroupwithallindividuals within a group having the same strength of interactionHereweconsideramoregeneralsocialstructurewhereindividualsinteractwithallpossiblesocialinteractantsingroupsizenwithvaria-bleconnectionstrengthsirangingfrom0to1giving
wherethesummationistakenacrossalln minus1possiblesocialinterac-tionsforeachindividualsandψrepresentstheinteractioncoefficientwhichdetermines thestrengthanddirectionof the indirectpheno-typic effect of individual social interactantsHere and elsewhere aprimeindicatesaparameterbelongingtoasocialpartnerAnysocialnetworkstructurecanbemodeledbychangingthedistributionofs High-densitysocialnetworkswithstrongconnectionswillhavemanylargevaluesofswhilesparsernetworkswithweakerconnectionswillhavemanyweaksvalueswithmanyequaltozeroConsideringphenotypicfeedback(asdoMooreetal1997)insuch
The value of the two covariance terms represents how stronglystrengthofinteractiondependsonthegenesandenvironmentofin-dividualsocialpartnersThiscovarianceisdeterminedforeachindi-vidualandmayvaryacrossindividualsTheseshouldbepositiveunderhomophilyandnegativeunderheterophilyTakingthemeanandas-suming
=e=0
where double overbars indicate global means and large overbarswithintheparenthesesindicatemeanstakenacrossindividualsbasedonsummarystatisticsoftheirsocialgroupsThiscanbeexpandedasaboveto
The remainingcovariance terms represent theaveragedegree towhichindividualconnectionstrengthsareadjustedbasedonthephe-notypeofpotentialinteractantsInthecaseofhomophilyorheteroph-ilyindividualswillmakethisadjustmentbasedontheirownphenotypewithlargeindividualshavingapositivecovarianceandsmallindividu-alshavinganegativecovariance(orviceversa)ThereforeweexpecttheseaveragecovariancetermstotendtowardzeroMakingthisas-sumptionandrearrangingprovidesEquation2inthetext
EXTENSION TO MULTIPLE GROUPS
EquationA8iswrittenassumingthatthepopulationconsistsofasin-gle social networkwhere individualsmay interact in anywayNowassumethatthepopulationisdividedintomultiplegroupswhereindi-vidualsmay interactwithanystrengthswithinagroupanddonotinteract at all between groups Assuming the covariance terms inEquationA8arezeroandthatenvironmentaldeviationsdonotvaryamonggroupsthemeanofeachgroupwillbe
where overbars now indicate within-groupmeans Assuming equalgroupsizethepopulationmeanisnow
(IfgroupsvaryinsizethenEquationA10canbemodifiedtogiveaweightedmean) Ifconnectionstrengthhasnoheritablebasis thenthe covariance term become zero and EquationA10 collapses toEquation2inthetextWemaycalculateamong-groupvariancemosteasilybymakingafewassumptionsthatarealsomadeinoursimula-tionsFirstasaboveweassumethatgroupsareofequalsizeSecondweassume thatmean interactiondoesnotvaryacrossgroups ands=
=sMakingtheseassumptions
Thisshowsthat indirectgeneticeffectswillmagnifyslightdiffer-ences in genetic values across groups regardless of sign Strongermeanconnectionstrengthswillintensifythiseffect
RESPONSE TO SELECTION
FollowingMoore etal (1997) andMcGlothlin etal (2010) and as-suming that thecovariance terms inEquationA8areeither zeroorpopulation parameters that do not have a heritable component anindividualrsquostotalbreedingvaluecanbewrittenasthegeneticcontri-butiontothepopulationmean
where Ristheregressionofsaprimeonaandisthusanalogoustorelated-ness This assumes thatCov[aseprime] is negligible Positive values ofR indicatehomophilyandnegativevaluesindicateheterophilyMakingthissubstitutiongivesEquation4inthetextEquation4canalsobeexpresseddifferentlybyrearrangingas
hasnoeffectonthemeanphenotypeofeachgroup(Figure5)whichis consistent with our analytical model (Equation2) However in-creasednetworkassortmentisassociatedwithanincreaseinthevari-anceinindirectgeneticeffectsexperiencedbyindividualsinagivengroup(seethethirdterminEquation3Figure6a)Becauseindividu-alsinteractmorestronglywithconspecificsthathavesimilarbreedingvalues(highwithhighlowwithlow)thedirectandindirectgeneticcontributions to phenotypes act in concert and covary positively(fourthterm inEquation3Figure6b)Thesetwoeffectscontributetowardincreasingphenotypicvarianceobservedwithinagivengroup(Figure6c)Theseeffectsarereversedwhenψgisnegativedirectandindirect contributions to individual phenotypes act to oppose eachothertherebyreducingtheamountofphenotypicvarianceobservedin the population (see FigureS7) Increasing network assortmentalsoleadstoasmalldecreaseinthevarianceintotalbreedingvalues(Figure6dredline)Thisisattributabletotheslightdecreaseinden-sityassociatedwithhigherlevelsofnetworkassortment(ieindividu-alshavetheabilitytoreducetheconnectionstrengthwithparticulargroupmembers)aphenomenonnotcapturedbyouranalyticalmodel
Applying selection to groups with varying network assortmentshowsthatasynergybetweendirectandindirectgeneticeffectsleadstoanincreaseinevolutionarychangewithincreasingnetworkassort-ment(Figure7redline)Thisresultisinaccordwiththepredictionsofouranalyticalmodelwhichpredictsanincreasedresponsetoselec-tionwithincreasingR(Equation4)AlthoughEquation4suggestsden-sityandhomophilyshouldhavesymmetricaleffectstheincreaseseeninFigure7isnotasdramaticasthatinFigure4perhapsbecauseoftheconcomitantdecreaseindensitycausedbyallowinghomophilyinoursimulationsUnlikenetworkdensitynetworkassortmentdoesnotaffectthevariationofevolutionaryresponsesamonggroups(Figure7graydots)
4emsp |emspDISCUSSION
Inthisstudyweexploretheconsequencesofsocialplasticityandthestructureofinteractionsinshapingtheamountofphenotypicvariationwithingroupsof interactingindividualsandtheevolutionaryresponseofthesegroupstoselectionWeconsiderreplicategroupswithvary-ingstructuresofinteractionsSuchreplicatescouldbeseenasmultiplegroups of individualswithin a given population (eg tribes packs orcolonies)orasmultipleisolatedpopulationswithinanecologicalcom-munityThroughananalyticalmodelandagent-basedsimulationsweshowthatthestructureofsocialnetworksmodulatedtheimpactofin-directgeneticeffectsontheamountofphenotypicvarianceavailablefor selectionOur resultsemphasize that thenumberandstrengthofconnectionsamongindividuals(networkdensity)aswellaspreferentialassociations among individualswith a similar phenotype (network as-sortment)haveimportanteffectsonthecontributionofindirectgeneticeffectsNetworkdensityandassortmentalsomodulatetheabilityfortraitstoexhibitevolutionarychangeinresponsetoselectionIncreasingthenumberofinteractionsamonggroupmembers(networkdensity)in-creasestheaverageevolutionaryresponseofgroupstoselectionandin-creasesthevariationinresponsetoselectionamonggroupsBycontrastincreasednetworkassortmentleadstoanincreaseintheaverageevolu-tionaryresponseofgroupstoselectionbutdoesnotaffectthevariationinevolutionary responseamonggroupsOur resultshavewidespreadimplicationsforstudiesofsocialevolutionmultilevelselectionandtheemergenceofkeystoneindividuals(ModlmeierKeiserWattersSihampPruitt2014)andniche-constructingtraits(egSihampWatters2005)
41emsp|emspComparison with earlier interacting phenotype models
Our analytical results show that given some simplifying assump-tions (most importantly ignoring the potential for phenotypic
F IGURE 4emspEvolutionaryresponseofphenotypetoaselectiongradientvarieswithnetworkdensityTheaveragechangeinphenotypemeanresultingfromselectionincreasedwithnetworkdensity(redline)Groupswithdensernetworksofinteractionsexhibitedmorevariationinthechangeinphenotypicmean(graydots)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4
F IGURE 5emspTheaveragephenotypeofindividualsasafunctionofnetworkhomophily(redline)Eachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4Networkscouldnotreachhomophilyvaluesof1becauseweusedacontinuoustraitvalueratherthandiscretevalues(seeFarine2014)
1458emsp |emsp emspensp MONTIGLIO eT aL
feedback) considering more general social structures does notgreatlyalter theconclusionsofearliermodelsof interactingphe-notypeevolution(egMcGlothlinetal2010Mooreetal1997)First indirect genetic effects still alter the response to selectionby increasing the amount of genetic variance exposed to selec-tionNote thatbecausewedonotmodel feedback thiseffect is
directional with positiveψg (ie becomingmore similar to onersquosneighbors)increasingtheresponsetoselectionandnegativevalues(iebecomingmoredifferentfromonersquosneighbors)decreasingitSecondhomophilyheterophilyplaysa rolesimilar to relatednessinpreviousmodelsinalteringtheresponsetoselection(McGlothlinetal2010)IndeedMcGlothlinetal(2010)noted(ashavemanyothers)thatrelatednessperseisjustaspecialcaseofphenotypicassortment
Themostnotabledifferencebetweenourmodelandearliermod-elsisthatindividualsareallowedtodifferintheirinfluenceonsocialplasticityduetovariation inconnectionstrength (s)Perhapsunsur-prisingly responsetoselection ismorestrongly influencedbysocialinteractions indensernetworkswhere interactionsarestrongerandmorecommonaneffect that isapparent inbothouranalyticalandsimulation results Inour simulation resultswealso find thatvaria-tioninresponsetoselectionamongincreaseswithgreaterconnectionstrengthThis could occur because in some groups themostwell-connectedindividualshappentohaverelativelyhighorlowbreedingvaluesThesewell-connected individualswould thenhaveadispro-portionateeffectonthephenotypeofothers (relativeto individualsclosertothepopulationrsquosaveragebreedingvalue)byexertingastrongeffectonthemeansocialenvironmentexperiencedbyindividualsIndoingsowell-connectedextremeindividualscangeneratevariabilityinthecovariancebetweenbreedingvaluesandphenotypeandthusintheresponsetoselectionFuturemodelsshouldallowconnectionstrength to display a heritable component which would allow thesocialnetworkstructureitselftoevolveinresponsetosucheffects
F IGURE 6emspEffectofnetworkhomophilyon(a)thevariationinindirecteffects(b)thecorrelationbetweendirectandindirectgeneticeffects(c)therelativechangeinphenotypicvariancewithingroupsand(d)therelativechangeintotalgeneticvariationEachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4HomophilysimultaneouslyincreasesvariationamongindividualsinindirectgeneticeffectswithingroupsandgeneratesastrongpositivecovariancebetweendirectandindirectgeneticeffectstherebysubstantiallyincreasingthephenotypicvarianceobservedwithingroupsHoweverthisincreaseinphenotypicvarianceisnotassociatedwithanychangeatthegeneticlevel
F IGURE 7emspEvolutionaryresponseofphenotypetoaselectiongradientincreaseswithnetworkhomophily(redlineandgraydots)Eachdotrepresentsthechangeinmeangenotypeacrossgenerationsinasinglesimulatednetworkorgroupof50individuals(Ngroup=50)TheredlinerepresentstheaverageevolutionaryresponseasafunctionofnetworkdensityIndirectgeneticeffectsweregeneratedusingaψgof4
emspensp emsp | emsp1459MONTIGLIO eT aL
Studiesinthewildhaveshownthatpositioninasocialnetworkmaybe repeatable and have fitness consequences suggesting that con-nectionstrengthmaybeanevolvabletrait (AplinFirthetal2015FormicaWoodCookampBrodie2017Formicaetal2012)
42emsp|emspGroups with denser connections exert a stronger ldquopull to the meanrdquo
Our simulations show that groupswhere individuals have an in-termediatenumberorstrengthofsocialconnections (iegroupswithintermediatenetworkdensities)allowforthegreatestwithin-groupvariationinsocialenvironmentsexperiencedamongindivid-ualsThispatternariseswithinagenerationduetosocialplasticityratherthanasaresponsetoanyselectivepressureBygeneratinga greater range of phenotypes and social environments groupswithan intermediatedensityof social interactionscouldprovidethe basis for the emergence and evolution of alternative socialphenotypes (Bergmuumlller amp Taborsky 2010 Sinervo amp Calsbeek2010) When social phenotypes are subject to indirect geneticeffects the maintenance of variation in social behavior shouldthus be observed more frequently in groups with intermediateconnectedness
Whilelowtointermediatedensitiesofsocialinteractionsofferthewidestscopeforpromotingindividualvariationinphenotypegroupswith high densities exhibit a very different patternAs the numberand strengths of interactions increases among group members in-direct genetic effects experienced by each individual becomemoresimilarbecauseallgroupmembersstarttobecomeconnectedtooneanotherand theseconnectionsareuniformlystrong Inadditionasnetworksbecomemoreconnectedindividualsattheextremesofthedistributionofgenetic tendencies in thegroups (ie the individualsfurthest from the averagebreedingvalue) tend to experience a so-cialenvironmentexertinganopposingeffectontheirphenotype(ieCov[a+esa +se] in Equation3 becomes more negative) This ldquopullto themeanrdquo is stronger in smaller groups than in larger ones (seeFigureS5) anddecreases thepopulationphenotypicvariancewhenψg ispositive (egwhen individuals increasetheiraggressiveness inresponse to the aggression they receive) and increases it whenψg is negative (egwhen individuals inhibit their aggressiveness in re-sponsetotheaggressiontheyreceive)Whenindividualsexhibit im-portantphenotypicplasticitysuchaneffectappearssimilartosocialconformity where individuals express more similar phenotypes asgroupsthan in isolation (egHerbert-Readetal2013MagnhagenampBunnefeld2009)Conformity isusually thought toemergewhendissimilarindividualsareatafitnessdisadvantageForexamplepred-ators tend topick individuals that standout amonggroupsofpreyselecting forhomogeneousgroups (LandeauampTerborgh1986)Weshowherethatconformist-likepatternsinbehaviorcanemergefromverysimpleformsofsocialplasticity Importantlyweshowthatbe-havioralconformitycanemergeevenwhenindividualsarenotactivelycopyingthemostabundantphenotypeoftheirgroup inabsenceofanyselectivepressureExamplesofhighlyconnectedgroupsinnatureincludechorusesofmalesinsomespeciesoffrogsproducingmating
calls or leks ofmales displaying to attract females and adjust theirsignalingeffortinresponsetothesignalingoftheirrivals(Boatright-HorowitzHorowitzampSimmons2000SimmonsSimmonsampBates2008)Whenmalesareclosetoeachotherandeachmalecanadjustits signaling intensity to that of all the othermaleswe expect thisldquopulltothemeanrdquotodecreasethevariationinmalesignals(althoughsocialplasticitycantakemorecomplexpatternsthenismodeledhereGreenfieldampRand2000)Thiscandecreasetheeffectivenessoffe-malematechoiceandtheintensityofsexualselection
43emsp|emspGroups with denser connections potentiated the effect of keystone individuals
Aninsightfromoursimulationsisthatwheneverindividualsadjusttheirphenotypetotheaveragesocialenvironmentthattheyexperi-enceindividualsattheextremesofthegenotypicorphenotypicdis-tributionhavethegreatestimpactonthephenotypeofothergroupmembers This phenomenon arises because these individuals havethestrongest impacton themeansocialenvironmentexperiencedbytheirconspecificsTheevolutionofniche-constructingtraitsal-lowingsomeindividualstomanipulatetheirgroupinawaythatfa-vorstheirownsuccess(SaltzGeigerAndersonJohnsonampMarren2016) or to have a disproportionate effect on their group (Keiseramp Pruitt 2014 Modlmeier etal 2014 Pruitt amp Pinter-Wollman2015)hasbeenthefocusofmuchinterestrecentlySurprisinglynostudyhasexplored the implicationsof theexactpatternsofsocialplasticity for the identity and impact of such ldquokeystone individu-alsrdquo (Modlmeier etal 2014) It is reasonable to assume thatmostanimalsexhibitingsocialplasticityshouldadjusttheirphenotypeinresponse to theaverage socialconditions that theyexperience (al-thoughinsomecasessomeindividualscanadjusttheirphenotypeto themaximumor to theminimumphenotypicvalueof the indi-vidualswithwhomtheyinteractseeDyerCroftMorrellampKrause2009 for a potential example) Thus our simulations suggest thattheemergenceofkeystoneindividualsmightbeaphenomenonfarmore common than previously envisioned Keystone individualscouldemergeinanygroupofinteractingindividualsexhibitingphe-notypicplasticityanddenseinteractionnetworks(asinthelekkingexampleabove)Hencetheemergenceofkeystoneindividualsmightnotrequireacomplexsocialsystemdivisionoflabor(PruittBolnickSihDiRienzoampPinter-Wollman2016) collectivebehavior (PruittampPinter-Wollman2015)orniche-constructingtraits (egaggres-sivenesspolicingorelseChangampSih2013)butshouldbemostcommon in specieswhere individuals respond to thebehaviors ofthemajorityofgroupmembers
Denserinteractionsamongindividualswithinagrouppotentiatetheimpactofindividualswithextremephenotypicvaluesbyallow-ing these to interact and affect themajority of their groupmem-bersHencetheconsequencesofindividualsocialplasticitytendtobecomemuchgreater ingroupsasnetworkdensity increasesThisldquoamplificationrdquoeffectisalsostrongerwhengenotypesfollowauni-formdistribution (iewhenextremegenotypesaremorefrequentwithin groups) thanwhen they followaGaussiandistribution (ie
1460emsp |emsp emspensp MONTIGLIO eT aL
whenextremegenotypesarerarewithingroups)Networkdensityincreases the evolutionary response of groups on average groupswith denser connections also exhibit increasedvariation in evolu-tionaryresponsetoagivenselectiongradientSuchan increase inthevariationinevolutionaryresponseobservedinourstudyisap-parentbecauseourapproachallowsustorelaxtheassumptionthatindividualswithingroupsinteractequallywithallothergroupmem-bersbyintroducinganewparameter(averageconnectionstrength=s)intoourmodelandinsteadtoexplicitlyexploretheeffectofcon-nectiondensity
44emsp|emspHomophily affects the amount of phenotypic variation within groups
Our simulations also investigate the consequencesof social struc-turewhenindividualscaninteractpreferentiallywithindividualsthathaveasimilar(iehomophily)ordissimilar(ieheterophily)pheno-typeNetworkassortment(thenetworkmeasureofhomophily)doesnot have any impact on groupsrsquomean phenotype but can gener-ateagreatervariationinsocialenvironmentswithingroupsHenceassuming that different immediate social environments can favordifferent (alternative) phenotypes within groups our simulationssuggest that homophily should be associatedwith the emergenceof phenotypic variation among individuals (or social specializationBergmuumlller amp Taborsky 2010 Montiglio Ferrari amp Reacuteale 2013)Homophilyalsohasdirectconsequencesfortheevolutionofalter-nativephenotypesbycreatingsynergyoroppositionbetweendirectand indirect genetic effectsWhen social plasticity (ψg) is positive(egwheninteractingwithanaggressiveindividualincreasesafocalindividualrsquosaggression)andindividualsshowatendencytointeractwithsimilarphenotypesthesocialenvironmentactstoshapetheirphenotypeinthesamedirectionastheirgenotypeAsaresultsocialinteractionsandsocialplasticityincreasethephenotypicvarianceofthetraitrelativetoasituationinwhichconnectionsarerandominterms of their traits It also tends to increase the strength of theevolutionaryresponsetoselectioninresponsetoagivenselectiongradientThisincreaseinevolutionaryresponsearisesfromthesyn-ergybetweendirectandindirecteffect(orbetweensocialplasticityandhomophily)ratherthanfromachangeintotalgeneticvariationwithingroups
45emsp|emspPossible applications and tests of the model and future directions
