J Appl Entomol 2019143225ndash235 wileyonlinelibrarycomjournaljen emsp|emsp225copy 2018 Blackwell Verlag GmbH
Received3April2018emsp |emsp Revised13September2018emsp |emsp Accepted17October2018DOI101111jen12583
O R I G I N A L C O N T R I B U T I O N
Distance models as a tool for modelling detection probability and density of native bumblebees
Darin J McNeil12 emsp|emspClint R V Otto3 emsp|emspErin L Moser4emsp|emspKatherine R Urban‐Mead5emsp|emsp David E King6emsp|emspAmanda D Rodewald12 emsp|emspJeffery L Larkin4
1DepartmentofNaturalResourcesCornellUniversityIthacaNewYork2CornellLaboratoryofOrnithologyIthacaNewYork3USGeologicalSurveyNorthernPrairieWildlifeResearchCenterJamestownNewYork4DepartmentofBiologyIndianaUniversityofPennsylvaniaIndianaPennsylvania5DepartmentofEntomologyCornellUniversityIthacaNewYork6DepartmentofEnvironmentalConservationUniversityofMassachusettsAmherstMassachusetts
CorrespondenceDarinJMcNeilDepartmentofNaturalResourcesCornellUniversityIthacaNYEmaildjm462cornelledu
Funding informationUSDA‐NaturalResourceConservationServiceGrantAwardNumber68‐7482‐12‐502IndianaUniversityUnitedStatesDepartmentofAgricultureGrantAwardNumber68‐7482‐12‐502NaturalResourcesConservationService
AbstractEffectivemonitoringofnativebeepopulationsrequiresaccurateestimatesofpopu‐lationsizeandrelativeabundanceamonghabitatsCurrentbeesurveymethodssuchasnettingorpantrappingmaybeadequateforavarietyofstudyobjectivesbutarelimitedbyafailuretoaccountforimperfectdetectionBiasesduetoimperfectde‐tectioncouldresultininaccurateabundanceestimatesorerroneousinsightsabouttheresponseofbeestodifferentenvironmentsTogaugethepotentialbiasesofcur‐rentlyemployedsurveymethodswecomparedabundanceestimatesofbumblebees(Bombus spp)derivedfromhierarchicaldistancesamplingmodels(HDS)tobumble‐beecountscollectedfromfixed‐areanetsurveys(ldquonetcountsrdquo)andfixed‐widthtran‐sectcounts(ldquotransectcountsrdquo)at47early‐successionalforestpatchesinPennsylvaniaOurHDSmodelsindicatedthatdetectionprobabilitiesofBombussppwereimper‐fectandvariedwithsurvey‐andsite‐covariatesDespitebeingconspicuousBombus sppwerenotreliablydetectedbeyond5mHabitatassociationsofBombussppden‐sityweresimilaracrossmethodsbutthestrengthofassociationwithshrubcoverdifferedbetweenHDSandnetcountsAdditionallynetcountssuggestedsiteswithmoregrasshostedhigherBombussppdensitieswhereasHDSsuggestedthatgrasscoverwasassociatedwithhigherdetectionprobabilitybutnotBombussppdensityDensityestimatesgeneratedfromnetcountsandtransectcountswere80ndash89lowerthanestimatesgeneratedfromdistancesamplingOurfindingssuggestthatdistancemodelling provides a reliablemethod to assessBombus spp density andhabitat associationswhile accounting for imperfectdetection causedbydistancefrom observer vegetation structure and survey covariates However detectionnon‐detectiondatacollectedviapoint‐countsline‐transectsanddistancesamplingforBombussppareunlikelytoyieldspecies‐specificdensityestimatesunlessindi‐vidualscanbeidentifiedbysightwithoutcaptureOurresultswillbeusefulforin‐formingthedesignofmonitoringprogramsforBombus spp andotherpollinators
K E Y W O R D S
Bombusdetectionprobabilitydistancemodellingpollinatorssurveystransects
226emsp |emsp emspensp McNEIL Et aL
1emsp |emspINTRODUC TION
Native bees in North America are important pollinators of bothcropsandwildplants (Ashmanetal2004Garibaldiet al2013KremenWilliamsampThorp2002) Indeedbees alongwithotherpollinators are considered keystone species that facilitate sexualreproductionfor85ofangiospermsworldwide (Allen‐Wardelletal1998Kevan1990)InagriculturalportionsoftheUnitedStatespollinationservicesprovidedbynativebeesarevaluedat$3billionUSD annually (Calderone 2012) Even as the ecological and eco‐nomic importance of native bees is recognized there is amount‐ingevidence thatmanybee species aredeclining (Cameronet al2011GoulsonLyeampDarvill2008)ThesedeclinesincludenotonlymanagedspecieslikeApis melliferabutalsoNorthAmericannativetaxalikebumblebees(Bombusspp)andothers(Cameronetal2011GoulsonNichollsBotiacuteasampRotheray2015Pottsetal2010)Forexampletherustypatchedbumblebee(Bombus affinis)waslistedasFederally Endangeredunder theEndangeredSpeciesAct in 2017and several otherBombus species have been proposed for listing(JepsenEvansThorpHatfieldampBlack2013)Althoughthedriversresponsibleforpopulationdeclinesvaryamongspeciesthreatsin‐cludepesticidesnon‐nativepathogensandhabitatlossdegradation(Goulsonetal2015PerssonRundloumlfCloughampSmith2015)
Still while evidence is fairly clear regarding bee declines forsomeregionsandorspeciesthestatusofmanybeepopulationsre‐mainsunknown(TepedinoDurhamCameronampGoodell2015)In2015theUnitedStatesPollinatorHealthTaskForceproposedthedevelopmentofnationalpollinatormonitoringprogramstoestimatepopulation trends and identify environmental stressors affectingnative bees (VilsackampMcCarthy 2015) Central to accomplishingthesegoalsistheaccurateestimationofbeepopulationsizesacrossspeciesgeneramorphospeciesandfunctionalgroupstoestablishareferencebenchmark forevaluatingpopulation trends abundanceacrossdifferenthabitatsandassessingtheoutcomesofconserva‐tioninterventions
Althoughavarietyofmethodshavebeencommonlyusedtosam‐plewildbeepopulations (eg fixed‐areaaerialnettingbeebowlsvanetraps)each is limitedby inherentmethodologicalbiasesthatmakeinferenceoftruedensitiesdifficultInparticularfewmethodsaccountforthebiascausedbyimperfectdetection(egLofflandetal2017)inthatonlybeescapturedorotherwisedetectedbyanob‐serverarecountedandsubsequentlymodelledRegardlessofsam‐plingmethodonlyafractionoftheindividualspresentatalocationwillbedetected(KeacuteryampSchmidt2008)Rawcountswhichfailtoaccountfordetectionprobabilitywillinvariablygenerateestimatesofabundancethatarebiasedlowifsomeindividualsarepresentbutnotdetected(KeacuteryampSchmidt2008MacKenzieetal20022005)Thoughsuchmethodshavemeritundermanycircumstancesac‐curateestimateofabundanceorchangesinabundanceoverspaceandtimerequiresconsiderationofmethodologicalbiaseslikethosecaused by imperfect detection (MacKenzie et al 2005) In addi‐tionfailuretoaccountforimperfectdetectioncanobfuscatehab‐itat associations particularlywhen thehabitat conditions that are
attractivetotheorganismalsomakeitmoredifficultforobserverstodetecttheorganism(MacKenzie2006)Consequentlyresearch‐ersmightbeledtobelievethatcertainhabitatconditions(associatedwithlowbeecounts)arelow‐qualityhabitatswhilebeesmayinreal‐itybeofequalgreaterabundancebutlessdetectableorviceversa(MacKenzie2006)
Herewedemonstrate theutilityofhierarchical distance sam‐pling (HDS) forestimatinghabitat‐specificdensity (ie abundanceper unit area) anddetection probability of bumblebees in decidu‐ous forest of central PennsylvaniaHierarchical distance samplingisananalyticaltechniquethatallowsresearcherstomodelhabitat‐specificabundanceandheterogeneityinspeciesdetectionwithinaunifiedframework(HedleyampBuckland2004KeacuteryampRoyle2015Royle Dawson amp Bates 2004) It builds upon standard distancesampling which is a widely used method for estimating animalabundance while for accounting imperfect detection (BucklandAnderson Burnham amp Laake 2005) However HDS differs fromstandarddistancesamplinginthatitallowsforspatialvariabilityinabundanceanddetectionacrossmultiplesitestobeexplainedasafunctionofcovariates(KeacuteryampRoyle2015)Althoughothermethodsexistforestimatingabundancewhileaccountingfordetection(egoccupancyN‐mixture etc)most requiremultiple visits with theassumptionofpopulationclosurebetweensurveys (KeacuteryampRoyle2015MacKenzieetal2005)Distancesamplingmaybeparticu‐larlyuseful for insectstudiesbecause it requiresonlyasinglesitevisittoestimatedetectionprobabilityandmanyshort‐livedinsects(likesomebeespecies)maynotemergelongenoughtoallowmul‐tiplevisitsper siteDistance samplinghasbeen routinelyusedbywildlife researchers to model abundance and detection functionsfor multiple vertebrate taxa (Hammond et al 2002 Karanth ampSunquist1995MarquesThomasFancyampBuckland2007)Toourknowledgenopreviousresearchhasdemonstratedtheuseofdis‐tancesampling toestimatebeeabundanceorhabitatassociations(BendelHovickLimbampHarmon2018)Ourgoalswereto(a)useHDStoevaluatehowBombussppdetectionprobabilityvarieswithdistancesurveytechniqueandhabitatattributes(b)compareabun‐danceanddensityestimatesgeneratedfromHDStostandardsam‐plingapproaches(fixed‐widthtransectsandfixed‐radiusnetcounts)thatdonotaccountforimperfectdetectionand(c)identifysite‐spe‐cifichabitatrelationshipsforBombussppacrosssamplingmethods
2emsp |emspMATERIAL S AND METHODS
21emsp|emspStudy area
WesurveyedbeeswithinthePennsylvaniaWildsregionofnorth‐central Pennsylvania focusing on Centre and Clinton Counties(Figure 1) This region lies within the Appalachian Plateau of thenorthcentralAppalachianMountainsandischaracterizedbyarug‐ged series of high‐elevation ridges (300ndash600masl) punctuatedbylowvalleysalongtheAlleghenyFront(Shultz1999)Vegetationcommunities within the Pennsylvania Wilds are chiefly mature
emspensp emsp | emsp227McNEIL Et aL
deciduous‐ormixedforest (80ndash100yearspost‐harvestMcCaskilletal2009)withoak(Quercus spp)hickory(Caryaspp)andeast‐ern hemlock (Tsuga canadensis) among the most common species(WherryFoggampWahl1979)Weconcentratedoureffortswithindeciduous forests of Sproul andMoshannon State Forestswhereoak silviculture aims to restore young forest age classes throughtimber harvest and regeneration Because silvicultural practiceswithinthesetwoStateForestsaimtorestorehabitatforforestwild‐lifewefocusedoursurveyeffortswithinregeneratingoakstands0ndash9yearspost‐managementDuringsurveysavarietyoffloweringplantswereavailabletoBombussppincludinglow‐growingshrubslike hillside blueberry (Vaccinium pallidum) as well as herbaceousforbs like eastern teaberry (Gaultheria procumbens) and commoncow‐wheat(Mellampyrum linerare)MosttallwoodyplantswerenotfloweringexceptforDevilrsquoswalkingstick (Aralia spinosa)whichwedetectedonlywithinafewofoursites
22emsp|emspSite selection and survey placement
We randomly selected 47 timber stands within Sproul andMoshannon State Forests that had been recently treated withoverstory removal (basal area 23ndash92 m2ha) We attemptedto maximize the distance between sites such that our averagedistance‐to‐nearest‐site was 1110m (SE 107m range 464ndash4516m)Thisreducedthelikelihoodofindividualsbeingdetectedatmultiplesites(Redheadetal2016)Timberharvestunitsaver‐aged2314ha(SD1862harange254ndash10392ha)insizeAsin‐glesurveypointwaslocatedwithineachharvestusingarandompoint generator tool inArcGIS102 (ESRI 2011)Weattemptedtominimizeedgeeffectsbyensuringpointswererelativelycon‐sistent in their placementwith respect to timberharvest edgessamplingwas restricted to areas at least80m from theedgeoftimberharvestsandourfinalsampleofsiteswasameandistanceof11867m(SE624m)
23emsp|emspTransect surveys
Ateachpointwe sampledBombus sppusing three survey types(a) distance transects (b) transect counts and (c) aerial nettingcounts Both distance transects and fixed‐width transect countsoccurred simultaneously along 66m transects oriented north‐to‐south and centred at eachpoint locationAlong each transectobserverswalked forwardat a constant rate (~1mmin) such thattheobserverarrivedatthetransectendafter30minPriortosur‐veyseachobserver(n=2)wastrainedindistanceestimationusingdummytransectsalongwhichbeesrsquodistanceswerephysicallymeas‐uredaftereachattemptedestimateusingameasuring tapeOnceallobserverswereconsistentlyestimatingdistanceswithinplusmn025mfield surveyswere conductedwith a2m longmeasuring stick forconstantreferenceWhilewalkingalongeachsurveytransect theobserverrecordedBombussppdetectionssuchthatafinalcount()wasgeneratedforeachsurveycoupledwiththedistances(plusmn025m)betweeneachBombus sppandthetransectWedidnotattempttoidentify speciesor sex forBombus spp detected in situ thereforecountswerelikelymultiplespeciesandsexesSurveydataforeachpointincludedaBombussppcountandtheircorrespondingdetec‐tion distancesWe discerned betweenBombus spp andXylocopa virginica byabdomenpubescence(MichenerMcGinleyampDanforth1994)DistanceswererecordedastheperpendiculardistancefromthetransecttoeachbeeandnotedasthedistanceatwhichthebeewasfirstdetectedWhilewalkingalongeachtransectobserversat‐temptedtokeeptrackofpreviouslydetectedBombusspptoavoiddouble‐counting individualsthatmightbemovingamongfloralre‐sources near the transectWe anecdotally observed this methodlargely avoided double‐counting as Bombus spp are generallylarge‐bodiedconspicuousinsectsandeasilyaudibleinflightAllrawcountsanddetectiondistancesconstitutedourldquodistancetransectrdquodata(a)andrawcountswithin2mofthetransectconstitutedourldquotransectcountrdquodata(b)
F I G U R E 1 emspSurveylocationswithinthePennsylvaniaWildswhereweconductedsurveysforBombussppwithinregeneratingtimberharvests
228emsp |emsp emspensp McNEIL Et aL
We followed standard bee survey methods to avoid commoncausesofdetection failure (Wardetal2014)Surveyswerecon‐ductedonlyinbrightlightconditionslowwindwarmdays(ge16degC)andonlyduringlatemorningandafternoon(1000ndash1700)ThoughweattemptedtousestudydesigntoreducethepotentialimpactsofthesefactorsonBombus sppdetectabilitywealso includedthemindetectionmodellingAtthetimeofeachsurveywerecorded(a)surveyorID(b)cloudcover(c)timeofdayand(d)BeaufortWindIndex Local temperature data were downloaded from WeatherUnderground from the KUNV weather station in State CollegePennsylvania (WeatherUnderground Inc2018)Cloudcoverwasestimatedinthefieldtothenearest25(0ndash100)BeaufortWindIndexwasmeasuredonanincrementalscalefrom0to5with0rep‐resentingnowind at all (ie smokewould theoretically risewith‐outdrift)and5representinghighwindssuchthatentiretreesswayinthewind(HauampVonRenouard2006)Weavoidedsurveyinginwindindicesgt3andthusconsideredtwocategoriesofwind0ndash1ldquolowrdquo2ndash3ldquomoderaterdquoinouranalysesAllsurveystookplacefrom10to25July2017
24emsp|emspNet counts
TomeasureBombussppabundancewithinfixed‐radiusnetcountswe created 15m radius count surveys centred around each pointlocation (thecentreofeachdistancetransect)Nettedbeecountstookplaceimmediatelyupontheconclusionoftransectsurveys(de‐scribedabove)Withineachfixed‐radiusplotasingleobserverspent30minseeking‐andattemptingtocaptureallBombussppdetectedwithahandnetWechosefixed‐radiusnetsamplingbecauseitisastandardsamplingtechniquefornativebees (Perssonetal2015PottsVulliamyDafniNersquoemanampWillmer2003RoulstonSmithampBrewster2007)andwouldthereforeserveasabasisforcomparisontoourabundanceestimatesgeneratedfromHDSForeachBombus sppdetectedtheobserverattemptedtocaptureeachbeeusingahandnet(collapsible15rdquodiameternet17rdquohandleBioquipProduct7115CP)andoncecapturedallbeeswereheldcaptiveforthere‐mainderofthesurveyForeachcapturedbeethetimerwasstoppedwhiletheobserverplaced it intoaplasticzipperbagandresumedimmediately thereafter Thismethod prevented us from recaptur‐inganddouble‐countingbeeswithinthesameplotAfter30minofsurvey timehadelapsedeachBombus sppwas removed from itsbagwith forceps photographed for anotherproject and releasedunharmedInthefewoccasionswhereBombussppwereobservedbutevadedcapturetheyweretreatedasallotherBombussppcap‐turedforthepurposesofthisstudy(ieincluded)
25emsp|emspHabitat surveys
Wesurveyedregeneratingvegetationstructurewithin timberhar‐vestunitsfrom15Juneto15July2017VegetationsurveyssharedtheircentroidwithBombussppsurveysVegetationdataquantifiedhabitatstructureofwoodystemsandherbaceousunderstoryratherthan plant composition All vegetation data were collected along