differentialandmatechoicebyfemalesThestrengthofconnectionsbetweenmales of known phenotype could be increased artificiallyusingplaybacks tosimulatemore frequent interactionsamong indi-viduals(DabelsteenampPedersen1990Otteretal2001)tomonitorhowsuchincreasesinconnectionstrengthaffecttheextentofpheno-typicandgeneticadditivevariationAlternativelyonecanmanipulatethedistributionofterritoriesavailableandthepatternsofinteractionsby controlling the locationof nest boxes foodpatches or refugesSuchapproachescouldbeparticularlysuitableforcavity-nestingbirds(Both1998)
Ourmodel also studied the consequences of homophily for theevolutionary responses of phenotypic traits Assuming individualshave some level of control on their interactions homophily can beobservedwhen individualsexhibitpreferences to interactwithcon-specificsthatare(dis)similartothemSuchpreferencescouldexplainthemaintenanceofaltruisticbehaviorbecauseoftheirpotentialroleinshapingtheselectionpressuresactingonaltruismSomeworkonfruitflieshavereportedthatindividualpreferencesforparticularsocialenvironmentsisassociatedwithgeneticvariationandcanthuspoten-tiallyevolve (egSaltzampFoley2011)Onecould testourmodel insuchstudysystemsbyeitherallowingorpreventingtheexpressionofsocialpreferences(throughmixingofindividualsormanipulatingtheirinteractions) Alternatively homophily can also be observed whenindividualssegregateintheenvironmentasafunctionoftheirphe-notype(HelfensteinDanchinampWagner2004Ward1993WardampPorter1993)Forexamplemoreandlessaggressiveindividualsseg-regateinpatcheswithdifferentdensitiesofconspecifics(Duckworth2006)Thusbymanipulatingtheheterogeneityandthescaleatwhichitisobserved(iethesizeofpatchesofdifferenthabitat)onecouldtestthepredictionsofourmodelFutureworkwillexpandthemodelwe presented here to analyze the consequences of such traits forthemaintenanceofphenotypicvariationandtheevolutionofsocialstructure
One limitationofourmodel is thatweassumebothphenotypicfeedback(Mooreetal1997)andsocialselection(Wolfetal1999)tobeabsentIncludingfeedbackmayaltertheconclusionswehavepre-sentedhereasfeedbackeffectsmaycausesocialplasticitytomovethroughnetworksincounterintuitivewaysItispossiblethatnetworkmetricsbeyondconnectionstrength (suchasclusteringcoefficientsbetweennessetc)may influencewhetherfeedbackcontributessig-nificantly to variation and response to selection Regarding socialselectionwehaveshownherethatconnectionstrengthcontributestoamong-groupvariancewhichshould intensifyresponsetohigherlevelsofselectionsuchassocialselectionWewilltreatbothfeedbackandsocialselectioninfuturecontributions
5emsp |emspCONCLUSION
Wepresentbothananalyticmodelandsimulationsextendingpre-vious work on social phenotypic plasticity to more general socialstructuresOurstudygeneratesafirstsetofverygeneralandtest-able predictions on the role of social structure in modulating the
emspensp emsp | emsp1461MONTIGLIO eT aL
consequencesofsocialplasticityWeshowthatthebasiccharacter-isticsofthestructureofinteractionsamongindividualsingroupsandpopulationscanhaveimpactsontheconsequencesofsocialplasticityforthemeanphenotypeexpressedbytheindividualstheextentofphenotypicvariationavailableforselectionandfortheabilityofthepopulation to respond to selectivepressuresWehope that futurestudieswillbeabletotestourpredictionsempiricallybyapplyingourapproachtothestudyofsocialbehavior(egaggressionandcoop-eration)socialinformationuseoralternativematingtacticsinpopu-lationswithvaryingpatternsofsocialormatinginteractionsFromatheoreticalperspectivefutureresearchwouldwarrantinvestigatingthelinkbetweenindividualpositioninsocialnetworksandtheindi-rect genetic effects it experiences and thuswhether factors otherthan individualsrsquo breeding values can lead to keystone individualsFurtherinourstudyweassumethatallindividualsexpressedplas-ticityidenticallyHoweverindividualshavealsobeenshowntovaryintheirplasticity(DingemanseKazemReacutealeampWright2010NusseyWilsonampBrommer2007WestneatHatchWetzelampEnsminger2011)andsuchvariationmayalterthepredictionsofinteractingphe-notypemodels(KazancıoğluKlugampAlonzo2012)Linkingindividualdifferencesinbothsocialpositionandplasticitycouldyieldnewin-sightsandagreaterunderstandingoftheevolutionarymechanismsthatunderpinphenotypicvariationwithinindividualsbetweenindi-vidualsandamongpopulations
ACKNOWLEDGMENTS
We thank the Reader Hendry and Barrett laboratories in McGillUniversity forconstructivecommentsonadraftof thismanuscriptPOMwas supported by aNSERCpostdoctoral fellowshipDRF re-ceived funding from a grant to theBBSRC (BBL0060811 toBCSheldon)andtheMaxPlanckSociety
CONFLICT OF INTEREST
Nonedeclared
AUTHOR CONTRIBUTIONS
POMandDRFbuiltthesimulationsandJWMdevelopedthemodelPOMdrafted themanuscript andproduced the figuresAll authorscontributedtorevisionsandapprovedthefinalversionofthearticle
AplinLMFarineDRMorand-FerronJCockburnAThorntonAamp SheldonBC (2015) Experimentally induced innovations lead topersistentcultureviaconformityinwildbirdsNature518538ndash541
Aplin LMFirthJAFarineDRVoelklBCratesRACulinaAhellipSheldonBC (2015)Consistent individual differences in the so-cialphenotypesofwildgreattits(Parusmajor)Animal Behaviour108117ndash127httpsdoiorg101016janbehav201507016
BaileyNWampHoskins J L (2014)Detecting cryptic indirect geneticeffectsEvolution681871ndash1882httpsdoiorg101111evo12401
Bailey N W amp Zuk M (2012) Socially flexible female choice differsamongpopulationsofthePacificfieldcricketGeographicalvariationin the interaction coefficient psi (Ψ)Proceedings of the Royal Society of London Series B Biological Sciences 279 3589ndash3596 httpsdoiorg101098rspb20120631
Bergmuumlller R amp Taborsky M (2010) Animal personality due to socialnichespecialisationTrends in Ecology amp Evolution25504ndash511httpsdoiorg101016jtree201006012
Bijma P ampWade M J (2008) The joint effects of kin multilevel se-lection and indirect genetic effects on response to genetic selec-tion Journal of Evolutionary Biology 21 1175ndash1188 httpsdoiorg101111j1420-9101200801550x
Boatright-HorowitzSLHorowitzSSampSimmonsAM(2000)Patternsof vocal interactions n a BullfrogRana catesbeiana chorus preferen-tial responding to farneighborsEthology106701ndash712httpsdoiorg101046j1439-0310200000580x
BothC(1998)Experimentalevidencefordensitydependenceofrepro-ductioningreattitsJournal of Animal Ecology67667ndash674httpsdoiorg101046j1365-2656199800228x
Cappa E P amp Cantet R J C (2008) Direct and competition additiveeffects in treebreedingBayesianestimation froman individual treemixedmodelSilvae Genetica5745ndash56
ChangAampSihA (2013)Multilevel selection andeffects of keystonehyperaggressivemalesonmatingsuccessandbehaviorinstreamwaterstridersBehavioral Ecology241166ndash1176httpsdoiorg101093behecoart044
Clutton-BrockTH(1989)MammalianmatingsystemsProceedings of the Royal Society B236339ndash372httpsdoiorg101098rspb19890027
Crowley P H amp Cox J J (2011) Intraguild mutualism Trends in Ecology amp Evolution 26 627ndash633 httpsdoiorg101016jtree201107011
Duckworth R A (2006) Aggressive behaviour affects selection onmorphology by influencing settlement patterns in a passerine birdProceedings of the Royal Society B 273 1789ndash1795 httpsdoiorg101098rspb20063517
Farine D R (2014) Measuring phenotypic assortment in animal so-cial networks Weighted associations are more robust than binaryedges Animal Behavior 89 141ndash153 httpsdoiorg101016janbehav201401001
FarineDRampWhiteheadH(2015)Constructingconductingandinter-preting animal social network analysis Journal of Animal Ecology841144ndash1163httpsdoiorg1011111365-265612418
Fawcett TW amp Johnstone RA (2010) Learning your own strengthWinner and loser effects should change with age and experienceProceedings of the Royal Society of London Series B Biological Sciences2771427ndash1434httpsdoiorg101098rspb20092088
Fisher D N amp McAdam A G (2017) Social traits social networksand evolutionary biology Journal of Evolutionary Biology httpsdoiorg101111jeb13195Inpress
FormicaVAWood CW LarsenW B Butterfield R EAugatMEHougenHYampBrodieIIIED(2012)Fitnessconsequencesofsocialnetworkpositioninawildpopulationofforkedfungusbeetles(Bolitotherus cornutus) Journal of Evolutionary Biology 25 130ndash137httpsdoiorg101111j1420-9101201102411x
Greenfield M D amp Rand S A (2000) Frogs have rules selective at-tention algorithms regulate chorusing in Physalaemus pustulosus (Leptodactylidae)Ethology106131ndash147
Helfenstein FDanchin E ampWagner RH (2004)Assortativematingand sexual size dimorphism in blacklegged kittiwakes Waterbirds27 350ndash354 httpsdoiorg1016751524-4695(2004)027[0350AMASSD]20CO2
Herbert-Read J E Krause S Morrell L J Schaerf T M Krause JampWardAJW (2013)The roleof individuality in collectivegroupmovementProceedings of the Royal Society B- Biological Sciences28020122564
KeiserCNampPruittJN (2014)Personality composition ismore im-portantthangroupsizeindeterminingcollectiveforagingbehaviourinthewildProceedings of the Royal Society of London Series B Biological Sciences28120141424httpsdoiorg101098rspb20141424
Krause J amp Ruxton GD (2002) Living in groups Oxford UKOxfordUniversityPress
Landeau L ampTerborgh J (1986)Oddity and the ldquoconfusion effectrdquo inpredationAnimal Behavior341372ndash1380httpsdoiorg101016S0003-3472(86)80208-1
Magnhagen C amp Bunnefeld N (2009) Express your personality or goalong with the group What determines the behaviour of shoalingperchProceedings of the Royal Society B- Biological Sciences2763369ndash3375httpsdoiorg101098rspb20090851
McDonaldG C FarineD R Foster K R ampBiernaskie JM (2017)Assortment and the analysis of natural selection on social traitsEvolution712693ndash2702httpsdoiorg101111evo13365
McGlothlin JW amp Brodie III E D (2009) How to measure individ-ual genetic effects The congruence of trait-based and variance-partitioning approaches Evolution 63 1785ndash1795 httpsdoiorg101111j1558-5646200900676x
McGlothlin J W Moore A J Wolf J B amp Brodie III E D(2010) Interacting phenotypes and the evolutionary pro-cess III Social evolution Evolution 64 2558ndash2574 httpsdoiorg101111j1558-5646201001012x
MillerJRBAmentJMampSchmitzOJ (2014)Fearon themovePredatorhuntingmodepredictsvariation inpreymortalityandplas-ticityinpreyspatialresponseJournal of Animal Ecology83214ndash222httpsdoiorg1011111365-265612111
ModlmeierAPKeiserCNWattersJVSihAampPruittJN(2014)The keystone individual concept An ecological and evolutionaryoverview Animal Behavior 89 53ndash62 httpsdoiorg101016janbehav201312020
MontiglioP-OFerrariCampReacutealeD(2013)Socialnichespecializationunder constraints Personality social interactions and environmentalheterogeneityPhilosophical Transactions of the Royal Society of London Series B Biological Sciences36820120343httpsdoiorg101098rstb20120343
Moore A J Brodie III E D ampWolf J B (1997) Interacting pheno-types and the evolutionary process I Direct and indirect geneticeffects of social interactions Evolution 51 1352ndash1362 httpsdoiorg101111j1558-56461997tb01458x
NonacsPampKapheimKM(2007)Socialheterosisandthemaintenanceof genetic diversity Journal of Evolutionary Biology 20 2253ndash2265httpsdoiorg101111j1420-9101200701418x
Nussey D H Wilson A J amp Brommer J E (2007) The evolution-ary ecology of individual phenotypic plasticity in wild popula-tions Journal of Evolutionary Biology 20 831ndash844 httpsdoiorg101111j1420-9101200701300x
OtterKAStewartIRKMcGregorPKTerryAMRDabelsteenTampBurkeT(2001)Extra-pairpaternityamonggreattitsParus major following manipulation of male signals Journal of Avian Biology 32338ndash344httpsdoiorg101111j0908-88572001320408x
Pruitt J N Bolnick D I Sih A DiRienzo N amp Pinter-Wollman N(2016)Behavioralhypervolumesofspidercoloniespredictscommu-nity performance and disbandmentProceedings of the Royal Society B- Biological Sciences 283 20161409 httpsdoiorg101098rspb20161409
PruittJNampPinter-WollmanN(2015)Thelegacyeffectsofkeystonein-dividualsoncollectivebehaviourscaletohowlongtheyremainwithina group Proceedings of the Royal Society B- Biological Sciences 28220151766httpsdoiorg101098rspb20151766
RoyleNJHartley IROwens I P FampParkerGA (1999) Siblingcompetition and the evolution of growth rates in birds Proceedings of the Royal Society B 266 923ndash932 httpsdoiorg101098rspb19990725
SaltzJBampFoleyBR(2011)Naturalgeneticvariationinsocialnicheconstruction Social effects of aggression drive disruptive sexual se-lectioninDrosophila melanogaster American Naturalist177645ndash654httpsdoiorg101086659631
ShusterSM LonsdorfEVWimpGMBaileyJKampWhithamTG (2006) Community heritabilitymeasures the evolutionary conse-quencesofindirectgeneticeffectsoncommunitystructureEvolution60991ndash1003httpsdoiorg101111j0014-38202006tb01177x
SimmonsAMSimmonsJAampBatesMA (2008)Analyzingacous-tic interactions in natural bullfrog (Rana catesbeiana) chorusesJournal of Comparative Psychology 122 274ndash282 httpsdoiorg1010370735-70361223274
Sinervo B R amp Calsbeek R (2010) Behavioral concepts of selectionExperiments and genetic causes of selection on the sexes In D FWestneatampCWFox(Eds)Evolutionary behavioral ecologyLondonUKOxfordUniversityPress
Thompson J N (1982) Interaction and coevolution Chicago USA TheUniversityofChicagoPress
emspensp emsp | emsp1463MONTIGLIO eT aL
VanderWaal K L ObandaV Omondi G P McCowan BWang HFushingHampIsbellLA (2016)Thestrengthofweaktiesandhel-minth parasitism in giraffe social networks Behavioral Ecology 271190ndash1197httpsdoiorg101093behecoarw035
Ward P I (1993) Micro-habitat segregation and the mating systemof Gammarus pulex Animal Behavior 45 191ndash192 httpsdoiorg101006anbe19931019
Ward P I amp PorterAH (1993)The relative role of habitat structureandmale-malecompetition in thematingsystemofGammarus pulex (CrustaceaAmphipoda)AsimulationstudyAnimal Behavior45119ndash133httpsdoiorg101006anbe19931011
West-EberhardMJ(1989)Phenotypicplasticityandtheoriginsofdiver-sityAnnual Review of Ecology and Systematics20249ndash278httpsdoiorg101146annureves20110189001341
Westneat D F Hatch M IWetzel D P amp Ensminger A L (2011)IndividualvariationinparentalcarereactionnormsIntegrationofper-sonalityandplasticityAmerican Naturalist178652ndash667httpsdoiorg101086662173
Wilson A J Gelin U Perron M-C amp Reacuteale D (2009) Indirect ge-neticeffectsandtheevolutionofaggression inavertebratesystemProceedings of the Royal Society of London Series B Biological Sciences276533ndash541httpsdoiorg101098rspb20081193
Additional Supporting Informationmay be found online in the sup-portinginformationtabforthisarticle
How to cite this articleMontiglioP-OMcGlothlinJWFarineDRSocialstructuremodulatestheevolutionaryconsequencesofsocialplasticityAsocialnetworkperspectiveoninteractingphenotypesEcol Evol 201881451ndash1464 httpsdoiorg101002ece33753
APPENDIX
PHENOTYPIC MEAN AND VARIANCE
FollowingMooreetal(1997)wemodelasinglephenotypeofanindi-vidual (z)asanadditivecombinationoftheeffectsof itsowngenes(iedirectgeneticeffectsa)thenonsocialenvironmentitexperiences(e)andaplasticcomponentthatissomefunctionofthephenotypesinitssocialgroupMooreetal(1997)originallymodeledthesocialeffectasafunctionofthephenotypeofoneinteractingindividualMcGlothlinandBrodie (2009)andMcGlothlinetal (2010)consideredsocialef-fectsinapopulationconsistingofgroupsofnindividualswhereinter-actionswereassumedtooccursimultaneouslywithinagroupwithallindividuals within a group having the same strength of interactionHereweconsideramoregeneralsocialstructurewhereindividualsinteractwithallpossiblesocialinteractantsingroupsizenwithvaria-bleconnectionstrengthsirangingfrom0to1giving
wherethesummationistakenacrossalln minus1possiblesocialinterac-tionsforeachindividualsandψrepresentstheinteractioncoefficientwhichdetermines thestrengthanddirectionof the indirectpheno-typic effect of individual social interactantsHere and elsewhere aprimeindicatesaparameterbelongingtoasocialpartnerAnysocialnetworkstructurecanbemodeledbychangingthedistributionofs High-densitysocialnetworkswithstrongconnectionswillhavemanylargevaluesofswhilesparsernetworkswithweakerconnectionswillhavemanyweaksvalueswithmanyequaltozeroConsideringphenotypicfeedback(asdoMooreetal1997)insuch
The value of the two covariance terms represents how stronglystrengthofinteractiondependsonthegenesandenvironmentofin-dividualsocialpartnersThiscovarianceisdeterminedforeachindi-vidualandmayvaryacrossindividualsTheseshouldbepositiveunderhomophilyandnegativeunderheterophilyTakingthemeanandas-suming
=e=0
where double overbars indicate global means and large overbarswithintheparenthesesindicatemeanstakenacrossindividualsbasedonsummarystatisticsoftheirsocialgroupsThiscanbeexpandedasaboveto
The remainingcovariance terms represent theaveragedegree towhichindividualconnectionstrengthsareadjustedbasedonthephe-notypeofpotentialinteractantsInthecaseofhomophilyorheteroph-ilyindividualswillmakethisadjustmentbasedontheirownphenotypewithlargeindividualshavingapositivecovarianceandsmallindividu-alshavinganegativecovariance(orviceversa)ThereforeweexpecttheseaveragecovariancetermstotendtowardzeroMakingthisas-sumptionandrearrangingprovidesEquation2inthetext
EXTENSION TO MULTIPLE GROUPS
EquationA8iswrittenassumingthatthepopulationconsistsofasin-gle social networkwhere individualsmay interact in anywayNowassumethatthepopulationisdividedintomultiplegroupswhereindi-vidualsmay interactwithanystrengthswithinagroupanddonotinteract at all between groups Assuming the covariance terms inEquationA8arezeroandthatenvironmentaldeviationsdonotvaryamonggroupsthemeanofeachgroupwillbe
where overbars now indicate within-groupmeans Assuming equalgroupsizethepopulationmeanisnow
(IfgroupsvaryinsizethenEquationA10canbemodifiedtogiveaweightedmean) Ifconnectionstrengthhasnoheritablebasis thenthe covariance term become zero and EquationA10 collapses toEquation2inthetextWemaycalculateamong-groupvariancemosteasilybymakingafewassumptionsthatarealsomadeinoursimula-tionsFirstasaboveweassumethatgroupsareofequalsizeSecondweassume thatmean interactiondoesnotvaryacrossgroups ands=
=sMakingtheseassumptions
Thisshowsthat indirectgeneticeffectswillmagnifyslightdiffer-ences in genetic values across groups regardless of sign Strongermeanconnectionstrengthswillintensifythiseffect
RESPONSE TO SELECTION
FollowingMoore etal (1997) andMcGlothlin etal (2010) and as-suming that thecovariance terms inEquationA8areeither zeroorpopulation parameters that do not have a heritable component anindividualrsquostotalbreedingvaluecanbewrittenasthegeneticcontri-butiontothepopulationmean
where Ristheregressionofsaprimeonaandisthusanalogoustorelated-ness This assumes thatCov[aseprime] is negligible Positive values ofR indicatehomophilyandnegativevaluesindicateheterophilyMakingthissubstitutiongivesEquation4inthetextEquation4canalsobeexpresseddifferentlybyrearrangingas