three50mradialtransectseachorientedat0deg120degand240degfrompoint centreAlong each transectwe recordedplant strata at 10ldquostopsrdquo(10mapartn=30netcountlocation)Vegetationstratare‐cordedateachstopconsistedofthepresenceabsenceofsaplingshrub forbandgrasssedgeSaplingswereyoungtreeslt10cm (indiameterbreastheight)Thissamplingregimegaveusadequateres‐olutiontoassessvegetationstructure(15stopssite)whileremain‐ingof comparable scale toourbee sampling transects (33m)Wefoundvegetationstructuretobehighlycorrelatedacrossscalesaslargeas100mandthereforebelieveour50mvegetationplotsrep‐resentedsiteconditionsreasonablywellShrubswerewoodyplantswithmultipleprimarystems(incontrasttosingle‐stemmedsaplings)Forbswerebroad‐leafeddicotyledonousplants(egSolidagospp)The plant category ldquograssrdquo included any monocotyledonous plant(grassessedgesetc)Werecordedplantstratawithanoculartubesuchthatonlystratathat intersectedwithcrosshairs intheoculartube were considered present (James amp Shugart 1970) While asinglestopcouldincludemultiplestratatypeseachstratumcouldonlyberepresentedonceperstopandthuseachsitecouldhaveamaximumofn=15occurrencesforeachstratumWeanalyzedplantstrata values as percentages Prior to all analyses we calculatedSpearmanrsquosrho(ρ)forallpairsofcovariatestobemodelledBecausenonewerestronglycorrelated(Spearmanrsquosρ lt 060)nocovariateswereredundantandallweresuitableformodelling
26emsp|emspHierarchical distance models
Weanalyzeddistancetransectdata(beecountsanddistances)usingHDS models implemented in the R package ldquounmarkedrdquo (Fiske ampChandler2011RCoreampTeam2018)Thepackageunmarkedfitslinearmodelsinamaximumlikelihoodframeworkandcanbecom‐bined with an Information‐Theoretic approach (Anderson 2007)forthepurposeofmodelselection(egusingAkaikersquosInformationCriterionAICBurnhamampAnderson2002)Hierarchicaldistancemodels allowed us to create and rank candidate models each ofwhich contained independent model components for detectionprobability (p) and expected animal abundance (density λ) HDSmodelsassume(a)subjectsareaccuratelyidentified(egnofalse‐presences)(b)thatallsubjectsonthetransect(distance=0m)aredetectedperfectly(p=10)(c)subjectsaredetectedattheiroriginallocation(iemovement isnot influencedbytheobserver) (d)dis‐tancesareaccuratelymeasuredand(e)detectionofeachindividualis independentofthedetectionofallotherindividuals(Thomasetal2010)Bumblebeesappeartoconstitutegoodcandidatesfordis‐tancesamplingastheycanbeeasilyidentified(togenus)inthefield(Micheneretal1994)areeasilyapproachedbyobservers(Wardetal2014)andremainrelativelystillduringpollinationsuchthataccu‐ratedistanceestimationscouldbemadeforeachworkerAlthoughdistances were measured in the field directly we binned detec‐tions as recommended by Buckland et al (2005) 0ndash1 1ndash2 2ndash33ndash4and4ndash5mMoreovertopreparedistance‐basedtransectdatawe truncated the outer 10of our data such that analyseswereconductedusingonly the closest 90ofBombus spp detections
emspensp emsp | emsp229McNEIL Et aL
asrecommendedfordistanceanalysesbyBucklandetal(2005)Bytruncating thedata in thiswayalldetectionswerelt5mfromtheobserver
Distance models provide robust estimates of abundance byadjusting animal counts by the probability of detection for givendistances (Buckland et al 2005) This is accomplished by fittingdetectiondistancedata to a ldquodetection functionrdquo that describes adecayindetectionprobabilityassubjectsarefurtherfromtheob‐server (Bucklandetal2005KeacuteryampRoyle2015)Toevaluateanappropriatedetectionfunctionweevaluatedmodelseachfitusingoneofthefollowingdetectionfunctions(a)exponential(b)hazardrateor(c)half‐normal(Bucklandetal2005)ThiswasdonepriortoallcovariatemodellingEachdetectionfunctionisusedtoestimatetheaverageprobabilityofdetectionwhichisthenusedtoadjustrawcountssuchthatdensitypredictionscanbemade(Bucklandetal2005)OncethemostappropriatedetectionfunctionwasselectedbasedonAICcrankitwasusedtomodeldetectionprobabilityanddensityinconsecutivemodelsWemodelleddetectionprobabilityintwotiersdetectiontier1(surveycovariatesondetection)andde‐tectiontier2(habitatcovariatesondetection)Becauseoursamplesizewasmodestweusedonlysingle‐covariatedetectionmodelstoavoidoverfittingHDSmodelsDetectiontier1includedunivariatemodels for (a) timeof day (b) surveyor (c) temperature (d) cloudcover(e)windindexand(f)anull(intercept‐only)modelDetectiontier 2 (fit independently of detection tier 1) included univariatemodelsfor(a)saplingcover(b)shrubcover(c)forbcover(d)grasscoverand(e)anullmodelWithinbothmodeltiersweusedaglobalhabitatmodel(iesapling+shrub+forb+grass)fordensitytoen‐sure thatvariation indensitywas reasonablywell explainedwhileassessingdetectionprobabilityWeconsideredcovariatestobein‐formativeiftheywerebothgt20AICclessthanthenullmodelandhadβcoefficient95confidenceintervalsthatdidnotincludezeroUsing the informative covariates fromdetection tiers1and2weconstructedasetofdensitymodels(habitatcovariatesondensity)thataccountedfor imperfectdetection (a)saplingcover (b)shrubcover (c) forbcover (d)grasscoverand (e)anullmodelThenullmodelcontainedonlyintercepttermsandtheinformativeparame‐tersfordetectionPriortomodellingallcontinuouscovariateswerestandardizedusingthescalefunctioninbaseRModelrankingwasdoneusing the ldquoaictabrdquo functionof thepackage ldquoAICcmodavgrdquoAllmodelswerefitassumingaPoissondistributioninldquogdistsamprdquoandmodelfitwasassessedbycalculatingavarianceinflationfactor(chatchatchatc)usingtheunmarkedfunctionldquofitstatsrdquo (KeacuteryampRoyle2015)Weconsideredallmodelslt20AICctobecompetingandequallysupportedbythedata(BurnhamampAnderson2002)
27emsp|emspPoisson generalized linear models
WeusedaPoissongeneralized linearmodels inR (using the ldquoglmrdquofunction)tomodelBombus sppabundancealongfixed‐radiustran‐sectsandnetcountsThisallowedustocomparehabitat‐abundancerelationshipsgeneratedfromHDSmodelstothosegeneratedfrommethodsthatdonotaccountfordetectionprobabilityAswithour
HDSmodels Poisson regressionmodels allowed us tomodel beecountsasafunctionofhabitatcovariates(a)saplingcover(b)shrubcover (c) forbcover (d)grasscover and (e) anull (intercept‐only)modelWemodelled our fixed‐radius transect counts by truncat‐ing allHDS‐transect databy2mof the transect line and treatingthedataasarawcount(HanleyAwbiampFranco2014Scheperetal 2015) which is a standard technique when conducting visualencounter surveys Net count data were modelled in a compara‐blemanner such that raw countsweremodelled as a function ofhabitat covariatesWedid not account for imperfect detection ineither of these models but rather modelled Bombus spp countarea interpretedasadensityWeagainusedan information‐theo‐reticapproach(Anderson2007)withmodelrankingbasedonAICc consideringmodelslt20AICctobeequallysupportedbythedata(BurnhamampAnderson2002)Wealsousedsingle‐covariatemodelstoavoidoverlycomplexmodelsandtheinclusionofuninformativeparameterswithintopmodels(Arnold2010)
3emsp |emspRESULTS
Wedetected194individualBombus sppwithin5mofwhich136werewithin2mof the transect lineDuringaerialnetcountswecapturedn = 201 BombussppworkersOfthebeescapturedduringaerial net countsover50wereB impatienswith the remainderbeingamixedcommunityoflesscommonspecieslikeB bimaculatus and B vagans
31emsp|emspDetection probability
Ofthreedetectionfunctionmodelsweranthebest‐rankedmodelincludedanexponentialdetectionfunctionwheredetectionprob‐abilitygt5mfromthetransectwasasymp0(Figure2)Usinganexponen‐tialdetection functionwe foundthatdetectionprobabilityvariedas a functionof time since1000 (theearliestpossible start time)
F I G U R E 2 emspFrequencyofdetections(greybarsrightaxis)forBombussppwithinregeneratingtimberharvestsDetectionprobability(leftaxis)declinedasafunctionofdistancefromtransectandwasfittoanexponentialdetectionfunction(blackline)Bombussppwereonlyrarelydetectedfurtherthan5mfromthetransectline
230emsp |emsp emspensp McNEIL Et aL
andobserverIDsuggestingthatthelatestsurveysofeachdayhadthe lowestdetectionprobability and thatobserverswereunequalin their ability to detectBombus spp (Table 1 Figure 3a) Amongmodels investigating the relationship between habitat covariatesand Bombus spp detection the model that included grass cover()wastheonlysupportedmodelandsuggestedthatBombussppweremorereadilydetectedatsiteswithmoregrasscover(Table1Figure3b)Allothercovariatesmodelledintiers1and2weregt20AICc less than the nullmodel and theβ 95 confidence intervalsoverlappedzero