feedback) considering more general social structures does notgreatlyalter theconclusionsofearliermodelsof interactingphe-notypeevolution(egMcGlothlinetal2010Mooreetal1997)First indirect genetic effects still alter the response to selectionby increasing the amount of genetic variance exposed to selec-tionNote thatbecausewedonotmodel feedback thiseffect is
directional with positiveψg (ie becomingmore similar to onersquosneighbors)increasingtheresponsetoselectionandnegativevalues(iebecomingmoredifferentfromonersquosneighbors)decreasingitSecondhomophilyheterophilyplaysa rolesimilar to relatednessinpreviousmodelsinalteringtheresponsetoselection(McGlothlinetal2010)IndeedMcGlothlinetal(2010)noted(ashavemanyothers)thatrelatednessperseisjustaspecialcaseofphenotypicassortment
Themostnotabledifferencebetweenourmodelandearliermod-elsisthatindividualsareallowedtodifferintheirinfluenceonsocialplasticityduetovariation inconnectionstrength (s)Perhapsunsur-prisingly responsetoselection ismorestrongly influencedbysocialinteractions indensernetworkswhere interactionsarestrongerandmorecommonaneffect that isapparent inbothouranalyticalandsimulation results Inour simulation resultswealso find thatvaria-tioninresponsetoselectionamongincreaseswithgreaterconnectionstrengthThis could occur because in some groups themostwell-connectedindividualshappentohaverelativelyhighorlowbreedingvaluesThesewell-connected individualswould thenhaveadispro-portionateeffectonthephenotypeofothers (relativeto individualsclosertothepopulationrsquosaveragebreedingvalue)byexertingastrongeffectonthemeansocialenvironmentexperiencedbyindividualsIndoingsowell-connectedextremeindividualscangeneratevariabilityinthecovariancebetweenbreedingvaluesandphenotypeandthusintheresponsetoselectionFuturemodelsshouldallowconnectionstrength to display a heritable component which would allow thesocialnetworkstructureitselftoevolveinresponsetosucheffects
F IGURE 6emspEffectofnetworkhomophilyon(a)thevariationinindirecteffects(b)thecorrelationbetweendirectandindirectgeneticeffects(c)therelativechangeinphenotypicvariancewithingroupsand(d)therelativechangeintotalgeneticvariationEachdotrepresentsasimulatednetworkorgroupof50individuals(Ngroup=50)Indirectgeneticeffectsweregeneratedusingaψgof4HomophilysimultaneouslyincreasesvariationamongindividualsinindirectgeneticeffectswithingroupsandgeneratesastrongpositivecovariancebetweendirectandindirectgeneticeffectstherebysubstantiallyincreasingthephenotypicvarianceobservedwithingroupsHoweverthisincreaseinphenotypicvarianceisnotassociatedwithanychangeatthegeneticlevel
F IGURE 7emspEvolutionaryresponseofphenotypetoaselectiongradientincreaseswithnetworkhomophily(redlineandgraydots)Eachdotrepresentsthechangeinmeangenotypeacrossgenerationsinasinglesimulatednetworkorgroupof50individuals(Ngroup=50)TheredlinerepresentstheaverageevolutionaryresponseasafunctionofnetworkdensityIndirectgeneticeffectsweregeneratedusingaψgof4
emspensp emsp | emsp1459MONTIGLIO eT aL
Studiesinthewildhaveshownthatpositioninasocialnetworkmaybe repeatable and have fitness consequences suggesting that con-nectionstrengthmaybeanevolvabletrait (AplinFirthetal2015FormicaWoodCookampBrodie2017Formicaetal2012)
42emsp|emspGroups with denser connections exert a stronger ldquopull to the meanrdquo
Our simulations show that groupswhere individuals have an in-termediatenumberorstrengthofsocialconnections (iegroupswithintermediatenetworkdensities)allowforthegreatestwithin-groupvariationinsocialenvironmentsexperiencedamongindivid-ualsThispatternariseswithinagenerationduetosocialplasticityratherthanasaresponsetoanyselectivepressureBygeneratinga greater range of phenotypes and social environments groupswithan intermediatedensityof social interactionscouldprovidethe basis for the emergence and evolution of alternative socialphenotypes (Bergmuumlller amp Taborsky 2010 Sinervo amp Calsbeek2010) When social phenotypes are subject to indirect geneticeffects the maintenance of variation in social behavior shouldthus be observed more frequently in groups with intermediateconnectedness
Whilelowtointermediatedensitiesofsocialinteractionsofferthewidestscopeforpromotingindividualvariationinphenotypegroupswith high densities exhibit a very different patternAs the numberand strengths of interactions increases among group members in-direct genetic effects experienced by each individual becomemoresimilarbecauseallgroupmembersstarttobecomeconnectedtooneanotherand theseconnectionsareuniformlystrong Inadditionasnetworksbecomemoreconnectedindividualsattheextremesofthedistributionofgenetic tendencies in thegroups (ie the individualsfurthest from the averagebreedingvalue) tend to experience a so-cialenvironmentexertinganopposingeffectontheirphenotype(ieCov[a+esa +se] in Equation3 becomes more negative) This ldquopullto themeanrdquo is stronger in smaller groups than in larger ones (seeFigureS5) anddecreases thepopulationphenotypicvariancewhenψg ispositive (egwhen individuals increasetheiraggressiveness inresponse to the aggression they receive) and increases it whenψg is negative (egwhen individuals inhibit their aggressiveness in re-sponsetotheaggressiontheyreceive)Whenindividualsexhibit im-portantphenotypicplasticitysuchaneffectappearssimilartosocialconformity where individuals express more similar phenotypes asgroupsthan in isolation (egHerbert-Readetal2013MagnhagenampBunnefeld2009)Conformity isusually thought toemergewhendissimilarindividualsareatafitnessdisadvantageForexamplepred-ators tend topick individuals that standout amonggroupsofpreyselecting forhomogeneousgroups (LandeauampTerborgh1986)Weshowherethatconformist-likepatternsinbehaviorcanemergefromverysimpleformsofsocialplasticity Importantlyweshowthatbe-havioralconformitycanemergeevenwhenindividualsarenotactivelycopyingthemostabundantphenotypeoftheirgroup inabsenceofanyselectivepressureExamplesofhighlyconnectedgroupsinnatureincludechorusesofmalesinsomespeciesoffrogsproducingmating
calls or leks ofmales displaying to attract females and adjust theirsignalingeffortinresponsetothesignalingoftheirrivals(Boatright-HorowitzHorowitzampSimmons2000SimmonsSimmonsampBates2008)Whenmalesareclosetoeachotherandeachmalecanadjustits signaling intensity to that of all the othermaleswe expect thisldquopulltothemeanrdquotodecreasethevariationinmalesignals(althoughsocialplasticitycantakemorecomplexpatternsthenismodeledhereGreenfieldampRand2000)Thiscandecreasetheeffectivenessoffe-malematechoiceandtheintensityofsexualselection
43emsp|emspGroups with denser connections potentiated the effect of keystone individuals
Aninsightfromoursimulationsisthatwheneverindividualsadjusttheirphenotypetotheaveragesocialenvironmentthattheyexperi-enceindividualsattheextremesofthegenotypicorphenotypicdis-tributionhavethegreatestimpactonthephenotypeofothergroupmembers This phenomenon arises because these individuals havethestrongest impacton themeansocialenvironmentexperiencedbytheirconspecificsTheevolutionofniche-constructingtraitsal-lowingsomeindividualstomanipulatetheirgroupinawaythatfa-vorstheirownsuccess(SaltzGeigerAndersonJohnsonampMarren2016) or to have a disproportionate effect on their group (Keiseramp Pruitt 2014 Modlmeier etal 2014 Pruitt amp Pinter-Wollman2015)hasbeenthefocusofmuchinterestrecentlySurprisinglynostudyhasexplored the implicationsof theexactpatternsofsocialplasticity for the identity and impact of such ldquokeystone individu-alsrdquo (Modlmeier etal 2014) It is reasonable to assume thatmostanimalsexhibitingsocialplasticityshouldadjusttheirphenotypeinresponse to theaverage socialconditions that theyexperience (al-thoughinsomecasessomeindividualscanadjusttheirphenotypeto themaximumor to theminimumphenotypicvalueof the indi-vidualswithwhomtheyinteractseeDyerCroftMorrellampKrause2009 for a potential example) Thus our simulations suggest thattheemergenceofkeystoneindividualsmightbeaphenomenonfarmore common than previously envisioned Keystone individualscouldemergeinanygroupofinteractingindividualsexhibitingphe-notypicplasticityanddenseinteractionnetworks(asinthelekkingexampleabove)Hencetheemergenceofkeystoneindividualsmightnotrequireacomplexsocialsystemdivisionoflabor(PruittBolnickSihDiRienzoampPinter-Wollman2016) collectivebehavior (PruittampPinter-Wollman2015)orniche-constructingtraits (egaggres-sivenesspolicingorelseChangampSih2013)butshouldbemostcommon in specieswhere individuals respond to thebehaviors ofthemajorityofgroupmembers
Denserinteractionsamongindividualswithinagrouppotentiatetheimpactofindividualswithextremephenotypicvaluesbyallow-ing these to interact and affect themajority of their groupmem-bersHencetheconsequencesofindividualsocialplasticitytendtobecomemuchgreater ingroupsasnetworkdensity increasesThisldquoamplificationrdquoeffectisalsostrongerwhengenotypesfollowauni-formdistribution (iewhenextremegenotypesaremorefrequentwithin groups) thanwhen they followaGaussiandistribution (ie
1460emsp |emsp emspensp MONTIGLIO eT aL
whenextremegenotypesarerarewithingroups)Networkdensityincreases the evolutionary response of groups on average groupswith denser connections also exhibit increasedvariation in evolu-tionaryresponsetoagivenselectiongradientSuchan increase inthevariationinevolutionaryresponseobservedinourstudyisap-parentbecauseourapproachallowsustorelaxtheassumptionthatindividualswithingroupsinteractequallywithallothergroupmem-bersbyintroducinganewparameter(averageconnectionstrength=s)intoourmodelandinsteadtoexplicitlyexploretheeffectofcon-nectiondensity
44emsp|emspHomophily affects the amount of phenotypic variation within groups
Our simulations also investigate the consequencesof social struc-turewhenindividualscaninteractpreferentiallywithindividualsthathaveasimilar(iehomophily)ordissimilar(ieheterophily)pheno-typeNetworkassortment(thenetworkmeasureofhomophily)doesnot have any impact on groupsrsquomean phenotype but can gener-ateagreatervariationinsocialenvironmentswithingroupsHenceassuming that different immediate social environments can favordifferent (alternative) phenotypes within groups our simulationssuggest that homophily should be associatedwith the emergenceof phenotypic variation among individuals (or social specializationBergmuumlller amp Taborsky 2010 Montiglio Ferrari amp Reacuteale 2013)Homophilyalsohasdirectconsequencesfortheevolutionofalter-nativephenotypesbycreatingsynergyoroppositionbetweendirectand indirect genetic effectsWhen social plasticity (ψg) is positive(egwheninteractingwithanaggressiveindividualincreasesafocalindividualrsquosaggression)andindividualsshowatendencytointeractwithsimilarphenotypesthesocialenvironmentactstoshapetheirphenotypeinthesamedirectionastheirgenotypeAsaresultsocialinteractionsandsocialplasticityincreasethephenotypicvarianceofthetraitrelativetoasituationinwhichconnectionsarerandominterms of their traits It also tends to increase the strength of theevolutionaryresponsetoselectioninresponsetoagivenselectiongradientThisincreaseinevolutionaryresponsearisesfromthesyn-ergybetweendirectandindirecteffect(orbetweensocialplasticityandhomophily)ratherthanfromachangeintotalgeneticvariationwithingroups
45emsp|emspPossible applications and tests of the model and future directions
differentialandmatechoicebyfemalesThestrengthofconnectionsbetweenmales of known phenotype could be increased artificiallyusingplaybacks tosimulatemore frequent interactionsamong indi-viduals(DabelsteenampPedersen1990Otteretal2001)tomonitorhowsuchincreasesinconnectionstrengthaffecttheextentofpheno-typicandgeneticadditivevariationAlternativelyonecanmanipulatethedistributionofterritoriesavailableandthepatternsofinteractionsby controlling the locationof nest boxes foodpatches or refugesSuchapproachescouldbeparticularlysuitableforcavity-nestingbirds(Both1998)
Ourmodel also studied the consequences of homophily for theevolutionary responses of phenotypic traits Assuming individualshave some level of control on their interactions homophily can beobservedwhen individualsexhibitpreferences to interactwithcon-specificsthatare(dis)similartothemSuchpreferencescouldexplainthemaintenanceofaltruisticbehaviorbecauseoftheirpotentialroleinshapingtheselectionpressuresactingonaltruismSomeworkonfruitflieshavereportedthatindividualpreferencesforparticularsocialenvironmentsisassociatedwithgeneticvariationandcanthuspoten-tiallyevolve (egSaltzampFoley2011)Onecould testourmodel insuchstudysystemsbyeitherallowingorpreventingtheexpressionofsocialpreferences(throughmixingofindividualsormanipulatingtheirinteractions) Alternatively homophily can also be observed whenindividualssegregateintheenvironmentasafunctionoftheirphe-notype(HelfensteinDanchinampWagner2004Ward1993WardampPorter1993)Forexamplemoreandlessaggressiveindividualsseg-regateinpatcheswithdifferentdensitiesofconspecifics(Duckworth2006)Thusbymanipulatingtheheterogeneityandthescaleatwhichitisobserved(iethesizeofpatchesofdifferenthabitat)onecouldtestthepredictionsofourmodelFutureworkwillexpandthemodelwe presented here to analyze the consequences of such traits forthemaintenanceofphenotypicvariationandtheevolutionofsocialstructure
One limitationofourmodel is thatweassumebothphenotypicfeedback(Mooreetal1997)andsocialselection(Wolfetal1999)tobeabsentIncludingfeedbackmayaltertheconclusionswehavepre-sentedhereasfeedbackeffectsmaycausesocialplasticitytomovethroughnetworksincounterintuitivewaysItispossiblethatnetworkmetricsbeyondconnectionstrength (suchasclusteringcoefficientsbetweennessetc)may influencewhetherfeedbackcontributessig-nificantly to variation and response to selection Regarding socialselectionwehaveshownherethatconnectionstrengthcontributestoamong-groupvariancewhichshould intensifyresponsetohigherlevelsofselectionsuchassocialselectionWewilltreatbothfeedbackandsocialselectioninfuturecontributions
5emsp |emspCONCLUSION
Wepresentbothananalyticmodelandsimulationsextendingpre-vious work on social phenotypic plasticity to more general socialstructuresOurstudygeneratesafirstsetofverygeneralandtest-able predictions on the role of social structure in modulating the
emspensp emsp | emsp1461MONTIGLIO eT aL
consequencesofsocialplasticityWeshowthatthebasiccharacter-isticsofthestructureofinteractionsamongindividualsingroupsandpopulationscanhaveimpactsontheconsequencesofsocialplasticityforthemeanphenotypeexpressedbytheindividualstheextentofphenotypicvariationavailableforselectionandfortheabilityofthepopulation to respond to selectivepressuresWehope that futurestudieswillbeabletotestourpredictionsempiricallybyapplyingourapproachtothestudyofsocialbehavior(egaggressionandcoop-eration)socialinformationuseoralternativematingtacticsinpopu-lationswithvaryingpatternsofsocialormatinginteractionsFromatheoreticalperspectivefutureresearchwouldwarrantinvestigatingthelinkbetweenindividualpositioninsocialnetworksandtheindi-rect genetic effects it experiences and thuswhether factors otherthan individualsrsquo breeding values can lead to keystone individualsFurtherinourstudyweassumethatallindividualsexpressedplas-ticityidenticallyHoweverindividualshavealsobeenshowntovaryintheirplasticity(DingemanseKazemReacutealeampWright2010NusseyWilsonampBrommer2007WestneatHatchWetzelampEnsminger2011)andsuchvariationmayalterthepredictionsofinteractingphe-notypemodels(KazancıoğluKlugampAlonzo2012)Linkingindividualdifferencesinbothsocialpositionandplasticitycouldyieldnewin-sightsandagreaterunderstandingoftheevolutionarymechanismsthatunderpinphenotypicvariationwithinindividualsbetweenindi-vidualsandamongpopulations
ACKNOWLEDGMENTS
We thank the Reader Hendry and Barrett laboratories in McGillUniversity forconstructivecommentsonadraftof thismanuscriptPOMwas supported by aNSERCpostdoctoral fellowshipDRF re-ceived funding from a grant to theBBSRC (BBL0060811 toBCSheldon)andtheMaxPlanckSociety
CONFLICT OF INTEREST
Nonedeclared
AUTHOR CONTRIBUTIONS
POMandDRFbuiltthesimulationsandJWMdevelopedthemodelPOMdrafted themanuscript andproduced the figuresAll authorscontributedtorevisionsandapprovedthefinalversionofthearticle
AplinLMFarineDRMorand-FerronJCockburnAThorntonAamp SheldonBC (2015) Experimentally induced innovations lead topersistentcultureviaconformityinwildbirdsNature518538ndash541
Aplin LMFirthJAFarineDRVoelklBCratesRACulinaAhellipSheldonBC (2015)Consistent individual differences in the so-cialphenotypesofwildgreattits(Parusmajor)Animal Behaviour108117ndash127httpsdoiorg101016janbehav201507016
BaileyNWampHoskins J L (2014)Detecting cryptic indirect geneticeffectsEvolution681871ndash1882httpsdoiorg101111evo12401
Bailey N W amp Zuk M (2012) Socially flexible female choice differsamongpopulationsofthePacificfieldcricketGeographicalvariationin the interaction coefficient psi (Ψ)Proceedings of the Royal Society of London Series B Biological Sciences 279 3589ndash3596 httpsdoiorg101098rspb20120631
Bergmuumlller R amp Taborsky M (2010) Animal personality due to socialnichespecialisationTrends in Ecology amp Evolution25504ndash511httpsdoiorg101016jtree201006012
Bijma P ampWade M J (2008) The joint effects of kin multilevel se-lection and indirect genetic effects on response to genetic selec-tion Journal of Evolutionary Biology 21 1175ndash1188 httpsdoiorg101111j1420-9101200801550x
Boatright-HorowitzSLHorowitzSSampSimmonsAM(2000)Patternsof vocal interactions n a BullfrogRana catesbeiana chorus preferen-tial responding to farneighborsEthology106701ndash712httpsdoiorg101046j1439-0310200000580x
BothC(1998)Experimentalevidencefordensitydependenceofrepro-ductioningreattitsJournal of Animal Ecology67667ndash674httpsdoiorg101046j1365-2656199800228x
Cappa E P amp Cantet R J C (2008) Direct and competition additiveeffects in treebreedingBayesianestimation froman individual treemixedmodelSilvae Genetica5745ndash56
ChangAampSihA (2013)Multilevel selection andeffects of keystonehyperaggressivemalesonmatingsuccessandbehaviorinstreamwaterstridersBehavioral Ecology241166ndash1176httpsdoiorg101093behecoart044
Clutton-BrockTH(1989)MammalianmatingsystemsProceedings of the Royal Society B236339ndash372httpsdoiorg101098rspb19890027
Crowley P H amp Cox J J (2011) Intraguild mutualism Trends in Ecology amp Evolution 26 627ndash633 httpsdoiorg101016jtree201107011
Duckworth R A (2006) Aggressive behaviour affects selection onmorphology by influencing settlement patterns in a passerine birdProceedings of the Royal Society B 273 1789ndash1795 httpsdoiorg101098rspb20063517
Farine D R (2014) Measuring phenotypic assortment in animal so-cial networks Weighted associations are more robust than binaryedges Animal Behavior 89 141ndash153 httpsdoiorg101016janbehav201401001
FarineDRampWhiteheadH(2015)Constructingconductingandinter-preting animal social network analysis Journal of Animal Ecology841144ndash1163httpsdoiorg1011111365-265612418