32emsp|emspHabitat modelling
Models from all three analyses yielded discernable habitat asso‐ciationswithBombus sppabundance (Table2Figure4)All threeanalyses indicated thatBombus spp abundanceduring the surveyperiodwas negatively associatedwith per cent sapling cover andnotassociatedwithforbcover (Table2Figure4)The importanceofshrubcoverandgrasscoveraspredictorsofBombussppcountsandestimatedabundancevariedacrossmethods(Table2)HDSandtransectcountsrevealedsupportforshrubcoverasaninformativecovariatebeinggt20AICc less than thenull andhavingparameter
95confidence intervals thatdidnotoverlapzero (Table2)Onlynet counts suggested that grass cover was positively associatedwithBombus sppabundancewhileHDSsuggestedthatgrasscoverwasinsteadcorrelatedpositivelywithdetectionprobabilitybutnotabundance (Table 2 Figure 4) In contrast our net count analysissuggestednoeffectofshrubcoveronbeecountswiththeldquoshrubrdquomodel ranked lower than thenullmodeland the shrubparameter95confidenceintervalsoverlappingzero(Table2)Ourtop‐rankedHDSmodel(ldquosaplingrdquo)showedevidenceofminoroverdispersion(chatchatchatc=133)whilemostothermodelsdidnotappearoverdispersed (chatchatchatclt10 with a mean chatchatchatc=101acrossmodels inourfinalHDSmodelset)Weconsidered this an acceptable level of overdispersion and did notuse a variance inflation factor to adjust our parameter estimates(BurnhamampAnderson2002)
33emsp|emspDensity estimation
Inadditiontoexaminingabundanceasafunctionofhabitatamongthe three methods we compared their estimated mean densitiesof foragingBombus spp basedon intercept‐only abundancemod‐els(includingdetectioncovariatesforHDS)EstimatedBombusspp
Model name K AICc ΔAICc AICc Wt β estimate (95CI)
Surveycovariatesondetectionprobability
p(observer) 7 34893 000 078 058(021to095)
p(time) 7 35156 264 021 minus023(minus038tominus008)
p () 6 35829 936 001 ‐
p(wind) 7 35987 1094 000 minus016(minus044to013)
p(temp) 7 36064 1172 000 minus005(minus019to009)
Sitecovariatesondetectionprobability
p(grass) 7 35267 000 085 035(007to063)
p(forb) 7 35827 561 005 017(minus004to037)
p() 6 35829 562 005 ‐
p(shrub) 7 35965 699 003 minus013(minus035to009)
p (sapling) 7 36048 782 002 010(minus016to036)
NoteModelsareranked indescendingorderofAkaikersquos InformationCriterionadjustedforsmallsamplesize(AICc)Surveycovariatesincludedtimesincesurveystarttime(continuousldquotimerdquo)tem‐perature(continuous)cloudcover(overcastcontinuous)observer(categorical)andwindindex(categorical)Sitecovariatesincludedpercentcoverasmeasuredby50mradiusvegetationsurveysforvegetationstructuresaplingsshrubs forbsandgrassBothcandidatemodelsetsarerankedagainstanullintercept‐onlymodelBelowwereportnumberofmodelparameters(k)ΔAICcAICc weight(AICcWt)andβparameterestimates(95confidenceinterval)
TA B L E 1 emspHierarchicaldistancemodelsofdetectionprobabilityasafunctionofsurveycovariates(Tier1top)andsitecovariates(Tier2bottom)
F I G U R E 3 emspModelsofBombussppdetectionprobabilityasafunctionofsurveytime(left)percentgrasscover(centre)andobserver(right)whilealsobeingmostdetectableclosesttothetransect(all)
emspensp emsp | emsp231McNEIL Et aL
forager density within timber harvests was highest for the HDSmodels(192foragingworkersha95CI153ndash240)andlowestfornetcounts(21foragingworkersha95CI19ndash23Figure5)an89differencebetween the twomethodsTransect countsyielded in‐termediate estimates of density (40 foragingworkersha 95CI34ndash47)andwere80lowerthandensityestimatesfromHDSSite‐specific HDS modelled densities and netting count raw densitieswerecorrelated (Pearsonrsquos r = 031 p=003) though the relation‐shipwasnot11(Figure5)
4emsp |emspDISCUSSION
Ourstudyprovidesthefirstempiricalevidencethatdetectionprob‐abilitiesofBombus sppvaryinwaysthatcanaffectabundanceesti‐matesandinferencesabouthabitatrelationshipsObservationerrorcaused by imperfect detection is one of the central challenges ofecologicalmonitoringprograms(Thompson2002YoccozNicholsampBoulinier 2001)buthas yet tobewidely applied tomonitoringofmany invertebrates includingpollinators (but seeBendeletal2018Lofflandetal2017Mackenzie2003VanStrienTermaatGroenendijkMensingampKery 2010)Methods like distance sam‐plingwhileofferingapotential solution to this challenge are stillunder‐utilized in entomological research Meanwhile distance
samplingandsimilarmethodshavebeenastapleofvertebratewild‐liferesearchfordecades(Bucklandetal2005BurnhamAndersonampLaake1980Seber1986Thomasetal2002)andhavebeenex‐pandedtoestimatepopulationsizehabitat‐specificabundanceforindividualspeciesandcommunities(SillettChandlerRoyleKeacuteryampMorrison2012SollmannGardnerWilliamsGilbertampVeit2016)Althoughourstudyisnotthefirstestimateandaccountfordetec‐tionprobabilityofbumblebees(Lofflandetal2017)nostudybe‐foreourshasdescribedfactorsassociatedwithdetectionprobabilityanddonesoinaHDSframework
Wefoundthatdistancesamplingtransectswerebothasimpleandeffectivesurveymethodforestimatingdensityandhabitatre‐lationships (Buckland et al 2005) Hierarchical distance samplingmodelsareoneofthefewavailablemethodsthatallowresearcherstomodel detection‐adjusted abundancewithonly a single visit toeachsite(Bucklandetal2005KeacuteryampRoyle2015MacKenzieetal 2005)Themethodusesonlynon‐lethal samplingunlike trap‐pingnettingmethods(Tepedinoetal2015)whichisespeciallyde‐sirablewhen sampling for speciesof conservation concern or forcommonspecies in areaswherecapture‐based sampling isnot al‐lowedAdditionallyHDSmodelsarealsousefulbecausetheoutputisaneasily interpretedlatentstatedensitywithunits inldquoanimalsareardquo In our study HDS models generated estimates of foragingBombus sppworkerdensity
Model name K AICc ΔAICc AICc Wt β estimate (95CI)
Hierarchicaldistancesampling
λ(sapling) 6 33769 000 098 minus030(minus045tominus014)
λ(shrub) 6 34583 813 002 021(005to037)
λ() 5 3502 1251 000 ndash
λ(grass) 6 35041 1271 000 minus017(minus038to005)
λ(forb) 6 35282 1513 000 minus001(minus016to014)
Transectcounts
λ(sapling) 2 27763 000 096 minus144(minus220tominus069)
λ(shrub) 2 28448 685 003 085(025to144)
λ(grass) 2 2898 1217 000 minus093(minus214to028)
λ() 1 29007 1244 000 ‐
λ(forb) 2 29216 1454 000 0133(minus074to101)
Netcounts
λ(sapling) 2 36071 000 100 minus163(minus226tominus101)
λ(grass) 2 38438 2367 000 085(003to167)
λ(shrub) 2 38565 2494 000 041(minus009to090)
λ() 1 38608 2537 000 ndash
λ(forb) 2 38709 2638 000 039(minus031to109)
NoteModelsareranked indescendingorderofAkaikersquos InformationCriterionadjustedforsmallsamplesize(AICc)DistancetransectdataincludedBombussppdetectedfrom0to5malong66mtransectsTransectcounts includedBombus sppdetected from0ndash2malong66m transectsnetcountdatawerecountsofBombus sppwithin15mradiusplotsSitecovariatesincludedpercentcover asmeasured by 50m radius vegetation surveys for vegetation structure saplings shrubsforbsandgrassBelowwereportnumberofmodelparameters(k)AICcΔAICcAICc weight(AICc Wt)andeachcovariateβparameterestimateandβparameterestimates(95confidenceinterval)
TA B L E 2 emspHabitatmodelsderivedfromhierarchicaldistancemodels(top)fixed‐widthtransectmodels(centre)andlinearmodelsofnetcountdata(bottom)allfitusingaPoissondistribution
232emsp |emsp emspensp McNEIL Et aL
DespitebeingamongthelargestandmostconspicuousofNorthAmerican bees (Michener et al 1994) we found that detectionprobability of Bombus spp was imperfect and declined markedlywithdistancefromthesurveytransectwithalmostnodetectionsbeyond5mDetectionprobabilitiesinourstudywereinfluencedbysurvey‐specific(egtimeofday)andsite‐specific(eggrasscover)variableswithdetectionprobabilityhighestinthemorninginmid‐summerandinhabitatswithabundantgrasscoverWithinregener‐atingtimberharvestsinourstudyarealdquograssrdquocoverwastypicallylow‐growing monocotyledons like Carex pennsylvanica Abundantlow‐growing sedge allowed observers to view Bombus spp fromgreaterdistancesthanwhensitesweredominatedbytallsaplingsshrubs or forbs (egSolidago) Consequently studieswithin habi‐tatsdominatedbylowgrassorothershortvegetationmightfindde‐tectionprobabilityforBombusspptobereliableatdistancesgt5mAlthoughweareuncertainastowhyBombussppwerelessdetect‐ableduringsurveysconductedlaterintheafternoononeplausibleexplanationisthatlongershadowscastbylateafternoonlightmade