Fawcett TW amp Johnstone RA (2010) Learning your own strengthWinner and loser effects should change with age and experienceProceedings of the Royal Society of London Series B Biological Sciences2771427ndash1434httpsdoiorg101098rspb20092088
Fisher D N amp McAdam A G (2017) Social traits social networksand evolutionary biology Journal of Evolutionary Biology httpsdoiorg101111jeb13195Inpress
FormicaVAWood CW LarsenW B Butterfield R EAugatMEHougenHYampBrodieIIIED(2012)Fitnessconsequencesofsocialnetworkpositioninawildpopulationofforkedfungusbeetles(Bolitotherus cornutus) Journal of Evolutionary Biology 25 130ndash137httpsdoiorg101111j1420-9101201102411x
Greenfield M D amp Rand S A (2000) Frogs have rules selective at-tention algorithms regulate chorusing in Physalaemus pustulosus (Leptodactylidae)Ethology106131ndash147
Helfenstein FDanchin E ampWagner RH (2004)Assortativematingand sexual size dimorphism in blacklegged kittiwakes Waterbirds27 350ndash354 httpsdoiorg1016751524-4695(2004)027[0350AMASSD]20CO2
Herbert-Read J E Krause S Morrell L J Schaerf T M Krause JampWardAJW (2013)The roleof individuality in collectivegroupmovementProceedings of the Royal Society B- Biological Sciences28020122564
KeiserCNampPruittJN (2014)Personality composition ismore im-portantthangroupsizeindeterminingcollectiveforagingbehaviourinthewildProceedings of the Royal Society of London Series B Biological Sciences28120141424httpsdoiorg101098rspb20141424
Krause J amp Ruxton GD (2002) Living in groups Oxford UKOxfordUniversityPress
Landeau L ampTerborgh J (1986)Oddity and the ldquoconfusion effectrdquo inpredationAnimal Behavior341372ndash1380httpsdoiorg101016S0003-3472(86)80208-1
Magnhagen C amp Bunnefeld N (2009) Express your personality or goalong with the group What determines the behaviour of shoalingperchProceedings of the Royal Society B- Biological Sciences2763369ndash3375httpsdoiorg101098rspb20090851
McDonaldG C FarineD R Foster K R ampBiernaskie JM (2017)Assortment and the analysis of natural selection on social traitsEvolution712693ndash2702httpsdoiorg101111evo13365
McGlothlin JW amp Brodie III E D (2009) How to measure individ-ual genetic effects The congruence of trait-based and variance-partitioning approaches Evolution 63 1785ndash1795 httpsdoiorg101111j1558-5646200900676x
McGlothlin J W Moore A J Wolf J B amp Brodie III E D(2010) Interacting phenotypes and the evolutionary pro-cess III Social evolution Evolution 64 2558ndash2574 httpsdoiorg101111j1558-5646201001012x
MillerJRBAmentJMampSchmitzOJ (2014)Fearon themovePredatorhuntingmodepredictsvariation inpreymortalityandplas-ticityinpreyspatialresponseJournal of Animal Ecology83214ndash222httpsdoiorg1011111365-265612111
ModlmeierAPKeiserCNWattersJVSihAampPruittJN(2014)The keystone individual concept An ecological and evolutionaryoverview Animal Behavior 89 53ndash62 httpsdoiorg101016janbehav201312020
MontiglioP-OFerrariCampReacutealeD(2013)Socialnichespecializationunder constraints Personality social interactions and environmentalheterogeneityPhilosophical Transactions of the Royal Society of London Series B Biological Sciences36820120343httpsdoiorg101098rstb20120343
Moore A J Brodie III E D ampWolf J B (1997) Interacting pheno-types and the evolutionary process I Direct and indirect geneticeffects of social interactions Evolution 51 1352ndash1362 httpsdoiorg101111j1558-56461997tb01458x
NonacsPampKapheimKM(2007)Socialheterosisandthemaintenanceof genetic diversity Journal of Evolutionary Biology 20 2253ndash2265httpsdoiorg101111j1420-9101200701418x
Nussey D H Wilson A J amp Brommer J E (2007) The evolution-ary ecology of individual phenotypic plasticity in wild popula-tions Journal of Evolutionary Biology 20 831ndash844 httpsdoiorg101111j1420-9101200701300x
OtterKAStewartIRKMcGregorPKTerryAMRDabelsteenTampBurkeT(2001)Extra-pairpaternityamonggreattitsParus major following manipulation of male signals Journal of Avian Biology 32338ndash344httpsdoiorg101111j0908-88572001320408x
Pruitt J N Bolnick D I Sih A DiRienzo N amp Pinter-Wollman N(2016)Behavioralhypervolumesofspidercoloniespredictscommu-nity performance and disbandmentProceedings of the Royal Society B- Biological Sciences 283 20161409 httpsdoiorg101098rspb20161409
PruittJNampPinter-WollmanN(2015)Thelegacyeffectsofkeystonein-dividualsoncollectivebehaviourscaletohowlongtheyremainwithina group Proceedings of the Royal Society B- Biological Sciences 28220151766httpsdoiorg101098rspb20151766
RoyleNJHartley IROwens I P FampParkerGA (1999) Siblingcompetition and the evolution of growth rates in birds Proceedings of the Royal Society B 266 923ndash932 httpsdoiorg101098rspb19990725
SaltzJBampFoleyBR(2011)Naturalgeneticvariationinsocialnicheconstruction Social effects of aggression drive disruptive sexual se-lectioninDrosophila melanogaster American Naturalist177645ndash654httpsdoiorg101086659631
ShusterSM LonsdorfEVWimpGMBaileyJKampWhithamTG (2006) Community heritabilitymeasures the evolutionary conse-quencesofindirectgeneticeffectsoncommunitystructureEvolution60991ndash1003httpsdoiorg101111j0014-38202006tb01177x
SimmonsAMSimmonsJAampBatesMA (2008)Analyzingacous-tic interactions in natural bullfrog (Rana catesbeiana) chorusesJournal of Comparative Psychology 122 274ndash282 httpsdoiorg1010370735-70361223274
Sinervo B R amp Calsbeek R (2010) Behavioral concepts of selectionExperiments and genetic causes of selection on the sexes In D FWestneatampCWFox(Eds)Evolutionary behavioral ecologyLondonUKOxfordUniversityPress
Thompson J N (1982) Interaction and coevolution Chicago USA TheUniversityofChicagoPress
emspensp emsp | emsp1463MONTIGLIO eT aL
VanderWaal K L ObandaV Omondi G P McCowan BWang HFushingHampIsbellLA (2016)Thestrengthofweaktiesandhel-minth parasitism in giraffe social networks Behavioral Ecology 271190ndash1197httpsdoiorg101093behecoarw035
Ward P I (1993) Micro-habitat segregation and the mating systemof Gammarus pulex Animal Behavior 45 191ndash192 httpsdoiorg101006anbe19931019
Ward P I amp PorterAH (1993)The relative role of habitat structureandmale-malecompetition in thematingsystemofGammarus pulex (CrustaceaAmphipoda)AsimulationstudyAnimal Behavior45119ndash133httpsdoiorg101006anbe19931011
West-EberhardMJ(1989)Phenotypicplasticityandtheoriginsofdiver-sityAnnual Review of Ecology and Systematics20249ndash278httpsdoiorg101146annureves20110189001341
Westneat D F Hatch M IWetzel D P amp Ensminger A L (2011)IndividualvariationinparentalcarereactionnormsIntegrationofper-sonalityandplasticityAmerican Naturalist178652ndash667httpsdoiorg101086662173
Wilson A J Gelin U Perron M-C amp Reacuteale D (2009) Indirect ge-neticeffectsandtheevolutionofaggression inavertebratesystemProceedings of the Royal Society of London Series B Biological Sciences276533ndash541httpsdoiorg101098rspb20081193
Additional Supporting Informationmay be found online in the sup-portinginformationtabforthisarticle
How to cite this articleMontiglioP-OMcGlothlinJWFarineDRSocialstructuremodulatestheevolutionaryconsequencesofsocialplasticityAsocialnetworkperspectiveoninteractingphenotypesEcol Evol 201881451ndash1464 httpsdoiorg101002ece33753
APPENDIX
PHENOTYPIC MEAN AND VARIANCE
FollowingMooreetal(1997)wemodelasinglephenotypeofanindi-vidual (z)asanadditivecombinationoftheeffectsof itsowngenes(iedirectgeneticeffectsa)thenonsocialenvironmentitexperiences(e)andaplasticcomponentthatissomefunctionofthephenotypesinitssocialgroupMooreetal(1997)originallymodeledthesocialeffectasafunctionofthephenotypeofoneinteractingindividualMcGlothlinandBrodie (2009)andMcGlothlinetal (2010)consideredsocialef-fectsinapopulationconsistingofgroupsofnindividualswhereinter-actionswereassumedtooccursimultaneouslywithinagroupwithallindividuals within a group having the same strength of interactionHereweconsideramoregeneralsocialstructurewhereindividualsinteractwithallpossiblesocialinteractantsingroupsizenwithvaria-bleconnectionstrengthsirangingfrom0to1giving
wherethesummationistakenacrossalln minus1possiblesocialinterac-tionsforeachindividualsandψrepresentstheinteractioncoefficientwhichdetermines thestrengthanddirectionof the indirectpheno-typic effect of individual social interactantsHere and elsewhere aprimeindicatesaparameterbelongingtoasocialpartnerAnysocialnetworkstructurecanbemodeledbychangingthedistributionofs High-densitysocialnetworkswithstrongconnectionswillhavemanylargevaluesofswhilesparsernetworkswithweakerconnectionswillhavemanyweaksvalueswithmanyequaltozeroConsideringphenotypicfeedback(asdoMooreetal1997)insuch
The value of the two covariance terms represents how stronglystrengthofinteractiondependsonthegenesandenvironmentofin-dividualsocialpartnersThiscovarianceisdeterminedforeachindi-vidualandmayvaryacrossindividualsTheseshouldbepositiveunderhomophilyandnegativeunderheterophilyTakingthemeanandas-suming
=e=0
where double overbars indicate global means and large overbarswithintheparenthesesindicatemeanstakenacrossindividualsbasedonsummarystatisticsoftheirsocialgroupsThiscanbeexpandedasaboveto
The remainingcovariance terms represent theaveragedegree towhichindividualconnectionstrengthsareadjustedbasedonthephe-notypeofpotentialinteractantsInthecaseofhomophilyorheteroph-ilyindividualswillmakethisadjustmentbasedontheirownphenotypewithlargeindividualshavingapositivecovarianceandsmallindividu-alshavinganegativecovariance(orviceversa)ThereforeweexpecttheseaveragecovariancetermstotendtowardzeroMakingthisas-sumptionandrearrangingprovidesEquation2inthetext
EXTENSION TO MULTIPLE GROUPS
EquationA8iswrittenassumingthatthepopulationconsistsofasin-gle social networkwhere individualsmay interact in anywayNowassumethatthepopulationisdividedintomultiplegroupswhereindi-vidualsmay interactwithanystrengthswithinagroupanddonotinteract at all between groups Assuming the covariance terms inEquationA8arezeroandthatenvironmentaldeviationsdonotvaryamonggroupsthemeanofeachgroupwillbe
where overbars now indicate within-groupmeans Assuming equalgroupsizethepopulationmeanisnow
(IfgroupsvaryinsizethenEquationA10canbemodifiedtogiveaweightedmean) Ifconnectionstrengthhasnoheritablebasis thenthe covariance term become zero and EquationA10 collapses toEquation2inthetextWemaycalculateamong-groupvariancemosteasilybymakingafewassumptionsthatarealsomadeinoursimula-tionsFirstasaboveweassumethatgroupsareofequalsizeSecondweassume thatmean interactiondoesnotvaryacrossgroups ands=
=sMakingtheseassumptions
Thisshowsthat indirectgeneticeffectswillmagnifyslightdiffer-ences in genetic values across groups regardless of sign Strongermeanconnectionstrengthswillintensifythiseffect
RESPONSE TO SELECTION
FollowingMoore etal (1997) andMcGlothlin etal (2010) and as-suming that thecovariance terms inEquationA8areeither zeroorpopulation parameters that do not have a heritable component anindividualrsquostotalbreedingvaluecanbewrittenasthegeneticcontri-butiontothepopulationmean
where Ristheregressionofsaprimeonaandisthusanalogoustorelated-ness This assumes thatCov[aseprime] is negligible Positive values ofR indicatehomophilyandnegativevaluesindicateheterophilyMakingthissubstitutiongivesEquation4inthetextEquation4canalsobeexpresseddifferentlybyrearrangingas
Studiesinthewildhaveshownthatpositioninasocialnetworkmaybe repeatable and have fitness consequences suggesting that con-nectionstrengthmaybeanevolvabletrait (AplinFirthetal2015FormicaWoodCookampBrodie2017Formicaetal2012)
42emsp|emspGroups with denser connections exert a stronger ldquopull to the meanrdquo
Our simulations show that groupswhere individuals have an in-termediatenumberorstrengthofsocialconnections (iegroupswithintermediatenetworkdensities)allowforthegreatestwithin-groupvariationinsocialenvironmentsexperiencedamongindivid-ualsThispatternariseswithinagenerationduetosocialplasticityratherthanasaresponsetoanyselectivepressureBygeneratinga greater range of phenotypes and social environments groupswithan intermediatedensityof social interactionscouldprovidethe basis for the emergence and evolution of alternative socialphenotypes (Bergmuumlller amp Taborsky 2010 Sinervo amp Calsbeek2010) When social phenotypes are subject to indirect geneticeffects the maintenance of variation in social behavior shouldthus be observed more frequently in groups with intermediateconnectedness
Whilelowtointermediatedensitiesofsocialinteractionsofferthewidestscopeforpromotingindividualvariationinphenotypegroupswith high densities exhibit a very different patternAs the numberand strengths of interactions increases among group members in-direct genetic effects experienced by each individual becomemoresimilarbecauseallgroupmembersstarttobecomeconnectedtooneanotherand theseconnectionsareuniformlystrong Inadditionasnetworksbecomemoreconnectedindividualsattheextremesofthedistributionofgenetic tendencies in thegroups (ie the individualsfurthest from the averagebreedingvalue) tend to experience a so-cialenvironmentexertinganopposingeffectontheirphenotype(ieCov[a+esa +se] in Equation3 becomes more negative) This ldquopullto themeanrdquo is stronger in smaller groups than in larger ones (seeFigureS5) anddecreases thepopulationphenotypicvariancewhenψg ispositive (egwhen individuals increasetheiraggressiveness inresponse to the aggression they receive) and increases it whenψg is negative (egwhen individuals inhibit their aggressiveness in re-sponsetotheaggressiontheyreceive)Whenindividualsexhibit im-portantphenotypicplasticitysuchaneffectappearssimilartosocialconformity where individuals express more similar phenotypes asgroupsthan in isolation (egHerbert-Readetal2013MagnhagenampBunnefeld2009)Conformity isusually thought toemergewhendissimilarindividualsareatafitnessdisadvantageForexamplepred-ators tend topick individuals that standout amonggroupsofpreyselecting forhomogeneousgroups (LandeauampTerborgh1986)Weshowherethatconformist-likepatternsinbehaviorcanemergefromverysimpleformsofsocialplasticity Importantlyweshowthatbe-havioralconformitycanemergeevenwhenindividualsarenotactivelycopyingthemostabundantphenotypeoftheirgroup inabsenceofanyselectivepressureExamplesofhighlyconnectedgroupsinnatureincludechorusesofmalesinsomespeciesoffrogsproducingmating
calls or leks ofmales displaying to attract females and adjust theirsignalingeffortinresponsetothesignalingoftheirrivals(Boatright-HorowitzHorowitzampSimmons2000SimmonsSimmonsampBates2008)Whenmalesareclosetoeachotherandeachmalecanadjustits signaling intensity to that of all the othermaleswe expect thisldquopulltothemeanrdquotodecreasethevariationinmalesignals(althoughsocialplasticitycantakemorecomplexpatternsthenismodeledhereGreenfieldampRand2000)Thiscandecreasetheeffectivenessoffe-malematechoiceandtheintensityofsexualselection
43emsp|emspGroups with denser connections potentiated the effect of keystone individuals
Aninsightfromoursimulationsisthatwheneverindividualsadjusttheirphenotypetotheaveragesocialenvironmentthattheyexperi-enceindividualsattheextremesofthegenotypicorphenotypicdis-tributionhavethegreatestimpactonthephenotypeofothergroupmembers This phenomenon arises because these individuals havethestrongest impacton themeansocialenvironmentexperiencedbytheirconspecificsTheevolutionofniche-constructingtraitsal-lowingsomeindividualstomanipulatetheirgroupinawaythatfa-vorstheirownsuccess(SaltzGeigerAndersonJohnsonampMarren2016) or to have a disproportionate effect on their group (Keiseramp Pruitt 2014 Modlmeier etal 2014 Pruitt amp Pinter-Wollman2015)hasbeenthefocusofmuchinterestrecentlySurprisinglynostudyhasexplored the implicationsof theexactpatternsofsocialplasticity for the identity and impact of such ldquokeystone individu-alsrdquo (Modlmeier etal 2014) It is reasonable to assume thatmostanimalsexhibitingsocialplasticityshouldadjusttheirphenotypeinresponse to theaverage socialconditions that theyexperience (al-thoughinsomecasessomeindividualscanadjusttheirphenotypeto themaximumor to theminimumphenotypicvalueof the indi-vidualswithwhomtheyinteractseeDyerCroftMorrellampKrause2009 for a potential example) Thus our simulations suggest thattheemergenceofkeystoneindividualsmightbeaphenomenonfarmore common than previously envisioned Keystone individualscouldemergeinanygroupofinteractingindividualsexhibitingphe-notypicplasticityanddenseinteractionnetworks(asinthelekkingexampleabove)Hencetheemergenceofkeystoneindividualsmightnotrequireacomplexsocialsystemdivisionoflabor(PruittBolnickSihDiRienzoampPinter-Wollman2016) collectivebehavior (PruittampPinter-Wollman2015)orniche-constructingtraits (egaggres-sivenesspolicingorelseChangampSih2013)butshouldbemostcommon in specieswhere individuals respond to thebehaviors ofthemajorityofgroupmembers
Denserinteractionsamongindividualswithinagrouppotentiatetheimpactofindividualswithextremephenotypicvaluesbyallow-ing these to interact and affect themajority of their groupmem-bersHencetheconsequencesofindividualsocialplasticitytendtobecomemuchgreater ingroupsasnetworkdensity increasesThisldquoamplificationrdquoeffectisalsostrongerwhengenotypesfollowauni-formdistribution (iewhenextremegenotypesaremorefrequentwithin groups) thanwhen they followaGaussiandistribution (ie
1460emsp |emsp emspensp MONTIGLIO eT aL
whenextremegenotypesarerarewithingroups)Networkdensityincreases the evolutionary response of groups on average groupswith denser connections also exhibit increasedvariation in evolu-tionaryresponsetoagivenselectiongradientSuchan increase inthevariationinevolutionaryresponseobservedinourstudyisap-parentbecauseourapproachallowsustorelaxtheassumptionthatindividualswithingroupsinteractequallywithallothergroupmem-bersbyintroducinganewparameter(averageconnectionstrength=s)intoourmodelandinsteadtoexplicitlyexploretheeffectofcon-nectiondensity
44emsp|emspHomophily affects the amount of phenotypic variation within groups
Our simulations also investigate the consequencesof social struc-turewhenindividualscaninteractpreferentiallywithindividualsthathaveasimilar(iehomophily)ordissimilar(ieheterophily)pheno-typeNetworkassortment(thenetworkmeasureofhomophily)doesnot have any impact on groupsrsquomean phenotype but can gener-ateagreatervariationinsocialenvironmentswithingroupsHenceassuming that different immediate social environments can favordifferent (alternative) phenotypes within groups our simulationssuggest that homophily should be associatedwith the emergenceof phenotypic variation among individuals (or social specializationBergmuumlller amp Taborsky 2010 Montiglio Ferrari amp Reacuteale 2013)Homophilyalsohasdirectconsequencesfortheevolutionofalter-nativephenotypesbycreatingsynergyoroppositionbetweendirectand indirect genetic effectsWhen social plasticity (ψg) is positive(egwheninteractingwithanaggressiveindividualincreasesafocalindividualrsquosaggression)andindividualsshowatendencytointeractwithsimilarphenotypesthesocialenvironmentactstoshapetheirphenotypeinthesamedirectionastheirgenotypeAsaresultsocialinteractionsandsocialplasticityincreasethephenotypicvarianceofthetraitrelativetoasituationinwhichconnectionsarerandominterms of their traits It also tends to increase the strength of theevolutionaryresponsetoselectioninresponsetoagivenselectiongradientThisincreaseinevolutionaryresponsearisesfromthesyn-ergybetweendirectandindirecteffect(orbetweensocialplasticityandhomophily)ratherthanfromachangeintotalgeneticvariationwithingroups
45emsp|emspPossible applications and tests of the model and future directions
differentialandmatechoicebyfemalesThestrengthofconnectionsbetweenmales of known phenotype could be increased artificiallyusingplaybacks tosimulatemore frequent interactionsamong indi-viduals(DabelsteenampPedersen1990Otteretal2001)tomonitorhowsuchincreasesinconnectionstrengthaffecttheextentofpheno-typicandgeneticadditivevariationAlternativelyonecanmanipulatethedistributionofterritoriesavailableandthepatternsofinteractionsby controlling the locationof nest boxes foodpatches or refugesSuchapproachescouldbeparticularlysuitableforcavity-nestingbirds(Both1998)
Ourmodel also studied the consequences of homophily for theevolutionary responses of phenotypic traits Assuming individualshave some level of control on their interactions homophily can beobservedwhen individualsexhibitpreferences to interactwithcon-specificsthatare(dis)similartothemSuchpreferencescouldexplainthemaintenanceofaltruisticbehaviorbecauseoftheirpotentialroleinshapingtheselectionpressuresactingonaltruismSomeworkonfruitflieshavereportedthatindividualpreferencesforparticularsocialenvironmentsisassociatedwithgeneticvariationandcanthuspoten-tiallyevolve (egSaltzampFoley2011)Onecould testourmodel insuchstudysystemsbyeitherallowingorpreventingtheexpressionofsocialpreferences(throughmixingofindividualsormanipulatingtheirinteractions) Alternatively homophily can also be observed whenindividualssegregateintheenvironmentasafunctionoftheirphe-notype(HelfensteinDanchinampWagner2004Ward1993WardampPorter1993)Forexamplemoreandlessaggressiveindividualsseg-regateinpatcheswithdifferentdensitiesofconspecifics(Duckworth2006)Thusbymanipulatingtheheterogeneityandthescaleatwhichitisobserved(iethesizeofpatchesofdifferenthabitat)onecouldtestthepredictionsofourmodelFutureworkwillexpandthemodelwe presented here to analyze the consequences of such traits forthemaintenanceofphenotypicvariationandtheevolutionofsocialstructure
One limitationofourmodel is thatweassumebothphenotypicfeedback(Mooreetal1997)andsocialselection(Wolfetal1999)tobeabsentIncludingfeedbackmayaltertheconclusionswehavepre-sentedhereasfeedbackeffectsmaycausesocialplasticitytomovethroughnetworksincounterintuitivewaysItispossiblethatnetworkmetricsbeyondconnectionstrength (suchasclusteringcoefficientsbetweennessetc)may influencewhetherfeedbackcontributessig-nificantly to variation and response to selection Regarding socialselectionwehaveshownherethatconnectionstrengthcontributestoamong-groupvariancewhichshould intensifyresponsetohigherlevelsofselectionsuchassocialselectionWewilltreatbothfeedbackandsocialselectioninfuturecontributions
5emsp |emspCONCLUSION
Wepresentbothananalyticmodelandsimulationsextendingpre-vious work on social phenotypic plasticity to more general socialstructuresOurstudygeneratesafirstsetofverygeneralandtest-able predictions on the role of social structure in modulating the
emspensp emsp | emsp1461MONTIGLIO eT aL
consequencesofsocialplasticityWeshowthatthebasiccharacter-isticsofthestructureofinteractionsamongindividualsingroupsandpopulationscanhaveimpactsontheconsequencesofsocialplasticityforthemeanphenotypeexpressedbytheindividualstheextentofphenotypicvariationavailableforselectionandfortheabilityofthepopulation to respond to selectivepressuresWehope that futurestudieswillbeabletotestourpredictionsempiricallybyapplyingourapproachtothestudyofsocialbehavior(egaggressionandcoop-eration)socialinformationuseoralternativematingtacticsinpopu-lationswithvaryingpatternsofsocialormatinginteractionsFromatheoreticalperspectivefutureresearchwouldwarrantinvestigatingthelinkbetweenindividualpositioninsocialnetworksandtheindi-rect genetic effects it experiences and thuswhether factors otherthan individualsrsquo breeding values can lead to keystone individualsFurtherinourstudyweassumethatallindividualsexpressedplas-ticityidenticallyHoweverindividualshavealsobeenshowntovaryintheirplasticity(DingemanseKazemReacutealeampWright2010NusseyWilsonampBrommer2007WestneatHatchWetzelampEnsminger2011)andsuchvariationmayalterthepredictionsofinteractingphe-notypemodels(KazancıoğluKlugampAlonzo2012)Linkingindividualdifferencesinbothsocialpositionandplasticitycouldyieldnewin-sightsandagreaterunderstandingoftheevolutionarymechanismsthatunderpinphenotypicvariationwithinindividualsbetweenindi-vidualsandamongpopulations
ACKNOWLEDGMENTS
We thank the Reader Hendry and Barrett laboratories in McGillUniversity forconstructivecommentsonadraftof thismanuscriptPOMwas supported by aNSERCpostdoctoral fellowshipDRF re-ceived funding from a grant to theBBSRC (BBL0060811 toBCSheldon)andtheMaxPlanckSociety
CONFLICT OF INTEREST
Nonedeclared
AUTHOR CONTRIBUTIONS
POMandDRFbuiltthesimulationsandJWMdevelopedthemodelPOMdrafted themanuscript andproduced the figuresAll authorscontributedtorevisionsandapprovedthefinalversionofthearticle
AplinLMFarineDRMorand-FerronJCockburnAThorntonAamp SheldonBC (2015) Experimentally induced innovations lead topersistentcultureviaconformityinwildbirdsNature518538ndash541
Aplin LMFirthJAFarineDRVoelklBCratesRACulinaAhellipSheldonBC (2015)Consistent individual differences in the so-cialphenotypesofwildgreattits(Parusmajor)Animal Behaviour108117ndash127httpsdoiorg101016janbehav201507016
BaileyNWampHoskins J L (2014)Detecting cryptic indirect geneticeffectsEvolution681871ndash1882httpsdoiorg101111evo12401
Bailey N W amp Zuk M (2012) Socially flexible female choice differsamongpopulationsofthePacificfieldcricketGeographicalvariationin the interaction coefficient psi (Ψ)Proceedings of the Royal Society of London Series B Biological Sciences 279 3589ndash3596 httpsdoiorg101098rspb20120631
Bergmuumlller R amp Taborsky M (2010) Animal personality due to socialnichespecialisationTrends in Ecology amp Evolution25504ndash511httpsdoiorg101016jtree201006012
Bijma P ampWade M J (2008) The joint effects of kin multilevel se-lection and indirect genetic effects on response to genetic selec-tion Journal of Evolutionary Biology 21 1175ndash1188 httpsdoiorg101111j1420-9101200801550x
Boatright-HorowitzSLHorowitzSSampSimmonsAM(2000)Patternsof vocal interactions n a BullfrogRana catesbeiana chorus preferen-tial responding to farneighborsEthology106701ndash712httpsdoiorg101046j1439-0310200000580x
BothC(1998)Experimentalevidencefordensitydependenceofrepro-ductioningreattitsJournal of Animal Ecology67667ndash674httpsdoiorg101046j1365-2656199800228x
Cappa E P amp Cantet R J C (2008) Direct and competition additiveeffects in treebreedingBayesianestimation froman individual treemixedmodelSilvae Genetica5745ndash56
ChangAampSihA (2013)Multilevel selection andeffects of keystonehyperaggressivemalesonmatingsuccessandbehaviorinstreamwaterstridersBehavioral Ecology241166ndash1176httpsdoiorg101093behecoart044
Clutton-BrockTH(1989)MammalianmatingsystemsProceedings of the Royal Society B236339ndash372httpsdoiorg101098rspb19890027
Crowley P H amp Cox J J (2011) Intraguild mutualism Trends in Ecology amp Evolution 26 627ndash633 httpsdoiorg101016jtree201107011
Duckworth R A (2006) Aggressive behaviour affects selection onmorphology by influencing settlement patterns in a passerine birdProceedings of the Royal Society B 273 1789ndash1795 httpsdoiorg101098rspb20063517
Farine D R (2014) Measuring phenotypic assortment in animal so-cial networks Weighted associations are more robust than binaryedges Animal Behavior 89 141ndash153 httpsdoiorg101016janbehav201401001
FarineDRampWhiteheadH(2015)Constructingconductingandinter-preting animal social network analysis Journal of Animal Ecology841144ndash1163httpsdoiorg1011111365-265612418
Fawcett TW amp Johnstone RA (2010) Learning your own strengthWinner and loser effects should change with age and experienceProceedings of the Royal Society of London Series B Biological Sciences2771427ndash1434httpsdoiorg101098rspb20092088
Fisher D N amp McAdam A G (2017) Social traits social networksand evolutionary biology Journal of Evolutionary Biology httpsdoiorg101111jeb13195Inpress
FormicaVAWood CW LarsenW B Butterfield R EAugatMEHougenHYampBrodieIIIED(2012)Fitnessconsequencesofsocialnetworkpositioninawildpopulationofforkedfungusbeetles(Bolitotherus cornutus) Journal of Evolutionary Biology 25 130ndash137httpsdoiorg101111j1420-9101201102411x
Greenfield M D amp Rand S A (2000) Frogs have rules selective at-tention algorithms regulate chorusing in Physalaemus pustulosus (Leptodactylidae)Ethology106131ndash147
Helfenstein FDanchin E ampWagner RH (2004)Assortativematingand sexual size dimorphism in blacklegged kittiwakes Waterbirds27 350ndash354 httpsdoiorg1016751524-4695(2004)027[0350AMASSD]20CO2
Herbert-Read J E Krause S Morrell L J Schaerf T M Krause JampWardAJW (2013)The roleof individuality in collectivegroupmovementProceedings of the Royal Society B- Biological Sciences28020122564
KeiserCNampPruittJN (2014)Personality composition ismore im-portantthangroupsizeindeterminingcollectiveforagingbehaviourinthewildProceedings of the Royal Society of London Series B Biological Sciences28120141424httpsdoiorg101098rspb20141424
Krause J amp Ruxton GD (2002) Living in groups Oxford UKOxfordUniversityPress
Landeau L ampTerborgh J (1986)Oddity and the ldquoconfusion effectrdquo inpredationAnimal Behavior341372ndash1380httpsdoiorg101016S0003-3472(86)80208-1
Magnhagen C amp Bunnefeld N (2009) Express your personality or goalong with the group What determines the behaviour of shoalingperchProceedings of the Royal Society B- Biological Sciences2763369ndash3375httpsdoiorg101098rspb20090851
McDonaldG C FarineD R Foster K R ampBiernaskie JM (2017)Assortment and the analysis of natural selection on social traitsEvolution712693ndash2702httpsdoiorg101111evo13365
McGlothlin JW amp Brodie III E D (2009) How to measure individ-ual genetic effects The congruence of trait-based and variance-partitioning approaches Evolution 63 1785ndash1795 httpsdoiorg101111j1558-5646200900676x
McGlothlin J W Moore A J Wolf J B amp Brodie III E D(2010) Interacting phenotypes and the evolutionary pro-cess III Social evolution Evolution 64 2558ndash2574 httpsdoiorg101111j1558-5646201001012x
MillerJRBAmentJMampSchmitzOJ (2014)Fearon themovePredatorhuntingmodepredictsvariation inpreymortalityandplas-ticityinpreyspatialresponseJournal of Animal Ecology83214ndash222httpsdoiorg1011111365-265612111
ModlmeierAPKeiserCNWattersJVSihAampPruittJN(2014)The keystone individual concept An ecological and evolutionaryoverview Animal Behavior 89 53ndash62 httpsdoiorg101016janbehav201312020
MontiglioP-OFerrariCampReacutealeD(2013)Socialnichespecializationunder constraints Personality social interactions and environmentalheterogeneityPhilosophical Transactions of the Royal Society of London Series B Biological Sciences36820120343httpsdoiorg101098rstb20120343
Moore A J Brodie III E D ampWolf J B (1997) Interacting pheno-types and the evolutionary process I Direct and indirect geneticeffects of social interactions Evolution 51 1352ndash1362 httpsdoiorg101111j1558-56461997tb01458x
NonacsPampKapheimKM(2007)Socialheterosisandthemaintenanceof genetic diversity Journal of Evolutionary Biology 20 2253ndash2265httpsdoiorg101111j1420-9101200701418x
Nussey D H Wilson A J amp Brommer J E (2007) The evolution-ary ecology of individual phenotypic plasticity in wild popula-tions Journal of Evolutionary Biology 20 831ndash844 httpsdoiorg101111j1420-9101200701300x
OtterKAStewartIRKMcGregorPKTerryAMRDabelsteenTampBurkeT(2001)Extra-pairpaternityamonggreattitsParus major following manipulation of male signals Journal of Avian Biology 32338ndash344httpsdoiorg101111j0908-88572001320408x
Pruitt J N Bolnick D I Sih A DiRienzo N amp Pinter-Wollman N(2016)Behavioralhypervolumesofspidercoloniespredictscommu-nity performance and disbandmentProceedings of the Royal Society B- Biological Sciences 283 20161409 httpsdoiorg101098rspb20161409
PruittJNampPinter-WollmanN(2015)Thelegacyeffectsofkeystonein-dividualsoncollectivebehaviourscaletohowlongtheyremainwithina group Proceedings of the Royal Society B- Biological Sciences 28220151766httpsdoiorg101098rspb20151766
RoyleNJHartley IROwens I P FampParkerGA (1999) Siblingcompetition and the evolution of growth rates in birds Proceedings of the Royal Society B 266 923ndash932 httpsdoiorg101098rspb19990725
SaltzJBampFoleyBR(2011)Naturalgeneticvariationinsocialnicheconstruction Social effects of aggression drive disruptive sexual se-lectioninDrosophila melanogaster American Naturalist177645ndash654httpsdoiorg101086659631
ShusterSM LonsdorfEVWimpGMBaileyJKampWhithamTG (2006) Community heritabilitymeasures the evolutionary conse-quencesofindirectgeneticeffectsoncommunitystructureEvolution60991ndash1003httpsdoiorg101111j0014-38202006tb01177x
SimmonsAMSimmonsJAampBatesMA (2008)Analyzingacous-tic interactions in natural bullfrog (Rana catesbeiana) chorusesJournal of Comparative Psychology 122 274ndash282 httpsdoiorg1010370735-70361223274
Sinervo B R amp Calsbeek R (2010) Behavioral concepts of selectionExperiments and genetic causes of selection on the sexes In D FWestneatampCWFox(Eds)Evolutionary behavioral ecologyLondonUKOxfordUniversityPress
Thompson J N (1982) Interaction and coevolution Chicago USA TheUniversityofChicagoPress
emspensp emsp | emsp1463MONTIGLIO eT aL
VanderWaal K L ObandaV Omondi G P McCowan BWang HFushingHampIsbellLA (2016)Thestrengthofweaktiesandhel-minth parasitism in giraffe social networks Behavioral Ecology 271190ndash1197httpsdoiorg101093behecoarw035
Ward P I (1993) Micro-habitat segregation and the mating systemof Gammarus pulex Animal Behavior 45 191ndash192 httpsdoiorg101006anbe19931019
Ward P I amp PorterAH (1993)The relative role of habitat structureandmale-malecompetition in thematingsystemofGammarus pulex (CrustaceaAmphipoda)AsimulationstudyAnimal Behavior45119ndash133httpsdoiorg101006anbe19931011
West-EberhardMJ(1989)Phenotypicplasticityandtheoriginsofdiver-sityAnnual Review of Ecology and Systematics20249ndash278httpsdoiorg101146annureves20110189001341
Westneat D F Hatch M IWetzel D P amp Ensminger A L (2011)IndividualvariationinparentalcarereactionnormsIntegrationofper-sonalityandplasticityAmerican Naturalist178652ndash667httpsdoiorg101086662173
Wilson A J Gelin U Perron M-C amp Reacuteale D (2009) Indirect ge-neticeffectsandtheevolutionofaggression inavertebratesystemProceedings of the Royal Society of London Series B Biological Sciences276533ndash541httpsdoiorg101098rspb20081193
Additional Supporting Informationmay be found online in the sup-portinginformationtabforthisarticle
How to cite this articleMontiglioP-OMcGlothlinJWFarineDRSocialstructuremodulatestheevolutionaryconsequencesofsocialplasticityAsocialnetworkperspectiveoninteractingphenotypesEcol Evol 201881451ndash1464 httpsdoiorg101002ece33753
APPENDIX
PHENOTYPIC MEAN AND VARIANCE
FollowingMooreetal(1997)wemodelasinglephenotypeofanindi-vidual (z)asanadditivecombinationoftheeffectsof itsowngenes(iedirectgeneticeffectsa)thenonsocialenvironmentitexperiences(e)andaplasticcomponentthatissomefunctionofthephenotypesinitssocialgroupMooreetal(1997)originallymodeledthesocialeffectasafunctionofthephenotypeofoneinteractingindividualMcGlothlinandBrodie (2009)andMcGlothlinetal (2010)consideredsocialef-fectsinapopulationconsistingofgroupsofnindividualswhereinter-actionswereassumedtooccursimultaneouslywithinagroupwithallindividuals within a group having the same strength of interactionHereweconsideramoregeneralsocialstructurewhereindividualsinteractwithallpossiblesocialinteractantsingroupsizenwithvaria-bleconnectionstrengthsirangingfrom0to1giving
wherethesummationistakenacrossalln minus1possiblesocialinterac-tionsforeachindividualsandψrepresentstheinteractioncoefficientwhichdetermines thestrengthanddirectionof the indirectpheno-typic effect of individual social interactantsHere and elsewhere aprimeindicatesaparameterbelongingtoasocialpartnerAnysocialnetworkstructurecanbemodeledbychangingthedistributionofs High-densitysocialnetworkswithstrongconnectionswillhavemanylargevaluesofswhilesparsernetworkswithweakerconnectionswillhavemanyweaksvalueswithmanyequaltozeroConsideringphenotypicfeedback(asdoMooreetal1997)insuch
The value of the two covariance terms represents how stronglystrengthofinteractiondependsonthegenesandenvironmentofin-dividualsocialpartnersThiscovarianceisdeterminedforeachindi-vidualandmayvaryacrossindividualsTheseshouldbepositiveunderhomophilyandnegativeunderheterophilyTakingthemeanandas-suming
=e=0
where double overbars indicate global means and large overbarswithintheparenthesesindicatemeanstakenacrossindividualsbasedonsummarystatisticsoftheirsocialgroupsThiscanbeexpandedasaboveto
The remainingcovariance terms represent theaveragedegree towhichindividualconnectionstrengthsareadjustedbasedonthephe-notypeofpotentialinteractantsInthecaseofhomophilyorheteroph-ilyindividualswillmakethisadjustmentbasedontheirownphenotypewithlargeindividualshavingapositivecovarianceandsmallindividu-alshavinganegativecovariance(orviceversa)ThereforeweexpecttheseaveragecovariancetermstotendtowardzeroMakingthisas-sumptionandrearrangingprovidesEquation2inthetext
EXTENSION TO MULTIPLE GROUPS
EquationA8iswrittenassumingthatthepopulationconsistsofasin-gle social networkwhere individualsmay interact in anywayNowassumethatthepopulationisdividedintomultiplegroupswhereindi-vidualsmay interactwithanystrengthswithinagroupanddonotinteract at all between groups Assuming the covariance terms inEquationA8arezeroandthatenvironmentaldeviationsdonotvaryamonggroupsthemeanofeachgroupwillbe
where overbars now indicate within-groupmeans Assuming equalgroupsizethepopulationmeanisnow
(IfgroupsvaryinsizethenEquationA10canbemodifiedtogiveaweightedmean) Ifconnectionstrengthhasnoheritablebasis thenthe covariance term become zero and EquationA10 collapses toEquation2inthetextWemaycalculateamong-groupvariancemosteasilybymakingafewassumptionsthatarealsomadeinoursimula-tionsFirstasaboveweassumethatgroupsareofequalsizeSecondweassume thatmean interactiondoesnotvaryacrossgroups ands=
=sMakingtheseassumptions
Thisshowsthat indirectgeneticeffectswillmagnifyslightdiffer-ences in genetic values across groups regardless of sign Strongermeanconnectionstrengthswillintensifythiseffect
RESPONSE TO SELECTION