Bombussppmoredifficulttodetectwhenforagingin lowvegeta‐tionAdditionalworkexploringthedriversassociatedwithBombus sppdetectionwouldprovevaluabletomonitoringregimesaimedatsurveyingbumblebees
ThoughourstudyisnotacomprehensivehabitatassessmentforBombussppwithinregeneratingtimberharvestsofeasternforestsourresultsprovideaglimpseintothehabitatdynamicsofbumble‐beesinregeneratingforestsduringmid‐summerOurfindingsthatBombus sppwerepositivelyassociatedwithshrubsandnegativelyassociatedwithsaplingscanbeexplainedprimarilybyflowerphe‐nology during our survey window Regenerating saplings withinthe timber harvests we monitored were largely oaks hickoriesblackcherry (Prunus serotina)andredmaple (Acer rubrumWherryetal1979)Thesespeciesdonot flowerassmallsaplingsanddosoinearlyspringasmaturetrees(ieoutsidethesamplingperiodWherryetal1979)Incontrastseveralspeciesofshrubwereflow‐eringduringsamplingincludingblackhuckleberry(Gaylussacia bac‐cata)andhillsideblueberryIncontrastmostforbs(eggoldenrod
F I G U R E 4 emspModelledhabitatassociationsbetweenBombussppandstructuralvegetationfeatureswithinregeneratingtimberharvestsaspredictedbyhierarchicaldistancemodels(top)fixed‐width(4m)transectcounts(centre)andnetcounts(bottom)Variablesshownaresaplingcover(left)shrubcover(centre)andgrasscover(right)Solidlinesrepresentmodelpredictionswithdashedlinesas95confidenceintervalsRelationshipsmarkedwithanasteriskwerethosewithmodelsupport(iemoreinformativethananullmodelandβ95CInon‐overlappingzero)
F I G U R E 5 emspLeftBombusspppredictedmeandensityformodelsofnetcounts(ldquoncrdquo)transectcounts(ldquotcrdquo)andhierarchicaldistancesamplingmodels(ldquohdsrdquo)RightPredicteddensity(workersha)generatedfromourtop‐rankedhierarchicaldistancemodel(p [observer+time+grass]λ[sapling])regressedagainstcountdatafromBombus sppnetcounts
emspensp emsp | emsp233McNEIL Et aL
SolidagosppsnakerootAgeratina spp)hadnotbegunfloweringyetFutureworkshouldexplorehowBombussppmaytrackresourcesacrossagrowingseasontopersistwithineasternforestecosystems
Monitoringprograms forBombus spp andothernativepolli‐natorscanbeimprovedbyincorporatingstudydesignandmodel‐based approaches for minimizing detection error Although weincludedseveraldesign‐basedsolutionsforminimizingdetectionerror(egrestrictingsurveytimesonlysurveyinginfairweatherWard et al 2014) detection probability remained imperfectand varied due to time of day observer and vegetation coverConsequentlymethodsthatignoreddetectionprobabilitygener‐ated density estimates 80ndash89 lower than HDS Past studieshaveshowntheimportanceofusingdesign‐basedapproachestominimize false negativeswhen sampling bees (BuchananGibbsKomondyampSzendrei2017)Ourstudydemonstratesthevalueofusingbothdesign‐andmodel‐basedapproachesforreducingsam‐plingerrorscausedbyimperfectdetectionOtherstudysystemswith thick vegetation cover such as prairies and forested wet‐landsorobstructiveobjectssuchasurbanenvironmentsarealsolikely to underestimate bee abundance even if multiple design‐basedapproachesareusedWhiletraditionalsamplingtechniquesthat do not account for detection have numerous applicationsourstudyhighlightstheimportanceofincorporatingmodel‐basedapproachesforaccountingfordetectionprobabilitywithinnativebeesurveysparticularlywhenattemptingtoestimatebeeabun‐danceordensity
Althoughour results suggest thatHDS representsapromisingtoolformonitoringbumblebeesresearcherswishingtoemploythemethod should recognize its associated limitations For exampledistancemodelsassumethatallanimalsonthetransectlinearede‐tectedperfectlyAlthoughitislikelythisassumptionwasmetwithalargeinsectlikeBombussppthisassumptionmightbeviolatedwithsmallerinsectsMoreoversubjectsareassumedtobeuniformlydis‐tributedinamannerunaffectedbytheobserverWhileitispossiblethatBombussppwerefrightenedbyobserverswetookcaretonotethe locationof first detection forBombus spp apparently flushedandtheirloudflightmadeclosedetectionsalmostcertainWenotethat thismethodwouldnotworkwell for species‐level identifica‐tionbecauseobservationsaremadefromadistanceandsomebeegeneraareexceedinglydifficulttoidentifyevenwithamicroscope(Michener et al 1994)Misidentification of specieswould consti‐tuteafalsepositivewhichwouldviolateanassumptionofdistancesampling
Anotherconsiderationofthisstudydesignandmanymethodsofabundanceestimationisthatanimalsmayviolatetheclosureas‐sumptionInthecaseofBombussppthislikelyoccurredasforagersflew in‐ and out‐ of the effective survey area (~5m from the ob‐serverforHDS)WhilethismayconstituteaproblemforsomestudyobjectivesandmethodswehavenoreasontobelievethatBombus sppmovementwasnonrandomwithrespecttotheobserverandanaccuratedensitycouldthereforestillbemadewhenpassivecountingwasusedClosureviolationmaybeamoreimportantproblemwhenattempting tocalculatedensity fromanettingplotwhereanimals
mayentertheplotandbeunabletoleaveastheyarecapturedandhelduntil thesurveyhasfinished Insuchcasesmovementwouldbebiasedbyindividualsimmigratingintothemonitoredplotbutun‐abletoemigrateandmovementwouldbebiasedtowardstheplotAlthough net‐based sampling is often preferable for investigatingspecies‐specific habitat relationships the potential for movementbias highlights the need for cautious interpretation of net‐baseddensityestimatesforbeesSimilarlyresearchersshouldconsiderthepotentialfordouble‐countingsubjectsAlthoughBombussppinourstudywereapparentlyfewenoughandslowenoughtoavoidmostdouble‐countingthismaybeamoreimportantproblemtoconsiderformoreabundantinsectswithreduceddetectability(egHalictids)
Wealsoadvisecautionwith interpretationofhabitatrelation‐shipsreportedhereasourstudyshouldbe interpretedasasmallldquosnapshotrdquo in time and lacking species‐specific habitat relation‐ships(OlesenBascompteElberlingampJordano2008)Full‐seasonhabitat associations are temporally dynamic forBombus spp andvaryacrossspecies(Goulson1999JhaampKremen2013)Relativefloral resourceavailabilityofdifferentspecieschangesacrosstheseasonandfuturestudiesemployingthesemethodsatregularin‐tervals from early springwhen queens first emerge through lateautumnwould prove valuable In fact examination of queen beedensities would likely prove a better assessment of populationdensityandhabitatqualitythanworkerdensitywhenmonitoringorresearchingcolonialorganismssuchasbumblebeesestimatingthetruenumberofreproducingcoloniesisofmorevaluethanes‐timating the number of foragingworkers aswe have done hereConductingHDSduringthespringandearlysummerwhenqueensare theonly activebumblebee foragersmayprove auseful andnon‐lethalapproachtoestimating theabundanceof reproductiveindividualsandtheexpectednumbersummercoloniesforagivenarea However sampling queens would likely require additionalsamplingsitesorrepeatvisitbecausecountswouldbemuchlowerandHDSmodelsmayhavetroubleconvergingwithrelativelyfewsampling locations Caution should also be exercised with inter‐pretation ofBombus spp density estimates reported here as ourdensitieslikelyconsistofmultiplespeciesofBombus modelled and reportedasoneWealsorecommendfuturestudiesexplorehownon‐Bombusgenera(ormorphospeciesfunctionalgroups)performasthefocusofHDSmodelsAlthoughHDS isnotwithout limita‐tionwebelieveourstudyhighlightstheutilityofHDSmodelsforestimatingdensitiesandelucidatinghabitatassociationsofbumblebeeswhenindividualsaredetectedimperfectly
ACKNOWLEDG EMENTS
Wethank the following individuals andagencies for their supportandlandaccessSproulStateForestandMoshannonStateForestFunding was provided by the Indiana University of PennsylvaniaBUREfundandtheUnitedStatesDepartmentofAgricultureNaturalResources Conservation Service (68‐7482‐12‐502) through theConservationEffectsAssessmentProjectWeareverygrateful toJoanMilamandSamDroegefortheircommentsonearlyversions
234emsp |emsp emspensp McNEIL Et aL