FollowingMoore etal (1997) andMcGlothlin etal (2010) and as-suming that thecovariance terms inEquationA8areeither zeroorpopulation parameters that do not have a heritable component anindividualrsquostotalbreedingvaluecanbewrittenasthegeneticcontri-butiontothepopulationmean
where Ristheregressionofsaprimeonaandisthusanalogoustorelated-ness This assumes thatCov[aseprime] is negligible Positive values ofR indicatehomophilyandnegativevaluesindicateheterophilyMakingthissubstitutiongivesEquation4inthetextEquation4canalsobeexpresseddifferentlybyrearrangingas
whenextremegenotypesarerarewithingroups)Networkdensityincreases the evolutionary response of groups on average groupswith denser connections also exhibit increasedvariation in evolu-tionaryresponsetoagivenselectiongradientSuchan increase inthevariationinevolutionaryresponseobservedinourstudyisap-parentbecauseourapproachallowsustorelaxtheassumptionthatindividualswithingroupsinteractequallywithallothergroupmem-bersbyintroducinganewparameter(averageconnectionstrength=s)intoourmodelandinsteadtoexplicitlyexploretheeffectofcon-nectiondensity
44emsp|emspHomophily affects the amount of phenotypic variation within groups
Our simulations also investigate the consequencesof social struc-turewhenindividualscaninteractpreferentiallywithindividualsthathaveasimilar(iehomophily)ordissimilar(ieheterophily)pheno-typeNetworkassortment(thenetworkmeasureofhomophily)doesnot have any impact on groupsrsquomean phenotype but can gener-ateagreatervariationinsocialenvironmentswithingroupsHenceassuming that different immediate social environments can favordifferent (alternative) phenotypes within groups our simulationssuggest that homophily should be associatedwith the emergenceof phenotypic variation among individuals (or social specializationBergmuumlller amp Taborsky 2010 Montiglio Ferrari amp Reacuteale 2013)Homophilyalsohasdirectconsequencesfortheevolutionofalter-nativephenotypesbycreatingsynergyoroppositionbetweendirectand indirect genetic effectsWhen social plasticity (ψg) is positive(egwheninteractingwithanaggressiveindividualincreasesafocalindividualrsquosaggression)andindividualsshowatendencytointeractwithsimilarphenotypesthesocialenvironmentactstoshapetheirphenotypeinthesamedirectionastheirgenotypeAsaresultsocialinteractionsandsocialplasticityincreasethephenotypicvarianceofthetraitrelativetoasituationinwhichconnectionsarerandominterms of their traits It also tends to increase the strength of theevolutionaryresponsetoselectioninresponsetoagivenselectiongradientThisincreaseinevolutionaryresponsearisesfromthesyn-ergybetweendirectandindirecteffect(orbetweensocialplasticityandhomophily)ratherthanfromachangeintotalgeneticvariationwithingroups
45emsp|emspPossible applications and tests of the model and future directions
differentialandmatechoicebyfemalesThestrengthofconnectionsbetweenmales of known phenotype could be increased artificiallyusingplaybacks tosimulatemore frequent interactionsamong indi-viduals(DabelsteenampPedersen1990Otteretal2001)tomonitorhowsuchincreasesinconnectionstrengthaffecttheextentofpheno-typicandgeneticadditivevariationAlternativelyonecanmanipulatethedistributionofterritoriesavailableandthepatternsofinteractionsby controlling the locationof nest boxes foodpatches or refugesSuchapproachescouldbeparticularlysuitableforcavity-nestingbirds(Both1998)
Ourmodel also studied the consequences of homophily for theevolutionary responses of phenotypic traits Assuming individualshave some level of control on their interactions homophily can beobservedwhen individualsexhibitpreferences to interactwithcon-specificsthatare(dis)similartothemSuchpreferencescouldexplainthemaintenanceofaltruisticbehaviorbecauseoftheirpotentialroleinshapingtheselectionpressuresactingonaltruismSomeworkonfruitflieshavereportedthatindividualpreferencesforparticularsocialenvironmentsisassociatedwithgeneticvariationandcanthuspoten-tiallyevolve (egSaltzampFoley2011)Onecould testourmodel insuchstudysystemsbyeitherallowingorpreventingtheexpressionofsocialpreferences(throughmixingofindividualsormanipulatingtheirinteractions) Alternatively homophily can also be observed whenindividualssegregateintheenvironmentasafunctionoftheirphe-notype(HelfensteinDanchinampWagner2004Ward1993WardampPorter1993)Forexamplemoreandlessaggressiveindividualsseg-regateinpatcheswithdifferentdensitiesofconspecifics(Duckworth2006)Thusbymanipulatingtheheterogeneityandthescaleatwhichitisobserved(iethesizeofpatchesofdifferenthabitat)onecouldtestthepredictionsofourmodelFutureworkwillexpandthemodelwe presented here to analyze the consequences of such traits forthemaintenanceofphenotypicvariationandtheevolutionofsocialstructure
One limitationofourmodel is thatweassumebothphenotypicfeedback(Mooreetal1997)andsocialselection(Wolfetal1999)tobeabsentIncludingfeedbackmayaltertheconclusionswehavepre-sentedhereasfeedbackeffectsmaycausesocialplasticitytomovethroughnetworksincounterintuitivewaysItispossiblethatnetworkmetricsbeyondconnectionstrength (suchasclusteringcoefficientsbetweennessetc)may influencewhetherfeedbackcontributessig-nificantly to variation and response to selection Regarding socialselectionwehaveshownherethatconnectionstrengthcontributestoamong-groupvariancewhichshould intensifyresponsetohigherlevelsofselectionsuchassocialselectionWewilltreatbothfeedbackandsocialselectioninfuturecontributions
5emsp |emspCONCLUSION
Wepresentbothananalyticmodelandsimulationsextendingpre-vious work on social phenotypic plasticity to more general socialstructuresOurstudygeneratesafirstsetofverygeneralandtest-able predictions on the role of social structure in modulating the
emspensp emsp | emsp1461MONTIGLIO eT aL
consequencesofsocialplasticityWeshowthatthebasiccharacter-isticsofthestructureofinteractionsamongindividualsingroupsandpopulationscanhaveimpactsontheconsequencesofsocialplasticityforthemeanphenotypeexpressedbytheindividualstheextentofphenotypicvariationavailableforselectionandfortheabilityofthepopulation to respond to selectivepressuresWehope that futurestudieswillbeabletotestourpredictionsempiricallybyapplyingourapproachtothestudyofsocialbehavior(egaggressionandcoop-eration)socialinformationuseoralternativematingtacticsinpopu-lationswithvaryingpatternsofsocialormatinginteractionsFromatheoreticalperspectivefutureresearchwouldwarrantinvestigatingthelinkbetweenindividualpositioninsocialnetworksandtheindi-rect genetic effects it experiences and thuswhether factors otherthan individualsrsquo breeding values can lead to keystone individualsFurtherinourstudyweassumethatallindividualsexpressedplas-ticityidenticallyHoweverindividualshavealsobeenshowntovaryintheirplasticity(DingemanseKazemReacutealeampWright2010NusseyWilsonampBrommer2007WestneatHatchWetzelampEnsminger2011)andsuchvariationmayalterthepredictionsofinteractingphe-notypemodels(KazancıoğluKlugampAlonzo2012)Linkingindividualdifferencesinbothsocialpositionandplasticitycouldyieldnewin-sightsandagreaterunderstandingoftheevolutionarymechanismsthatunderpinphenotypicvariationwithinindividualsbetweenindi-vidualsandamongpopulations
ACKNOWLEDGMENTS
We thank the Reader Hendry and Barrett laboratories in McGillUniversity forconstructivecommentsonadraftof thismanuscriptPOMwas supported by aNSERCpostdoctoral fellowshipDRF re-ceived funding from a grant to theBBSRC (BBL0060811 toBCSheldon)andtheMaxPlanckSociety
CONFLICT OF INTEREST
Nonedeclared
AUTHOR CONTRIBUTIONS
POMandDRFbuiltthesimulationsandJWMdevelopedthemodelPOMdrafted themanuscript andproduced the figuresAll authorscontributedtorevisionsandapprovedthefinalversionofthearticle
AplinLMFarineDRMorand-FerronJCockburnAThorntonAamp SheldonBC (2015) Experimentally induced innovations lead topersistentcultureviaconformityinwildbirdsNature518538ndash541
Aplin LMFirthJAFarineDRVoelklBCratesRACulinaAhellipSheldonBC (2015)Consistent individual differences in the so-cialphenotypesofwildgreattits(Parusmajor)Animal Behaviour108117ndash127httpsdoiorg101016janbehav201507016
BaileyNWampHoskins J L (2014)Detecting cryptic indirect geneticeffectsEvolution681871ndash1882httpsdoiorg101111evo12401
Bailey N W amp Zuk M (2012) Socially flexible female choice differsamongpopulationsofthePacificfieldcricketGeographicalvariationin the interaction coefficient psi (Ψ)Proceedings of the Royal Society of London Series B Biological Sciences 279 3589ndash3596 httpsdoiorg101098rspb20120631
Bergmuumlller R amp Taborsky M (2010) Animal personality due to socialnichespecialisationTrends in Ecology amp Evolution25504ndash511httpsdoiorg101016jtree201006012
Bijma P ampWade M J (2008) The joint effects of kin multilevel se-lection and indirect genetic effects on response to genetic selec-tion Journal of Evolutionary Biology 21 1175ndash1188 httpsdoiorg101111j1420-9101200801550x
Boatright-HorowitzSLHorowitzSSampSimmonsAM(2000)Patternsof vocal interactions n a BullfrogRana catesbeiana chorus preferen-tial responding to farneighborsEthology106701ndash712httpsdoiorg101046j1439-0310200000580x
BothC(1998)Experimentalevidencefordensitydependenceofrepro-ductioningreattitsJournal of Animal Ecology67667ndash674httpsdoiorg101046j1365-2656199800228x
Cappa E P amp Cantet R J C (2008) Direct and competition additiveeffects in treebreedingBayesianestimation froman individual treemixedmodelSilvae Genetica5745ndash56
ChangAampSihA (2013)Multilevel selection andeffects of keystonehyperaggressivemalesonmatingsuccessandbehaviorinstreamwaterstridersBehavioral Ecology241166ndash1176httpsdoiorg101093behecoart044
Clutton-BrockTH(1989)MammalianmatingsystemsProceedings of the Royal Society B236339ndash372httpsdoiorg101098rspb19890027
Crowley P H amp Cox J J (2011) Intraguild mutualism Trends in Ecology amp Evolution 26 627ndash633 httpsdoiorg101016jtree201107011
Duckworth R A (2006) Aggressive behaviour affects selection onmorphology by influencing settlement patterns in a passerine birdProceedings of the Royal Society B 273 1789ndash1795 httpsdoiorg101098rspb20063517
Farine D R (2014) Measuring phenotypic assortment in animal so-cial networks Weighted associations are more robust than binaryedges Animal Behavior 89 141ndash153 httpsdoiorg101016janbehav201401001
FarineDRampWhiteheadH(2015)Constructingconductingandinter-preting animal social network analysis Journal of Animal Ecology841144ndash1163httpsdoiorg1011111365-265612418
Fawcett TW amp Johnstone RA (2010) Learning your own strengthWinner and loser effects should change with age and experienceProceedings of the Royal Society of London Series B Biological Sciences2771427ndash1434httpsdoiorg101098rspb20092088
Fisher D N amp McAdam A G (2017) Social traits social networksand evolutionary biology Journal of Evolutionary Biology httpsdoiorg101111jeb13195Inpress
FormicaVAWood CW LarsenW B Butterfield R EAugatMEHougenHYampBrodieIIIED(2012)Fitnessconsequencesofsocialnetworkpositioninawildpopulationofforkedfungusbeetles(Bolitotherus cornutus) Journal of Evolutionary Biology 25 130ndash137httpsdoiorg101111j1420-9101201102411x
Greenfield M D amp Rand S A (2000) Frogs have rules selective at-tention algorithms regulate chorusing in Physalaemus pustulosus (Leptodactylidae)Ethology106131ndash147
Helfenstein FDanchin E ampWagner RH (2004)Assortativematingand sexual size dimorphism in blacklegged kittiwakes Waterbirds27 350ndash354 httpsdoiorg1016751524-4695(2004)027[0350AMASSD]20CO2
Herbert-Read J E Krause S Morrell L J Schaerf T M Krause JampWardAJW (2013)The roleof individuality in collectivegroupmovementProceedings of the Royal Society B- Biological Sciences28020122564
KeiserCNampPruittJN (2014)Personality composition ismore im-portantthangroupsizeindeterminingcollectiveforagingbehaviourinthewildProceedings of the Royal Society of London Series B Biological Sciences28120141424httpsdoiorg101098rspb20141424
Krause J amp Ruxton GD (2002) Living in groups Oxford UKOxfordUniversityPress
Landeau L ampTerborgh J (1986)Oddity and the ldquoconfusion effectrdquo inpredationAnimal Behavior341372ndash1380httpsdoiorg101016S0003-3472(86)80208-1
Magnhagen C amp Bunnefeld N (2009) Express your personality or goalong with the group What determines the behaviour of shoalingperchProceedings of the Royal Society B- Biological Sciences2763369ndash3375httpsdoiorg101098rspb20090851
McDonaldG C FarineD R Foster K R ampBiernaskie JM (2017)Assortment and the analysis of natural selection on social traitsEvolution712693ndash2702httpsdoiorg101111evo13365
McGlothlin JW amp Brodie III E D (2009) How to measure individ-ual genetic effects The congruence of trait-based and variance-partitioning approaches Evolution 63 1785ndash1795 httpsdoiorg101111j1558-5646200900676x
McGlothlin J W Moore A J Wolf J B amp Brodie III E D(2010) Interacting phenotypes and the evolutionary pro-cess III Social evolution Evolution 64 2558ndash2574 httpsdoiorg101111j1558-5646201001012x
MillerJRBAmentJMampSchmitzOJ (2014)Fearon themovePredatorhuntingmodepredictsvariation inpreymortalityandplas-ticityinpreyspatialresponseJournal of Animal Ecology83214ndash222httpsdoiorg1011111365-265612111
ModlmeierAPKeiserCNWattersJVSihAampPruittJN(2014)The keystone individual concept An ecological and evolutionaryoverview Animal Behavior 89 53ndash62 httpsdoiorg101016janbehav201312020
MontiglioP-OFerrariCampReacutealeD(2013)Socialnichespecializationunder constraints Personality social interactions and environmentalheterogeneityPhilosophical Transactions of the Royal Society of London Series B Biological Sciences36820120343httpsdoiorg101098rstb20120343
Moore A J Brodie III E D ampWolf J B (1997) Interacting pheno-types and the evolutionary process I Direct and indirect geneticeffects of social interactions Evolution 51 1352ndash1362 httpsdoiorg101111j1558-56461997tb01458x
NonacsPampKapheimKM(2007)Socialheterosisandthemaintenanceof genetic diversity Journal of Evolutionary Biology 20 2253ndash2265httpsdoiorg101111j1420-9101200701418x
Nussey D H Wilson A J amp Brommer J E (2007) The evolution-ary ecology of individual phenotypic plasticity in wild popula-tions Journal of Evolutionary Biology 20 831ndash844 httpsdoiorg101111j1420-9101200701300x
OtterKAStewartIRKMcGregorPKTerryAMRDabelsteenTampBurkeT(2001)Extra-pairpaternityamonggreattitsParus major following manipulation of male signals Journal of Avian Biology 32338ndash344httpsdoiorg101111j0908-88572001320408x
Pruitt J N Bolnick D I Sih A DiRienzo N amp Pinter-Wollman N(2016)Behavioralhypervolumesofspidercoloniespredictscommu-nity performance and disbandmentProceedings of the Royal Society B- Biological Sciences 283 20161409 httpsdoiorg101098rspb20161409
PruittJNampPinter-WollmanN(2015)Thelegacyeffectsofkeystonein-dividualsoncollectivebehaviourscaletohowlongtheyremainwithina group Proceedings of the Royal Society B- Biological Sciences 28220151766httpsdoiorg101098rspb20151766
RoyleNJHartley IROwens I P FampParkerGA (1999) Siblingcompetition and the evolution of growth rates in birds Proceedings of the Royal Society B 266 923ndash932 httpsdoiorg101098rspb19990725
SaltzJBampFoleyBR(2011)Naturalgeneticvariationinsocialnicheconstruction Social effects of aggression drive disruptive sexual se-lectioninDrosophila melanogaster American Naturalist177645ndash654httpsdoiorg101086659631
ShusterSM LonsdorfEVWimpGMBaileyJKampWhithamTG (2006) Community heritabilitymeasures the evolutionary conse-quencesofindirectgeneticeffectsoncommunitystructureEvolution60991ndash1003httpsdoiorg101111j0014-38202006tb01177x
SimmonsAMSimmonsJAampBatesMA (2008)Analyzingacous-tic interactions in natural bullfrog (Rana catesbeiana) chorusesJournal of Comparative Psychology 122 274ndash282 httpsdoiorg1010370735-70361223274
Sinervo B R amp Calsbeek R (2010) Behavioral concepts of selectionExperiments and genetic causes of selection on the sexes In D FWestneatampCWFox(Eds)Evolutionary behavioral ecologyLondonUKOxfordUniversityPress
Thompson J N (1982) Interaction and coevolution Chicago USA TheUniversityofChicagoPress
emspensp emsp | emsp1463MONTIGLIO eT aL
VanderWaal K L ObandaV Omondi G P McCowan BWang HFushingHampIsbellLA (2016)Thestrengthofweaktiesandhel-minth parasitism in giraffe social networks Behavioral Ecology 271190ndash1197httpsdoiorg101093behecoarw035
Ward P I (1993) Micro-habitat segregation and the mating systemof Gammarus pulex Animal Behavior 45 191ndash192 httpsdoiorg101006anbe19931019
Ward P I amp PorterAH (1993)The relative role of habitat structureandmale-malecompetition in thematingsystemofGammarus pulex (CrustaceaAmphipoda)AsimulationstudyAnimal Behavior45119ndash133httpsdoiorg101006anbe19931011
West-EberhardMJ(1989)Phenotypicplasticityandtheoriginsofdiver-sityAnnual Review of Ecology and Systematics20249ndash278httpsdoiorg101146annureves20110189001341
Westneat D F Hatch M IWetzel D P amp Ensminger A L (2011)IndividualvariationinparentalcarereactionnormsIntegrationofper-sonalityandplasticityAmerican Naturalist178652ndash667httpsdoiorg101086662173
Wilson A J Gelin U Perron M-C amp Reacuteale D (2009) Indirect ge-neticeffectsandtheevolutionofaggression inavertebratesystemProceedings of the Royal Society of London Series B Biological Sciences276533ndash541httpsdoiorg101098rspb20081193
Additional Supporting Informationmay be found online in the sup-portinginformationtabforthisarticle
How to cite this articleMontiglioP-OMcGlothlinJWFarineDRSocialstructuremodulatestheevolutionaryconsequencesofsocialplasticityAsocialnetworkperspectiveoninteractingphenotypesEcol Evol 201881451ndash1464 httpsdoiorg101002ece33753
APPENDIX
PHENOTYPIC MEAN AND VARIANCE
FollowingMooreetal(1997)wemodelasinglephenotypeofanindi-vidual (z)asanadditivecombinationoftheeffectsof itsowngenes(iedirectgeneticeffectsa)thenonsocialenvironmentitexperiences(e)andaplasticcomponentthatissomefunctionofthephenotypesinitssocialgroupMooreetal(1997)originallymodeledthesocialeffectasafunctionofthephenotypeofoneinteractingindividualMcGlothlinandBrodie (2009)andMcGlothlinetal (2010)consideredsocialef-fectsinapopulationconsistingofgroupsofnindividualswhereinter-actionswereassumedtooccursimultaneouslywithinagroupwithallindividuals within a group having the same strength of interactionHereweconsideramoregeneralsocialstructurewhereindividualsinteractwithallpossiblesocialinteractantsingroupsizenwithvaria-bleconnectionstrengthsirangingfrom0to1giving
wherethesummationistakenacrossalln minus1possiblesocialinterac-tionsforeachindividualsandψrepresentstheinteractioncoefficientwhichdetermines thestrengthanddirectionof the indirectpheno-typic effect of individual social interactantsHere and elsewhere aprimeindicatesaparameterbelongingtoasocialpartnerAnysocialnetworkstructurecanbemodeledbychangingthedistributionofs High-densitysocialnetworkswithstrongconnectionswillhavemanylargevaluesofswhilesparsernetworkswithweakerconnectionswillhavemanyweaksvalueswithmanyequaltozeroConsideringphenotypicfeedback(asdoMooreetal1997)insuch
The value of the two covariance terms represents how stronglystrengthofinteractiondependsonthegenesandenvironmentofin-dividualsocialpartnersThiscovarianceisdeterminedforeachindi-vidualandmayvaryacrossindividualsTheseshouldbepositiveunderhomophilyandnegativeunderheterophilyTakingthemeanandas-suming
=e=0
where double overbars indicate global means and large overbarswithintheparenthesesindicatemeanstakenacrossindividualsbasedonsummarystatisticsoftheirsocialgroupsThiscanbeexpandedasaboveto
The remainingcovariance terms represent theaveragedegree towhichindividualconnectionstrengthsareadjustedbasedonthephe-notypeofpotentialinteractantsInthecaseofhomophilyorheteroph-ilyindividualswillmakethisadjustmentbasedontheirownphenotypewithlargeindividualshavingapositivecovarianceandsmallindividu-alshavinganegativecovariance(orviceversa)ThereforeweexpecttheseaveragecovariancetermstotendtowardzeroMakingthisas-sumptionandrearrangingprovidesEquation2inthetext
EXTENSION TO MULTIPLE GROUPS
EquationA8iswrittenassumingthatthepopulationconsistsofasin-gle social networkwhere individualsmay interact in anywayNowassumethatthepopulationisdividedintomultiplegroupswhereindi-vidualsmay interactwithanystrengthswithinagroupanddonotinteract at all between groups Assuming the covariance terms inEquationA8arezeroandthatenvironmentaldeviationsdonotvaryamonggroupsthemeanofeachgroupwillbe
where overbars now indicate within-groupmeans Assuming equalgroupsizethepopulationmeanisnow
(IfgroupsvaryinsizethenEquationA10canbemodifiedtogiveaweightedmean) Ifconnectionstrengthhasnoheritablebasis thenthe covariance term become zero and EquationA10 collapses toEquation2inthetextWemaycalculateamong-groupvariancemosteasilybymakingafewassumptionsthatarealsomadeinoursimula-tionsFirstasaboveweassumethatgroupsareofequalsizeSecondweassume thatmean interactiondoesnotvaryacrossgroups ands=
=sMakingtheseassumptions
Thisshowsthat indirectgeneticeffectswillmagnifyslightdiffer-ences in genetic values across groups regardless of sign Strongermeanconnectionstrengthswillintensifythiseffect
RESPONSE TO SELECTION
FollowingMoore etal (1997) andMcGlothlin etal (2010) and as-suming that thecovariance terms inEquationA8areeither zeroorpopulation parameters that do not have a heritable component anindividualrsquostotalbreedingvaluecanbewrittenasthegeneticcontri-butiontothepopulationmean
where Ristheregressionofsaprimeonaandisthusanalogoustorelated-ness This assumes thatCov[aseprime] is negligible Positive values ofR indicatehomophilyandnegativevaluesindicateheterophilyMakingthissubstitutiongivesEquation4inthetextEquation4canalsobeexpresseddifferentlybyrearrangingas
consequencesofsocialplasticityWeshowthatthebasiccharacter-isticsofthestructureofinteractionsamongindividualsingroupsandpopulationscanhaveimpactsontheconsequencesofsocialplasticityforthemeanphenotypeexpressedbytheindividualstheextentofphenotypicvariationavailableforselectionandfortheabilityofthepopulation to respond to selectivepressuresWehope that futurestudieswillbeabletotestourpredictionsempiricallybyapplyingourapproachtothestudyofsocialbehavior(egaggressionandcoop-eration)socialinformationuseoralternativematingtacticsinpopu-lationswithvaryingpatternsofsocialormatinginteractionsFromatheoreticalperspectivefutureresearchwouldwarrantinvestigatingthelinkbetweenindividualpositioninsocialnetworksandtheindi-rect genetic effects it experiences and thuswhether factors otherthan individualsrsquo breeding values can lead to keystone individualsFurtherinourstudyweassumethatallindividualsexpressedplas-ticityidenticallyHoweverindividualshavealsobeenshowntovaryintheirplasticity(DingemanseKazemReacutealeampWright2010NusseyWilsonampBrommer2007WestneatHatchWetzelampEnsminger2011)andsuchvariationmayalterthepredictionsofinteractingphe-notypemodels(KazancıoğluKlugampAlonzo2012)Linkingindividualdifferencesinbothsocialpositionandplasticitycouldyieldnewin-sightsandagreaterunderstandingoftheevolutionarymechanismsthatunderpinphenotypicvariationwithinindividualsbetweenindi-vidualsandamongpopulations
ACKNOWLEDGMENTS
We thank the Reader Hendry and Barrett laboratories in McGillUniversity forconstructivecommentsonadraftof thismanuscriptPOMwas supported by aNSERCpostdoctoral fellowshipDRF re-ceived funding from a grant to theBBSRC (BBL0060811 toBCSheldon)andtheMaxPlanckSociety
CONFLICT OF INTEREST
Nonedeclared
AUTHOR CONTRIBUTIONS
POMandDRFbuiltthesimulationsandJWMdevelopedthemodelPOMdrafted themanuscript andproduced the figuresAll authorscontributedtorevisionsandapprovedthefinalversionofthearticle
AplinLMFarineDRMorand-FerronJCockburnAThorntonAamp SheldonBC (2015) Experimentally induced innovations lead topersistentcultureviaconformityinwildbirdsNature518538ndash541
Aplin LMFirthJAFarineDRVoelklBCratesRACulinaAhellipSheldonBC (2015)Consistent individual differences in the so-cialphenotypesofwildgreattits(Parusmajor)Animal Behaviour108117ndash127httpsdoiorg101016janbehav201507016
BaileyNWampHoskins J L (2014)Detecting cryptic indirect geneticeffectsEvolution681871ndash1882httpsdoiorg101111evo12401
Bailey N W amp Zuk M (2012) Socially flexible female choice differsamongpopulationsofthePacificfieldcricketGeographicalvariationin the interaction coefficient psi (Ψ)Proceedings of the Royal Society of London Series B Biological Sciences 279 3589ndash3596 httpsdoiorg101098rspb20120631
Bergmuumlller R amp Taborsky M (2010) Animal personality due to socialnichespecialisationTrends in Ecology amp Evolution25504ndash511httpsdoiorg101016jtree201006012
Bijma P ampWade M J (2008) The joint effects of kin multilevel se-lection and indirect genetic effects on response to genetic selec-tion Journal of Evolutionary Biology 21 1175ndash1188 httpsdoiorg101111j1420-9101200801550x
Boatright-HorowitzSLHorowitzSSampSimmonsAM(2000)Patternsof vocal interactions n a BullfrogRana catesbeiana chorus preferen-tial responding to farneighborsEthology106701ndash712httpsdoiorg101046j1439-0310200000580x
BothC(1998)Experimentalevidencefordensitydependenceofrepro-ductioningreattitsJournal of Animal Ecology67667ndash674httpsdoiorg101046j1365-2656199800228x
Cappa E P amp Cantet R J C (2008) Direct and competition additiveeffects in treebreedingBayesianestimation froman individual treemixedmodelSilvae Genetica5745ndash56
ChangAampSihA (2013)Multilevel selection andeffects of keystonehyperaggressivemalesonmatingsuccessandbehaviorinstreamwaterstridersBehavioral Ecology241166ndash1176httpsdoiorg101093behecoart044
Clutton-BrockTH(1989)MammalianmatingsystemsProceedings of the Royal Society B236339ndash372httpsdoiorg101098rspb19890027
Crowley P H amp Cox J J (2011) Intraguild mutualism Trends in Ecology amp Evolution 26 627ndash633 httpsdoiorg101016jtree201107011
Duckworth R A (2006) Aggressive behaviour affects selection onmorphology by influencing settlement patterns in a passerine birdProceedings of the Royal Society B 273 1789ndash1795 httpsdoiorg101098rspb20063517
Farine D R (2014) Measuring phenotypic assortment in animal so-cial networks Weighted associations are more robust than binaryedges Animal Behavior 89 141ndash153 httpsdoiorg101016janbehav201401001
FarineDRampWhiteheadH(2015)Constructingconductingandinter-preting animal social network analysis Journal of Animal Ecology841144ndash1163httpsdoiorg1011111365-265612418
Fawcett TW amp Johnstone RA (2010) Learning your own strengthWinner and loser effects should change with age and experienceProceedings of the Royal Society of London Series B Biological Sciences2771427ndash1434httpsdoiorg101098rspb20092088
Fisher D N amp McAdam A G (2017) Social traits social networksand evolutionary biology Journal of Evolutionary Biology httpsdoiorg101111jeb13195Inpress
FormicaVAWood CW LarsenW B Butterfield R EAugatMEHougenHYampBrodieIIIED(2012)Fitnessconsequencesofsocialnetworkpositioninawildpopulationofforkedfungusbeetles(Bolitotherus cornutus) Journal of Evolutionary Biology 25 130ndash137httpsdoiorg101111j1420-9101201102411x
Greenfield M D amp Rand S A (2000) Frogs have rules selective at-tention algorithms regulate chorusing in Physalaemus pustulosus (Leptodactylidae)Ethology106131ndash147
Helfenstein FDanchin E ampWagner RH (2004)Assortativematingand sexual size dimorphism in blacklegged kittiwakes Waterbirds27 350ndash354 httpsdoiorg1016751524-4695(2004)027[0350AMASSD]20CO2
Herbert-Read J E Krause S Morrell L J Schaerf T M Krause JampWardAJW (2013)The roleof individuality in collectivegroupmovementProceedings of the Royal Society B- Biological Sciences28020122564
KeiserCNampPruittJN (2014)Personality composition ismore im-portantthangroupsizeindeterminingcollectiveforagingbehaviourinthewildProceedings of the Royal Society of London Series B Biological Sciences28120141424httpsdoiorg101098rspb20141424
Krause J amp Ruxton GD (2002) Living in groups Oxford UKOxfordUniversityPress
Landeau L ampTerborgh J (1986)Oddity and the ldquoconfusion effectrdquo inpredationAnimal Behavior341372ndash1380httpsdoiorg101016S0003-3472(86)80208-1
Magnhagen C amp Bunnefeld N (2009) Express your personality or goalong with the group What determines the behaviour of shoalingperchProceedings of the Royal Society B- Biological Sciences2763369ndash3375httpsdoiorg101098rspb20090851
McDonaldG C FarineD R Foster K R ampBiernaskie JM (2017)Assortment and the analysis of natural selection on social traitsEvolution712693ndash2702httpsdoiorg101111evo13365
McGlothlin JW amp Brodie III E D (2009) How to measure individ-ual genetic effects The congruence of trait-based and variance-partitioning approaches Evolution 63 1785ndash1795 httpsdoiorg101111j1558-5646200900676x
McGlothlin J W Moore A J Wolf J B amp Brodie III E D(2010) Interacting phenotypes and the evolutionary pro-cess III Social evolution Evolution 64 2558ndash2574 httpsdoiorg101111j1558-5646201001012x
MillerJRBAmentJMampSchmitzOJ (2014)Fearon themovePredatorhuntingmodepredictsvariation inpreymortalityandplas-ticityinpreyspatialresponseJournal of Animal Ecology83214ndash222httpsdoiorg1011111365-265612111
ModlmeierAPKeiserCNWattersJVSihAampPruittJN(2014)The keystone individual concept An ecological and evolutionaryoverview Animal Behavior 89 53ndash62 httpsdoiorg101016janbehav201312020
MontiglioP-OFerrariCampReacutealeD(2013)Socialnichespecializationunder constraints Personality social interactions and environmentalheterogeneityPhilosophical Transactions of the Royal Society of London Series B Biological Sciences36820120343httpsdoiorg101098rstb20120343
Moore A J Brodie III E D ampWolf J B (1997) Interacting pheno-types and the evolutionary process I Direct and indirect geneticeffects of social interactions Evolution 51 1352ndash1362 httpsdoiorg101111j1558-56461997tb01458x
NonacsPampKapheimKM(2007)Socialheterosisandthemaintenanceof genetic diversity Journal of Evolutionary Biology 20 2253ndash2265httpsdoiorg101111j1420-9101200701418x
Nussey D H Wilson A J amp Brommer J E (2007) The evolution-ary ecology of individual phenotypic plasticity in wild popula-tions Journal of Evolutionary Biology 20 831ndash844 httpsdoiorg101111j1420-9101200701300x
OtterKAStewartIRKMcGregorPKTerryAMRDabelsteenTampBurkeT(2001)Extra-pairpaternityamonggreattitsParus major following manipulation of male signals Journal of Avian Biology 32338ndash344httpsdoiorg101111j0908-88572001320408x
Pruitt J N Bolnick D I Sih A DiRienzo N amp Pinter-Wollman N(2016)Behavioralhypervolumesofspidercoloniespredictscommu-nity performance and disbandmentProceedings of the Royal Society B- Biological Sciences 283 20161409 httpsdoiorg101098rspb20161409
PruittJNampPinter-WollmanN(2015)Thelegacyeffectsofkeystonein-dividualsoncollectivebehaviourscaletohowlongtheyremainwithina group Proceedings of the Royal Society B- Biological Sciences 28220151766httpsdoiorg101098rspb20151766
RoyleNJHartley IROwens I P FampParkerGA (1999) Siblingcompetition and the evolution of growth rates in birds Proceedings of the Royal Society B 266 923ndash932 httpsdoiorg101098rspb19990725
SaltzJBampFoleyBR(2011)Naturalgeneticvariationinsocialnicheconstruction Social effects of aggression drive disruptive sexual se-lectioninDrosophila melanogaster American Naturalist177645ndash654httpsdoiorg101086659631
ShusterSM LonsdorfEVWimpGMBaileyJKampWhithamTG (2006) Community heritabilitymeasures the evolutionary conse-quencesofindirectgeneticeffectsoncommunitystructureEvolution60991ndash1003httpsdoiorg101111j0014-38202006tb01177x
SimmonsAMSimmonsJAampBatesMA (2008)Analyzingacous-tic interactions in natural bullfrog (Rana catesbeiana) chorusesJournal of Comparative Psychology 122 274ndash282 httpsdoiorg1010370735-70361223274
Sinervo B R amp Calsbeek R (2010) Behavioral concepts of selectionExperiments and genetic causes of selection on the sexes In D FWestneatampCWFox(Eds)Evolutionary behavioral ecologyLondonUKOxfordUniversityPress
Thompson J N (1982) Interaction and coevolution Chicago USA TheUniversityofChicagoPress
emspensp emsp | emsp1463MONTIGLIO eT aL
VanderWaal K L ObandaV Omondi G P McCowan BWang HFushingHampIsbellLA (2016)Thestrengthofweaktiesandhel-minth parasitism in giraffe social networks Behavioral Ecology 271190ndash1197httpsdoiorg101093behecoarw035
Ward P I (1993) Micro-habitat segregation and the mating systemof Gammarus pulex Animal Behavior 45 191ndash192 httpsdoiorg101006anbe19931019
Ward P I amp PorterAH (1993)The relative role of habitat structureandmale-malecompetition in thematingsystemofGammarus pulex (CrustaceaAmphipoda)AsimulationstudyAnimal Behavior45119ndash133httpsdoiorg101006anbe19931011
West-EberhardMJ(1989)Phenotypicplasticityandtheoriginsofdiver-sityAnnual Review of Ecology and Systematics20249ndash278httpsdoiorg101146annureves20110189001341
Westneat D F Hatch M IWetzel D P amp Ensminger A L (2011)IndividualvariationinparentalcarereactionnormsIntegrationofper-sonalityandplasticityAmerican Naturalist178652ndash667httpsdoiorg101086662173
Wilson A J Gelin U Perron M-C amp Reacuteale D (2009) Indirect ge-neticeffectsandtheevolutionofaggression inavertebratesystemProceedings of the Royal Society of London Series B Biological Sciences276533ndash541httpsdoiorg101098rspb20081193
Additional Supporting Informationmay be found online in the sup-portinginformationtabforthisarticle
How to cite this articleMontiglioP-OMcGlothlinJWFarineDRSocialstructuremodulatestheevolutionaryconsequencesofsocialplasticityAsocialnetworkperspectiveoninteractingphenotypesEcol Evol 201881451ndash1464 httpsdoiorg101002ece33753
APPENDIX
PHENOTYPIC MEAN AND VARIANCE
FollowingMooreetal(1997)wemodelasinglephenotypeofanindi-vidual (z)asanadditivecombinationoftheeffectsof itsowngenes(iedirectgeneticeffectsa)thenonsocialenvironmentitexperiences(e)andaplasticcomponentthatissomefunctionofthephenotypesinitssocialgroupMooreetal(1997)originallymodeledthesocialeffectasafunctionofthephenotypeofoneinteractingindividualMcGlothlinandBrodie (2009)andMcGlothlinetal (2010)consideredsocialef-fectsinapopulationconsistingofgroupsofnindividualswhereinter-actionswereassumedtooccursimultaneouslywithinagroupwithallindividuals within a group having the same strength of interactionHereweconsideramoregeneralsocialstructurewhereindividualsinteractwithallpossiblesocialinteractantsingroupsizenwithvaria-bleconnectionstrengthsirangingfrom0to1giving
wherethesummationistakenacrossalln minus1possiblesocialinterac-tionsforeachindividualsandψrepresentstheinteractioncoefficientwhichdetermines thestrengthanddirectionof the indirectpheno-typic effect of individual social interactantsHere and elsewhere aprimeindicatesaparameterbelongingtoasocialpartnerAnysocialnetworkstructurecanbemodeledbychangingthedistributionofs High-densitysocialnetworkswithstrongconnectionswillhavemanylargevaluesofswhilesparsernetworkswithweakerconnectionswillhavemanyweaksvalueswithmanyequaltozeroConsideringphenotypicfeedback(asdoMooreetal1997)insuch
The value of the two covariance terms represents how stronglystrengthofinteractiondependsonthegenesandenvironmentofin-dividualsocialpartnersThiscovarianceisdeterminedforeachindi-vidualandmayvaryacrossindividualsTheseshouldbepositiveunderhomophilyandnegativeunderheterophilyTakingthemeanandas-suming
=e=0
where double overbars indicate global means and large overbarswithintheparenthesesindicatemeanstakenacrossindividualsbasedonsummarystatisticsoftheirsocialgroupsThiscanbeexpandedasaboveto
The remainingcovariance terms represent theaveragedegree towhichindividualconnectionstrengthsareadjustedbasedonthephe-notypeofpotentialinteractantsInthecaseofhomophilyorheteroph-ilyindividualswillmakethisadjustmentbasedontheirownphenotypewithlargeindividualshavingapositivecovarianceandsmallindividu-alshavinganegativecovariance(orviceversa)ThereforeweexpecttheseaveragecovariancetermstotendtowardzeroMakingthisas-sumptionandrearrangingprovidesEquation2inthetext
EXTENSION TO MULTIPLE GROUPS
EquationA8iswrittenassumingthatthepopulationconsistsofasin-gle social networkwhere individualsmay interact in anywayNowassumethatthepopulationisdividedintomultiplegroupswhereindi-vidualsmay interactwithanystrengthswithinagroupanddonotinteract at all between groups Assuming the covariance terms inEquationA8arezeroandthatenvironmentaldeviationsdonotvaryamonggroupsthemeanofeachgroupwillbe
where overbars now indicate within-groupmeans Assuming equalgroupsizethepopulationmeanisnow
(IfgroupsvaryinsizethenEquationA10canbemodifiedtogiveaweightedmean) Ifconnectionstrengthhasnoheritablebasis thenthe covariance term become zero and EquationA10 collapses toEquation2inthetextWemaycalculateamong-groupvariancemosteasilybymakingafewassumptionsthatarealsomadeinoursimula-tionsFirstasaboveweassumethatgroupsareofequalsizeSecondweassume thatmean interactiondoesnotvaryacrossgroups ands=
=sMakingtheseassumptions
Thisshowsthat indirectgeneticeffectswillmagnifyslightdiffer-ences in genetic values across groups regardless of sign Strongermeanconnectionstrengthswillintensifythiseffect
RESPONSE TO SELECTION
FollowingMoore etal (1997) andMcGlothlin etal (2010) and as-suming that thecovariance terms inEquationA8areeither zeroorpopulation parameters that do not have a heritable component anindividualrsquostotalbreedingvaluecanbewrittenasthegeneticcontri-butiontothepopulationmean
where Ristheregressionofsaprimeonaandisthusanalogoustorelated-ness This assumes thatCov[aseprime] is negligible Positive values ofR indicatehomophilyandnegativevaluesindicateheterophilyMakingthissubstitutiongivesEquation4inthetextEquation4canalsobeexpresseddifferentlybyrearrangingas
FarineDRampWhiteheadH(2015)Constructingconductingandinter-preting animal social network analysis Journal of Animal Ecology841144ndash1163httpsdoiorg1011111365-265612418