of thismanuscriptWearealsoverygrateful to threeanonymousreviewers spend considerable time strengthening thismanuscriptFundersofourprojectdidnothaveanyinfluenceonthecontentofthesubmittedmanuscriptnordidtheyrequireapprovalofthefinalmanuscripttobepublishedAnyuseoftradefirmorproductnamesisfordescriptivepurposesonlyanddoesnotimplyendorsementbytheUSGovernment
AUTHORSrsquo CONTRIBUTIONS
DJMCRVOELMandJLLconceived researchDJMandELMcol‐lected field data DJM CRVO and ELM conducted statisticalanalysesDJMCRVOELMKRUMDEKADRand JLLwrote themanuscriptJLLsecuredfundingAllauthorsreadandapprovedthemanuscript
ORCID
Darin J McNeil httporcidorg0000‐0003‐4595‐8354
Clint R V Otto httporcidorg0000‐0002‐7582‐3525
Amanda D Rodewald httporcidorg0000‐0002‐6719‐6306
R E FE R E N C E S
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AndersonDR(2007)Model based inference in the life sciences A primer on evidenceBerlinGermanySpringerScienceampBusinessMedia
Arnold T W (2010) Uninformative parameters and model selectionusingAkaikesInformationCriterionJournal of Wildlife Management741175ndash1178httpsdoiorg101111j1937‐28172010tb01236x
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BuchananALGibbsJKomondyLampSzendreiZ(2017)Beecom‐munityof commercial potato fields inMichigan andBombus impa‐tiensvisitationtoneonicotinoid‐treatedpotatoplantsInsects830httpsdoiorg103390insects8010030
BucklandSTAndersonDRBurnhamKPampLaake JL (2005)Distance samplingHobokenNJJohnWileyampSonsLtd
BurnhamKPampAndersonDR(2002)Model selection and multimodel inference A practical information‐theoretic approachBerlinGermanySpringerScienceampBusinessMedia
BurnhamKPAndersonDRampLaakeJL(1980)Estimationofden‐sity from line transect sampling of biological populationsWildlife Monographs723ndash202
Calderone N W (2012) Insect pollinated crops insect pollinatorsandUSagricultureTrendanalysisofaggregatedatafortheperiod1992ndash2009 PLoS ONE7 e37235 httpsdoiorg101371journalpone0037235
CameronSALozierJDStrangeJPKochJBCordesNSolterL F amp Griswold T L (2011) Patterns of widespread decline in
NorthAmericanbumblebeesProceedings of the National Academy of Sciences108662ndash667httpsdoiorg101073pnas1014743108
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Garibaldi L A Steffan‐Dewenter I Winfree R Aizen M ABommarcoRCunninghamSAhellipBartomeusI(2013)Wildpolli‐natorsenhancefruitsetofcropsregardlessofhoneybeeabundanceScience3391608ndash1611httpsdoiorg101126science1230200
Goulson D (1999) Foraging strategies of insects for gathering nec‐tar and pollen and implications for plant ecology and evolutionPerspectives in Plant Ecology Evolution and Systematics2 185ndash209httpsdoiorg1010781433‐8319‐00070
GoulsonDLyeGCampDarvillB(2008)DeclineandconservationofbumblebeesAnnual Review of Entomology53191ndash208httpsdoiorg101146annurevento53103106093454
GoulsonDNicholls E Botiacuteas C amp Rotheray E L (2015) Bee de‐clines driven by combined stress from parasites pesticides andlack of flowers Science 347 1255957 httpsdoiorg101126science1255957
Hammond P S Berggren P Benke H Borchers D L Collet AHeide‐Joslashrgensen M P hellip Oslashien N (2002) Abundance of har‐bour porpoise and other cetaceans in the North Sea and adja‐cent waters Journal of Applied Ecology 39 361ndash376 httpsdoiorg101046j1365‐2664200200713x
HanleyMEAwbiAJampFrancoM(2014)GoingnativeFlowerusebybumblebeesinEnglishurbangardensAnnals of Botany113799ndash806httpsdoiorg101093aobmcu006
Hau E amp Von Renouard H (2006) The wind resource London UKElsevier
Hedley S L amp Buckland S T (2004) Spatial models for line tran‐sect sampling Journal of Agricultural Biological and Environmental Statistics9181ndash199httpsdoiorg1011981085711043578
JamesFCampShugartHHJr(1970)AquantitativemethodofhabitatdescriptionAudubon Field Notes24727ndash736
Jepsen S Evans E Thorp R Hatfield R amp Black S H (2003)Petition to list the rusty patched bumble bee Bombus affinis (Cresson) 1863 as an endangered species under the US Endangered Species Act Retrieved from httpwwwxercesorgwp‐ontentuploads 201301Bombus‐petitionpdf
Jha S amp Kremen C (2013) Resource diversity and landscape‐levelhomogeneitydrivenativebee foragingProceedings of the National Academy of Sciences 110 555ndash558 httpsdoiorg101073pnas1208682110
KaranthKUampSunquistME(1995)PreyselectionbytigerleopardanddholeintropicalforestsJournal of Animal Ecology64439ndash450httpsdoiorg1023075647
KeacuteryMampRoyleJA (2015)Applied Hierarchical Modeling in Ecology Analysis of distribution abundance and species richness in R and BUGS Volume 1 Prelude and Static ModelsCambridgeMAAcademicPress
KeacuteryM amp Schmidt B R (2008) Imperfect detection and its conse‐quencesformonitoringforconservationCommunity Ecology9207ndash216httpsdoiorg101556ComEc92008210
Kevan PG (1990)Pollination keystone process in sustainable globalproductivity InVIInternationalSymposiumonPollination288(pp103‐110)
Kremen CWilliams NM amp Thorp RW (2002) Crop pollinationfromnativebeesatriskfromagriculturalintensificationProceedings of the National Academy of Sciences99 16812ndash16816 httpsdoiorg101073pnas262413599
emspensp emsp | emsp235McNEIL Et aL
LofflandH L Polasik J S TingleyMW Elsey E A Loffland CLebuhnGampSiegelRB(2017)Bumblebeeuseofpost‐firechap‐arralinthecentralSierraNevadaThe Journal of Wildlife Management811084ndash1097httpsdoiorg101002jwmg21280
MackenzieD I (2006)Modelingtheprobabilityof resourceuseTheeffectofanddealingwithdetectingaspeciesimperfectlyJournal of Wildlife Management70367ndash374httpsdoiorg1021930022‐541X(2006)70[367MTPORU]20CO2
MacKenzieDINicholsJDLachmanGBDroegeSAndrewRoyleJampLangtimmCA(2002)Estimatingsiteoccupancyrateswhende‐tectionprobabilitiesarelessthanoneEcology832248ndash2255httpsdoiorg1018900012‐9658(2002)083[2248ESORWD]20CO2
MacKenzieDINicholsJDRoyleJAPollockKHBaileyLampHinesJE(2005)Occupancy estimation and modeling Inferring pat‐terns and dynamics of species occurrenceLondonUKElsevier
Mackenzie D I (2003) Assessing site occupancymodelling as a toolfor monitoring Mahoenui giant weta populations Department ofConservation17
Marques T A Thomas L Fancy S G amp Buckland S T (2007)Improvingestimatesofbirddensityusingmultiple‐covariatedistancesamplingThe Auk1241229ndash1243httpsdoiorg1016420004‐8038(2007)124[1229IEOBDU]20CO2
McCaskillGLMcWilliamsWHAlerichCAButlerBJCrockerS JDomkeGMhellipWestfall JA (2009)Pennsylvaniarsquos Forests 2009NewtownSquarePAUSDepartmentofAgricultureForestServiceNorthernResearchStation
MichenerCDMcGinleyRJampDanforthBN(1994)The Bee Genera of North and Central AmericaWashingtonDCSmithsonianInstitutePress
OlesenJMBascompteJElberlingHampJordanoP(2008)TemporaldynamicsinapollinationnetworkEcology891573ndash1582httpsdoiorg10189007‐04511
PerssonA S RundloumlfMCloughYampSmithHG (2015)Bumblebees show trait‐dependent vulnerability to landscape simplifica‐tion Biodiversity and Conservation 24 3469ndash3489 httpsdoiorg101007s10531‐015‐1008‐3
Potts SGVulliamyBDafniANeemanGampWillmer P (2003)Linking bees and flowers How do floral communities structurepollinator communities Ecology 84 2628ndash2642 httpsdoiorg10189002‐0136
PottsSGBiesmeijerJCKremenCNeumannPSchweigerOampKuninWE (2010)Globalpollinatordeclinestrends impactsanddriversTrends in ecology amp evolution25(6)345ndash353
Redhead JW Dreier S Bourke A F HeardM S JordanW CSumner S hellip Carvell C (2016) Effects of habitat compositionandlandscapestructureonworkerforagingdistancesoffivebum‐ble bee species Ecological Applications 26 726ndash739 httpsdoiorg10189015‐0546
Roulston T A H Smith S A amp Brewster A L (2007) A com‐parison of pan trap and intensive net sampling techniques fordocumenting a bee (Hymenoptera Apiformes) fauna Journal of the Kansas Entomological Society 80 179ndash181 httpsdoiorg1023170022‐8567(2007)80[179ACOPTA]20CO2
Royle J A Dawson D K amp Bates S (2004) Modeling abundanceeffects in distance sampling Ecology 85 1591ndash1597 httpsdoiorg10189003‐3127
Scheper J Bommarco R Holzschuh A Potts S G Riedinger VRoberts S P hellipWickens V J (2015) Local and landscape‐level
floral resources explain effects of wildflower strips on wild beesacrossfourEuropeancountriesJournal of Applied Ecology521165ndash1175httpsdoiorg1011111365‐266412479
SeberGA(1986)AreviewofestimatinganimalabundanceBiometrics42267ndash292httpsdoiorg1023072531049
ShultzCH(1999)The Geology of PennsylvaniaPennsylvaniaGeologicalSurveyHarrisburgPAPennsylvaniaGeologicalSurvey
Sillett T S Chandler R B Royle J A KeacuteryM ampMorrison S A(2012) Hierarchical distance‐sampling models to estimate popu‐lation size and habitat‐specific abundance of an island endemicEcological Applications22(7)1997ndash2006
SollmannRGardnerBWilliamsKAGilbertATampVeitRR(2016)AhierarchicaldistancesamplingmodeltoestimateabundanceandcovariateassociationsofspeciesandcommunitiesMethods in Ecology and Evolution7529ndash537httpsdoiorg1011112041‐210X12518
Tepedino V J Durham S Cameron S A amp Goodell K (2015)Documenting bee decline or squandering scarce resourcesConservation Biology 29 280ndash282 httpsdoiorg101111cobi12439
Thomas LBuckland S TBurnhamKPAndersonDR Laake JL Borchers D L amp Strindberg S (2002) Distance samplingEncyclopediaofenvironmetrics
Thomas L Buckland S T Rexstad EA Laake J L Strindberg SHedley S L hellipBurnham K P (2010)Distance softwareDesignand analysis of distance sampling surveys for estimating pop‐ulation size Journal of Applied Ecology 47 5ndash14 httpsdoiorg101111j1365‐2664200901737x
ThompsonWL (2002)TowardsreliablebirdsurveysAccountingforindividualspresentbutnotdetectedThe Auk11918ndash25httpsdoiorg1016420004‐8038(2002)119[0018TRBSAF]20CO2
VanStrienA JTermaatTGroenendijkDMensingVampKeryM(2010) Site‐occupancy models may offer new opportunities fordragonflymonitoringbasedondailyspecies listsBasic and Applied Ecology11495ndash503httpsdoiorg101016jbaae201005003
VilsackTampMcCarthyG(2015)National strategy to promote the health of honey bees and other pollinatorsWashingtonDCReport IssuedbytheWhiteHousethePollinatorHealthTaskForce
WardKCariveauDMayERoswellMVaughanMWilliamsNhellip Gill K (2014) Streamlined Bee Monitoring Protocol for Assessing Pollinator HabitatPortlandORTheXercesSocietyforInvertebrateConservation
WeatherUndergroundInc(2018)WeatherForecastandReports‐LongRangeandLocalWundergroundRetrievedfromhttpswwwwun‐dergroundcom
WherryET Fogg JM JrampWahlHA (1979)Atlas of the flora of Pennsylvania Philadelphia PA The Morris Arboretum of theUniversityofPennsylvania
YoccozNGNichols JDampBoulinierT (2001)Monitoringofbio‐logicaldiversityinspaceandtimeTrends Ecology and Evolution16446ndash453
How to cite this articleMcNeilDJOttoCRVMoserELetalDistancemodelsasatoolformodellingdetectionprobabilityanddensityofnativebumblebeesJ Appl Entomol 2019143225ndash235 httpsdoiorg101111jen12583
226emsp |emsp emspensp McNEIL Et aL
1emsp |emspINTRODUC TION
Native bees in North America are important pollinators of bothcropsandwildplants (Ashmanetal2004Garibaldiet al2013KremenWilliamsampThorp2002) Indeedbees alongwithotherpollinators are considered keystone species that facilitate sexualreproductionfor85ofangiospermsworldwide (Allen‐Wardelletal1998Kevan1990)InagriculturalportionsoftheUnitedStatespollinationservicesprovidedbynativebeesarevaluedat$3billionUSD annually (Calderone 2012) Even as the ecological and eco‐nomic importance of native bees is recognized there is amount‐ingevidence thatmanybee species aredeclining (Cameronet al2011GoulsonLyeampDarvill2008)ThesedeclinesincludenotonlymanagedspecieslikeApis melliferabutalsoNorthAmericannativetaxalikebumblebees(Bombusspp)andothers(Cameronetal2011GoulsonNichollsBotiacuteasampRotheray2015Pottsetal2010)Forexampletherustypatchedbumblebee(Bombus affinis)waslistedasFederally Endangeredunder theEndangeredSpeciesAct in 2017and several otherBombus species have been proposed for listing(JepsenEvansThorpHatfieldampBlack2013)Althoughthedriversresponsibleforpopulationdeclinesvaryamongspeciesthreatsin‐cludepesticidesnon‐nativepathogensandhabitatlossdegradation(Goulsonetal2015PerssonRundloumlfCloughampSmith2015)
Still while evidence is fairly clear regarding bee declines forsomeregionsandorspeciesthestatusofmanybeepopulationsre‐mainsunknown(TepedinoDurhamCameronampGoodell2015)In2015theUnitedStatesPollinatorHealthTaskForceproposedthedevelopmentofnationalpollinatormonitoringprogramstoestimatepopulation trends and identify environmental stressors affectingnative bees (VilsackampMcCarthy 2015) Central to accomplishingthesegoalsistheaccurateestimationofbeepopulationsizesacrossspeciesgeneramorphospeciesandfunctionalgroupstoestablishareferencebenchmark forevaluatingpopulation trends abundanceacrossdifferenthabitatsandassessingtheoutcomesofconserva‐tioninterventions
Althoughavarietyofmethodshavebeencommonlyusedtosam‐plewildbeepopulations (eg fixed‐areaaerialnettingbeebowlsvanetraps)each is limitedby inherentmethodologicalbiasesthatmakeinferenceoftruedensitiesdifficultInparticularfewmethodsaccountforthebiascausedbyimperfectdetection(egLofflandetal2017)inthatonlybeescapturedorotherwisedetectedbyanob‐serverarecountedandsubsequentlymodelledRegardlessofsam‐plingmethodonlyafractionoftheindividualspresentatalocationwillbedetected(KeacuteryampSchmidt2008)Rawcountswhichfailtoaccountfordetectionprobabilitywillinvariablygenerateestimatesofabundancethatarebiasedlowifsomeindividualsarepresentbutnotdetected(KeacuteryampSchmidt2008MacKenzieetal20022005)Thoughsuchmethodshavemeritundermanycircumstancesac‐curateestimateofabundanceorchangesinabundanceoverspaceandtimerequiresconsiderationofmethodologicalbiaseslikethosecaused by imperfect detection (MacKenzie et al 2005) In addi‐tionfailuretoaccountforimperfectdetectioncanobfuscatehab‐itat associations particularlywhen thehabitat conditions that are
attractivetotheorganismalsomakeitmoredifficultforobserverstodetecttheorganism(MacKenzie2006)Consequentlyresearch‐ersmightbeledtobelievethatcertainhabitatconditions(associatedwithlowbeecounts)arelow‐qualityhabitatswhilebeesmayinreal‐itybeofequalgreaterabundancebutlessdetectableorviceversa(MacKenzie2006)
Herewedemonstrate theutilityofhierarchical distance sam‐pling (HDS) forestimatinghabitat‐specificdensity (ie abundanceper unit area) anddetection probability of bumblebees in decidu‐ous forest of central PennsylvaniaHierarchical distance samplingisananalyticaltechniquethatallowsresearcherstomodelhabitat‐specificabundanceandheterogeneityinspeciesdetectionwithinaunifiedframework(HedleyampBuckland2004KeacuteryampRoyle2015Royle Dawson amp Bates 2004) It builds upon standard distancesampling which is a widely used method for estimating animalabundance while for accounting imperfect detection (BucklandAnderson Burnham amp Laake 2005) However HDS differs fromstandarddistancesamplinginthatitallowsforspatialvariabilityinabundanceanddetectionacrossmultiplesitestobeexplainedasafunctionofcovariates(KeacuteryampRoyle2015)Althoughothermethodsexistforestimatingabundancewhileaccountingfordetection(egoccupancyN‐mixture etc)most requiremultiple visits with theassumptionofpopulationclosurebetweensurveys (KeacuteryampRoyle2015MacKenzieetal2005)Distancesamplingmaybeparticu‐larlyuseful for insectstudiesbecause it requiresonlyasinglesitevisittoestimatedetectionprobabilityandmanyshort‐livedinsects(likesomebeespecies)maynotemergelongenoughtoallowmul‐tiplevisitsper siteDistance samplinghasbeen routinelyusedbywildlife researchers to model abundance and detection functionsfor multiple vertebrate taxa (Hammond et al 2002 Karanth ampSunquist1995MarquesThomasFancyampBuckland2007)Toourknowledgenopreviousresearchhasdemonstratedtheuseofdis‐tancesampling toestimatebeeabundanceorhabitatassociations(BendelHovickLimbampHarmon2018)Ourgoalswereto(a)useHDStoevaluatehowBombussppdetectionprobabilityvarieswithdistancesurveytechniqueandhabitatattributes(b)compareabun‐danceanddensityestimatesgeneratedfromHDStostandardsam‐plingapproaches(fixed‐widthtransectsandfixed‐radiusnetcounts)thatdonotaccountforimperfectdetectionand(c)identifysite‐spe‐cifichabitatrelationshipsforBombussppacrosssamplingmethods