Fawcett TW amp Johnstone RA (2010) Learning your own strengthWinner and loser effects should change with age and experienceProceedings of the Royal Society of London Series B Biological Sciences2771427ndash1434httpsdoiorg101098rspb20092088
Fisher D N amp McAdam A G (2017) Social traits social networksand evolutionary biology Journal of Evolutionary Biology httpsdoiorg101111jeb13195Inpress
FormicaVAWood CW LarsenW B Butterfield R EAugatMEHougenHYampBrodieIIIED(2012)Fitnessconsequencesofsocialnetworkpositioninawildpopulationofforkedfungusbeetles(Bolitotherus cornutus) Journal of Evolutionary Biology 25 130ndash137httpsdoiorg101111j1420-9101201102411x
Greenfield M D amp Rand S A (2000) Frogs have rules selective at-tention algorithms regulate chorusing in Physalaemus pustulosus (Leptodactylidae)Ethology106131ndash147
Helfenstein FDanchin E ampWagner RH (2004)Assortativematingand sexual size dimorphism in blacklegged kittiwakes Waterbirds27 350ndash354 httpsdoiorg1016751524-4695(2004)027[0350AMASSD]20CO2
Herbert-Read J E Krause S Morrell L J Schaerf T M Krause JampWardAJW (2013)The roleof individuality in collectivegroupmovementProceedings of the Royal Society B- Biological Sciences28020122564
KeiserCNampPruittJN (2014)Personality composition ismore im-portantthangroupsizeindeterminingcollectiveforagingbehaviourinthewildProceedings of the Royal Society of London Series B Biological Sciences28120141424httpsdoiorg101098rspb20141424
Krause J amp Ruxton GD (2002) Living in groups Oxford UKOxfordUniversityPress
Landeau L ampTerborgh J (1986)Oddity and the ldquoconfusion effectrdquo inpredationAnimal Behavior341372ndash1380httpsdoiorg101016S0003-3472(86)80208-1
Magnhagen C amp Bunnefeld N (2009) Express your personality or goalong with the group What determines the behaviour of shoalingperchProceedings of the Royal Society B- Biological Sciences2763369ndash3375httpsdoiorg101098rspb20090851
McDonaldG C FarineD R Foster K R ampBiernaskie JM (2017)Assortment and the analysis of natural selection on social traitsEvolution712693ndash2702httpsdoiorg101111evo13365
McGlothlin JW amp Brodie III E D (2009) How to measure individ-ual genetic effects The congruence of trait-based and variance-partitioning approaches Evolution 63 1785ndash1795 httpsdoiorg101111j1558-5646200900676x
McGlothlin J W Moore A J Wolf J B amp Brodie III E D(2010) Interacting phenotypes and the evolutionary pro-cess III Social evolution Evolution 64 2558ndash2574 httpsdoiorg101111j1558-5646201001012x
MillerJRBAmentJMampSchmitzOJ (2014)Fearon themovePredatorhuntingmodepredictsvariation inpreymortalityandplas-ticityinpreyspatialresponseJournal of Animal Ecology83214ndash222httpsdoiorg1011111365-265612111
ModlmeierAPKeiserCNWattersJVSihAampPruittJN(2014)The keystone individual concept An ecological and evolutionaryoverview Animal Behavior 89 53ndash62 httpsdoiorg101016janbehav201312020
MontiglioP-OFerrariCampReacutealeD(2013)Socialnichespecializationunder constraints Personality social interactions and environmentalheterogeneityPhilosophical Transactions of the Royal Society of London Series B Biological Sciences36820120343httpsdoiorg101098rstb20120343
Moore A J Brodie III E D ampWolf J B (1997) Interacting pheno-types and the evolutionary process I Direct and indirect geneticeffects of social interactions Evolution 51 1352ndash1362 httpsdoiorg101111j1558-56461997tb01458x
NonacsPampKapheimKM(2007)Socialheterosisandthemaintenanceof genetic diversity Journal of Evolutionary Biology 20 2253ndash2265httpsdoiorg101111j1420-9101200701418x
Nussey D H Wilson A J amp Brommer J E (2007) The evolution-ary ecology of individual phenotypic plasticity in wild popula-tions Journal of Evolutionary Biology 20 831ndash844 httpsdoiorg101111j1420-9101200701300x
OtterKAStewartIRKMcGregorPKTerryAMRDabelsteenTampBurkeT(2001)Extra-pairpaternityamonggreattitsParus major following manipulation of male signals Journal of Avian Biology 32338ndash344httpsdoiorg101111j0908-88572001320408x
Pruitt J N Bolnick D I Sih A DiRienzo N amp Pinter-Wollman N(2016)Behavioralhypervolumesofspidercoloniespredictscommu-nity performance and disbandmentProceedings of the Royal Society B- Biological Sciences 283 20161409 httpsdoiorg101098rspb20161409
PruittJNampPinter-WollmanN(2015)Thelegacyeffectsofkeystonein-dividualsoncollectivebehaviourscaletohowlongtheyremainwithina group Proceedings of the Royal Society B- Biological Sciences 28220151766httpsdoiorg101098rspb20151766
RoyleNJHartley IROwens I P FampParkerGA (1999) Siblingcompetition and the evolution of growth rates in birds Proceedings of the Royal Society B 266 923ndash932 httpsdoiorg101098rspb19990725
SaltzJBampFoleyBR(2011)Naturalgeneticvariationinsocialnicheconstruction Social effects of aggression drive disruptive sexual se-lectioninDrosophila melanogaster American Naturalist177645ndash654httpsdoiorg101086659631
ShusterSM LonsdorfEVWimpGMBaileyJKampWhithamTG (2006) Community heritabilitymeasures the evolutionary conse-quencesofindirectgeneticeffectsoncommunitystructureEvolution60991ndash1003httpsdoiorg101111j0014-38202006tb01177x
SimmonsAMSimmonsJAampBatesMA (2008)Analyzingacous-tic interactions in natural bullfrog (Rana catesbeiana) chorusesJournal of Comparative Psychology 122 274ndash282 httpsdoiorg1010370735-70361223274
Sinervo B R amp Calsbeek R (2010) Behavioral concepts of selectionExperiments and genetic causes of selection on the sexes In D FWestneatampCWFox(Eds)Evolutionary behavioral ecologyLondonUKOxfordUniversityPress
Thompson J N (1982) Interaction and coevolution Chicago USA TheUniversityofChicagoPress
emspensp emsp | emsp1463MONTIGLIO eT aL
VanderWaal K L ObandaV Omondi G P McCowan BWang HFushingHampIsbellLA (2016)Thestrengthofweaktiesandhel-minth parasitism in giraffe social networks Behavioral Ecology 271190ndash1197httpsdoiorg101093behecoarw035
Ward P I (1993) Micro-habitat segregation and the mating systemof Gammarus pulex Animal Behavior 45 191ndash192 httpsdoiorg101006anbe19931019
Ward P I amp PorterAH (1993)The relative role of habitat structureandmale-malecompetition in thematingsystemofGammarus pulex (CrustaceaAmphipoda)AsimulationstudyAnimal Behavior45119ndash133httpsdoiorg101006anbe19931011
West-EberhardMJ(1989)Phenotypicplasticityandtheoriginsofdiver-sityAnnual Review of Ecology and Systematics20249ndash278httpsdoiorg101146annureves20110189001341
Westneat D F Hatch M IWetzel D P amp Ensminger A L (2011)IndividualvariationinparentalcarereactionnormsIntegrationofper-sonalityandplasticityAmerican Naturalist178652ndash667httpsdoiorg101086662173
Wilson A J Gelin U Perron M-C amp Reacuteale D (2009) Indirect ge-neticeffectsandtheevolutionofaggression inavertebratesystemProceedings of the Royal Society of London Series B Biological Sciences276533ndash541httpsdoiorg101098rspb20081193
Additional Supporting Informationmay be found online in the sup-portinginformationtabforthisarticle
How to cite this articleMontiglioP-OMcGlothlinJWFarineDRSocialstructuremodulatestheevolutionaryconsequencesofsocialplasticityAsocialnetworkperspectiveoninteractingphenotypesEcol Evol 201881451ndash1464 httpsdoiorg101002ece33753
APPENDIX
PHENOTYPIC MEAN AND VARIANCE
FollowingMooreetal(1997)wemodelasinglephenotypeofanindi-vidual (z)asanadditivecombinationoftheeffectsof itsowngenes(iedirectgeneticeffectsa)thenonsocialenvironmentitexperiences(e)andaplasticcomponentthatissomefunctionofthephenotypesinitssocialgroupMooreetal(1997)originallymodeledthesocialeffectasafunctionofthephenotypeofoneinteractingindividualMcGlothlinandBrodie (2009)andMcGlothlinetal (2010)consideredsocialef-fectsinapopulationconsistingofgroupsofnindividualswhereinter-actionswereassumedtooccursimultaneouslywithinagroupwithallindividuals within a group having the same strength of interactionHereweconsideramoregeneralsocialstructurewhereindividualsinteractwithallpossiblesocialinteractantsingroupsizenwithvaria-bleconnectionstrengthsirangingfrom0to1giving
wherethesummationistakenacrossalln minus1possiblesocialinterac-tionsforeachindividualsandψrepresentstheinteractioncoefficientwhichdetermines thestrengthanddirectionof the indirectpheno-typic effect of individual social interactantsHere and elsewhere aprimeindicatesaparameterbelongingtoasocialpartnerAnysocialnetworkstructurecanbemodeledbychangingthedistributionofs High-densitysocialnetworkswithstrongconnectionswillhavemanylargevaluesofswhilesparsernetworkswithweakerconnectionswillhavemanyweaksvalueswithmanyequaltozeroConsideringphenotypicfeedback(asdoMooreetal1997)insuch
The value of the two covariance terms represents how stronglystrengthofinteractiondependsonthegenesandenvironmentofin-dividualsocialpartnersThiscovarianceisdeterminedforeachindi-vidualandmayvaryacrossindividualsTheseshouldbepositiveunderhomophilyandnegativeunderheterophilyTakingthemeanandas-suming
=e=0
where double overbars indicate global means and large overbarswithintheparenthesesindicatemeanstakenacrossindividualsbasedonsummarystatisticsoftheirsocialgroupsThiscanbeexpandedasaboveto
The remainingcovariance terms represent theaveragedegree towhichindividualconnectionstrengthsareadjustedbasedonthephe-notypeofpotentialinteractantsInthecaseofhomophilyorheteroph-ilyindividualswillmakethisadjustmentbasedontheirownphenotypewithlargeindividualshavingapositivecovarianceandsmallindividu-alshavinganegativecovariance(orviceversa)ThereforeweexpecttheseaveragecovariancetermstotendtowardzeroMakingthisas-sumptionandrearrangingprovidesEquation2inthetext
EXTENSION TO MULTIPLE GROUPS
EquationA8iswrittenassumingthatthepopulationconsistsofasin-gle social networkwhere individualsmay interact in anywayNowassumethatthepopulationisdividedintomultiplegroupswhereindi-vidualsmay interactwithanystrengthswithinagroupanddonotinteract at all between groups Assuming the covariance terms inEquationA8arezeroandthatenvironmentaldeviationsdonotvaryamonggroupsthemeanofeachgroupwillbe
where overbars now indicate within-groupmeans Assuming equalgroupsizethepopulationmeanisnow
(IfgroupsvaryinsizethenEquationA10canbemodifiedtogiveaweightedmean) Ifconnectionstrengthhasnoheritablebasis thenthe covariance term become zero and EquationA10 collapses toEquation2inthetextWemaycalculateamong-groupvariancemosteasilybymakingafewassumptionsthatarealsomadeinoursimula-tionsFirstasaboveweassumethatgroupsareofequalsizeSecondweassume thatmean interactiondoesnotvaryacrossgroups ands=
=sMakingtheseassumptions
Thisshowsthat indirectgeneticeffectswillmagnifyslightdiffer-ences in genetic values across groups regardless of sign Strongermeanconnectionstrengthswillintensifythiseffect
RESPONSE TO SELECTION
FollowingMoore etal (1997) andMcGlothlin etal (2010) and as-suming that thecovariance terms inEquationA8areeither zeroorpopulation parameters that do not have a heritable component anindividualrsquostotalbreedingvaluecanbewrittenasthegeneticcontri-butiontothepopulationmean
where Ristheregressionofsaprimeonaandisthusanalogoustorelated-ness This assumes thatCov[aseprime] is negligible Positive values ofR indicatehomophilyandnegativevaluesindicateheterophilyMakingthissubstitutiongivesEquation4inthetextEquation4canalsobeexpresseddifferentlybyrearrangingas
VanderWaal K L ObandaV Omondi G P McCowan BWang HFushingHampIsbellLA (2016)Thestrengthofweaktiesandhel-minth parasitism in giraffe social networks Behavioral Ecology 271190ndash1197httpsdoiorg101093behecoarw035
Ward P I (1993) Micro-habitat segregation and the mating systemof Gammarus pulex Animal Behavior 45 191ndash192 httpsdoiorg101006anbe19931019
Ward P I amp PorterAH (1993)The relative role of habitat structureandmale-malecompetition in thematingsystemofGammarus pulex (CrustaceaAmphipoda)AsimulationstudyAnimal Behavior45119ndash133httpsdoiorg101006anbe19931011
West-EberhardMJ(1989)Phenotypicplasticityandtheoriginsofdiver-sityAnnual Review of Ecology and Systematics20249ndash278httpsdoiorg101146annureves20110189001341
Westneat D F Hatch M IWetzel D P amp Ensminger A L (2011)IndividualvariationinparentalcarereactionnormsIntegrationofper-sonalityandplasticityAmerican Naturalist178652ndash667httpsdoiorg101086662173
Wilson A J Gelin U Perron M-C amp Reacuteale D (2009) Indirect ge-neticeffectsandtheevolutionofaggression inavertebratesystemProceedings of the Royal Society of London Series B Biological Sciences276533ndash541httpsdoiorg101098rspb20081193
Additional Supporting Informationmay be found online in the sup-portinginformationtabforthisarticle
How to cite this articleMontiglioP-OMcGlothlinJWFarineDRSocialstructuremodulatestheevolutionaryconsequencesofsocialplasticityAsocialnetworkperspectiveoninteractingphenotypesEcol Evol 201881451ndash1464 httpsdoiorg101002ece33753
APPENDIX
PHENOTYPIC MEAN AND VARIANCE
FollowingMooreetal(1997)wemodelasinglephenotypeofanindi-vidual (z)asanadditivecombinationoftheeffectsof itsowngenes(iedirectgeneticeffectsa)thenonsocialenvironmentitexperiences(e)andaplasticcomponentthatissomefunctionofthephenotypesinitssocialgroupMooreetal(1997)originallymodeledthesocialeffectasafunctionofthephenotypeofoneinteractingindividualMcGlothlinandBrodie (2009)andMcGlothlinetal (2010)consideredsocialef-fectsinapopulationconsistingofgroupsofnindividualswhereinter-actionswereassumedtooccursimultaneouslywithinagroupwithallindividuals within a group having the same strength of interactionHereweconsideramoregeneralsocialstructurewhereindividualsinteractwithallpossiblesocialinteractantsingroupsizenwithvaria-bleconnectionstrengthsirangingfrom0to1giving
wherethesummationistakenacrossalln minus1possiblesocialinterac-tionsforeachindividualsandψrepresentstheinteractioncoefficientwhichdetermines thestrengthanddirectionof the indirectpheno-typic effect of individual social interactantsHere and elsewhere aprimeindicatesaparameterbelongingtoasocialpartnerAnysocialnetworkstructurecanbemodeledbychangingthedistributionofs High-densitysocialnetworkswithstrongconnectionswillhavemanylargevaluesofswhilesparsernetworkswithweakerconnectionswillhavemanyweaksvalueswithmanyequaltozeroConsideringphenotypicfeedback(asdoMooreetal1997)insuch
The value of the two covariance terms represents how stronglystrengthofinteractiondependsonthegenesandenvironmentofin-dividualsocialpartnersThiscovarianceisdeterminedforeachindi-vidualandmayvaryacrossindividualsTheseshouldbepositiveunderhomophilyandnegativeunderheterophilyTakingthemeanandas-suming
=e=0
where double overbars indicate global means and large overbarswithintheparenthesesindicatemeanstakenacrossindividualsbasedonsummarystatisticsoftheirsocialgroupsThiscanbeexpandedasaboveto
The remainingcovariance terms represent theaveragedegree towhichindividualconnectionstrengthsareadjustedbasedonthephe-notypeofpotentialinteractantsInthecaseofhomophilyorheteroph-ilyindividualswillmakethisadjustmentbasedontheirownphenotypewithlargeindividualshavingapositivecovarianceandsmallindividu-alshavinganegativecovariance(orviceversa)ThereforeweexpecttheseaveragecovariancetermstotendtowardzeroMakingthisas-sumptionandrearrangingprovidesEquation2inthetext
EXTENSION TO MULTIPLE GROUPS
EquationA8iswrittenassumingthatthepopulationconsistsofasin-gle social networkwhere individualsmay interact in anywayNowassumethatthepopulationisdividedintomultiplegroupswhereindi-vidualsmay interactwithanystrengthswithinagroupanddonotinteract at all between groups Assuming the covariance terms inEquationA8arezeroandthatenvironmentaldeviationsdonotvaryamonggroupsthemeanofeachgroupwillbe
where overbars now indicate within-groupmeans Assuming equalgroupsizethepopulationmeanisnow
(IfgroupsvaryinsizethenEquationA10canbemodifiedtogiveaweightedmean) Ifconnectionstrengthhasnoheritablebasis thenthe covariance term become zero and EquationA10 collapses toEquation2inthetextWemaycalculateamong-groupvariancemosteasilybymakingafewassumptionsthatarealsomadeinoursimula-tionsFirstasaboveweassumethatgroupsareofequalsizeSecondweassume thatmean interactiondoesnotvaryacrossgroups ands=
=sMakingtheseassumptions
Thisshowsthat indirectgeneticeffectswillmagnifyslightdiffer-ences in genetic values across groups regardless of sign Strongermeanconnectionstrengthswillintensifythiseffect
RESPONSE TO SELECTION
FollowingMoore etal (1997) andMcGlothlin etal (2010) and as-suming that thecovariance terms inEquationA8areeither zeroorpopulation parameters that do not have a heritable component anindividualrsquostotalbreedingvaluecanbewrittenasthegeneticcontri-butiontothepopulationmean
where Ristheregressionofsaprimeonaandisthusanalogoustorelated-ness This assumes thatCov[aseprime] is negligible Positive values ofR indicatehomophilyandnegativevaluesindicateheterophilyMakingthissubstitutiongivesEquation4inthetextEquation4canalsobeexpresseddifferentlybyrearrangingas
The remainingcovariance terms represent theaveragedegree towhichindividualconnectionstrengthsareadjustedbasedonthephe-notypeofpotentialinteractantsInthecaseofhomophilyorheteroph-ilyindividualswillmakethisadjustmentbasedontheirownphenotypewithlargeindividualshavingapositivecovarianceandsmallindividu-alshavinganegativecovariance(orviceversa)ThereforeweexpecttheseaveragecovariancetermstotendtowardzeroMakingthisas-sumptionandrearrangingprovidesEquation2inthetext
EXTENSION TO MULTIPLE GROUPS
EquationA8iswrittenassumingthatthepopulationconsistsofasin-gle social networkwhere individualsmay interact in anywayNowassumethatthepopulationisdividedintomultiplegroupswhereindi-vidualsmay interactwithanystrengthswithinagroupanddonotinteract at all between groups Assuming the covariance terms inEquationA8arezeroandthatenvironmentaldeviationsdonotvaryamonggroupsthemeanofeachgroupwillbe
where overbars now indicate within-groupmeans Assuming equalgroupsizethepopulationmeanisnow
(IfgroupsvaryinsizethenEquationA10canbemodifiedtogiveaweightedmean) Ifconnectionstrengthhasnoheritablebasis thenthe covariance term become zero and EquationA10 collapses toEquation2inthetextWemaycalculateamong-groupvariancemosteasilybymakingafewassumptionsthatarealsomadeinoursimula-tionsFirstasaboveweassumethatgroupsareofequalsizeSecondweassume thatmean interactiondoesnotvaryacrossgroups ands=
=sMakingtheseassumptions
Thisshowsthat indirectgeneticeffectswillmagnifyslightdiffer-ences in genetic values across groups regardless of sign Strongermeanconnectionstrengthswillintensifythiseffect
RESPONSE TO SELECTION
FollowingMoore etal (1997) andMcGlothlin etal (2010) and as-suming that thecovariance terms inEquationA8areeither zeroorpopulation parameters that do not have a heritable component anindividualrsquostotalbreedingvaluecanbewrittenasthegeneticcontri-butiontothepopulationmean
where Ristheregressionofsaprimeonaandisthusanalogoustorelated-ness This assumes thatCov[aseprime] is negligible Positive values ofR indicatehomophilyandnegativevaluesindicateheterophilyMakingthissubstitutiongivesEquation4inthetextEquation4canalsobeexpresseddifferentlybyrearrangingas