2emsp |emspMATERIAL S AND METHODS
21emsp|emspStudy area
WesurveyedbeeswithinthePennsylvaniaWildsregionofnorth‐central Pennsylvania focusing on Centre and Clinton Counties(Figure 1) This region lies within the Appalachian Plateau of thenorthcentralAppalachianMountainsandischaracterizedbyarug‐ged series of high‐elevation ridges (300ndash600masl) punctuatedbylowvalleysalongtheAlleghenyFront(Shultz1999)Vegetationcommunities within the Pennsylvania Wilds are chiefly mature
emspensp emsp | emsp227McNEIL Et aL
deciduous‐ormixedforest (80ndash100yearspost‐harvestMcCaskilletal2009)withoak(Quercus spp)hickory(Caryaspp)andeast‐ern hemlock (Tsuga canadensis) among the most common species(WherryFoggampWahl1979)Weconcentratedoureffortswithindeciduous forests of Sproul andMoshannon State Forestswhereoak silviculture aims to restore young forest age classes throughtimber harvest and regeneration Because silvicultural practiceswithinthesetwoStateForestsaimtorestorehabitatforforestwild‐lifewefocusedoursurveyeffortswithinregeneratingoakstands0ndash9yearspost‐managementDuringsurveysavarietyoffloweringplantswereavailabletoBombussppincludinglow‐growingshrubslike hillside blueberry (Vaccinium pallidum) as well as herbaceousforbs like eastern teaberry (Gaultheria procumbens) and commoncow‐wheat(Mellampyrum linerare)MosttallwoodyplantswerenotfloweringexceptforDevilrsquoswalkingstick (Aralia spinosa)whichwedetectedonlywithinafewofoursites
22emsp|emspSite selection and survey placement
We randomly selected 47 timber stands within Sproul andMoshannon State Forests that had been recently treated withoverstory removal (basal area 23ndash92 m2ha) We attemptedto maximize the distance between sites such that our averagedistance‐to‐nearest‐site was 1110m (SE 107m range 464ndash4516m)Thisreducedthelikelihoodofindividualsbeingdetectedatmultiplesites(Redheadetal2016)Timberharvestunitsaver‐aged2314ha(SD1862harange254ndash10392ha)insizeAsin‐glesurveypointwaslocatedwithineachharvestusingarandompoint generator tool inArcGIS102 (ESRI 2011)Weattemptedtominimizeedgeeffectsbyensuringpointswererelativelycon‐sistent in their placementwith respect to timberharvest edgessamplingwas restricted to areas at least80m from theedgeoftimberharvestsandourfinalsampleofsiteswasameandistanceof11867m(SE624m)
23emsp|emspTransect surveys
Ateachpointwe sampledBombus sppusing three survey types(a) distance transects (b) transect counts and (c) aerial nettingcounts Both distance transects and fixed‐width transect countsoccurred simultaneously along 66m transects oriented north‐to‐south and centred at eachpoint locationAlong each transectobserverswalked forwardat a constant rate (~1mmin) such thattheobserverarrivedatthetransectendafter30minPriortosur‐veyseachobserver(n=2)wastrainedindistanceestimationusingdummytransectsalongwhichbeesrsquodistanceswerephysicallymeas‐uredaftereachattemptedestimateusingameasuring tapeOnceallobserverswereconsistentlyestimatingdistanceswithinplusmn025mfield surveyswere conductedwith a2m longmeasuring stick forconstantreferenceWhilewalkingalongeachsurveytransect theobserverrecordedBombussppdetectionssuchthatafinalcount()wasgeneratedforeachsurveycoupledwiththedistances(plusmn025m)betweeneachBombus sppandthetransectWedidnotattempttoidentify speciesor sex forBombus spp detected in situ thereforecountswerelikelymultiplespeciesandsexesSurveydataforeachpointincludedaBombussppcountandtheircorrespondingdetec‐tion distancesWe discerned betweenBombus spp andXylocopa virginica byabdomenpubescence(MichenerMcGinleyampDanforth1994)DistanceswererecordedastheperpendiculardistancefromthetransecttoeachbeeandnotedasthedistanceatwhichthebeewasfirstdetectedWhilewalkingalongeachtransectobserversat‐temptedtokeeptrackofpreviouslydetectedBombusspptoavoiddouble‐counting individualsthatmightbemovingamongfloralre‐sources near the transectWe anecdotally observed this methodlargely avoided double‐counting as Bombus spp are generallylarge‐bodiedconspicuousinsectsandeasilyaudibleinflightAllrawcountsanddetectiondistancesconstitutedourldquodistancetransectrdquodata(a)andrawcountswithin2mofthetransectconstitutedourldquotransectcountrdquodata(b)
F I G U R E 1 emspSurveylocationswithinthePennsylvaniaWildswhereweconductedsurveysforBombussppwithinregeneratingtimberharvests
228emsp |emsp emspensp McNEIL Et aL
We followed standard bee survey methods to avoid commoncausesofdetection failure (Wardetal2014)Surveyswerecon‐ductedonlyinbrightlightconditionslowwindwarmdays(ge16degC)andonlyduringlatemorningandafternoon(1000ndash1700)ThoughweattemptedtousestudydesigntoreducethepotentialimpactsofthesefactorsonBombus sppdetectabilitywealso includedthemindetectionmodellingAtthetimeofeachsurveywerecorded(a)surveyorID(b)cloudcover(c)timeofdayand(d)BeaufortWindIndex Local temperature data were downloaded from WeatherUnderground from the KUNV weather station in State CollegePennsylvania (WeatherUnderground Inc2018)Cloudcoverwasestimatedinthefieldtothenearest25(0ndash100)BeaufortWindIndexwasmeasuredonanincrementalscalefrom0to5with0rep‐resentingnowind at all (ie smokewould theoretically risewith‐outdrift)and5representinghighwindssuchthatentiretreesswayinthewind(HauampVonRenouard2006)Weavoidedsurveyinginwindindicesgt3andthusconsideredtwocategoriesofwind0ndash1ldquolowrdquo2ndash3ldquomoderaterdquoinouranalysesAllsurveystookplacefrom10to25July2017
24emsp|emspNet counts
TomeasureBombussppabundancewithinfixed‐radiusnetcountswe created 15m radius count surveys centred around each pointlocation (thecentreofeachdistancetransect)Nettedbeecountstookplaceimmediatelyupontheconclusionoftransectsurveys(de‐scribedabove)Withineachfixed‐radiusplotasingleobserverspent30minseeking‐andattemptingtocaptureallBombussppdetectedwithahandnetWechosefixed‐radiusnetsamplingbecauseitisastandardsamplingtechniquefornativebees (Perssonetal2015PottsVulliamyDafniNersquoemanampWillmer2003RoulstonSmithampBrewster2007)andwouldthereforeserveasabasisforcomparisontoourabundanceestimatesgeneratedfromHDSForeachBombus sppdetectedtheobserverattemptedtocaptureeachbeeusingahandnet(collapsible15rdquodiameternet17rdquohandleBioquipProduct7115CP)andoncecapturedallbeeswereheldcaptiveforthere‐mainderofthesurveyForeachcapturedbeethetimerwasstoppedwhiletheobserverplaced it intoaplasticzipperbagandresumedimmediately thereafter Thismethod prevented us from recaptur‐inganddouble‐countingbeeswithinthesameplotAfter30minofsurvey timehadelapsedeachBombus sppwas removed from itsbagwith forceps photographed for anotherproject and releasedunharmedInthefewoccasionswhereBombussppwereobservedbutevadedcapturetheyweretreatedasallotherBombussppcap‐turedforthepurposesofthisstudy(ieincluded)
25emsp|emspHabitat surveys
Wesurveyedregeneratingvegetationstructurewithin timberhar‐vestunitsfrom15Juneto15July2017VegetationsurveyssharedtheircentroidwithBombussppsurveysVegetationdataquantifiedhabitatstructureofwoodystemsandherbaceousunderstoryratherthan plant composition All vegetation data were collected along
three50mradialtransectseachorientedat0deg120degand240degfrompoint centreAlong each transectwe recordedplant strata at 10ldquostopsrdquo(10mapartn=30netcountlocation)Vegetationstratare‐cordedateachstopconsistedofthepresenceabsenceofsaplingshrub forbandgrasssedgeSaplingswereyoungtreeslt10cm (indiameterbreastheight)Thissamplingregimegaveusadequateres‐olutiontoassessvegetationstructure(15stopssite)whileremain‐ingof comparable scale toourbee sampling transects (33m)Wefoundvegetationstructuretobehighlycorrelatedacrossscalesaslargeas100mandthereforebelieveour50mvegetationplotsrep‐resentedsiteconditionsreasonablywellShrubswerewoodyplantswithmultipleprimarystems(incontrasttosingle‐stemmedsaplings)Forbswerebroad‐leafeddicotyledonousplants(egSolidagospp)The plant category ldquograssrdquo included any monocotyledonous plant(grassessedgesetc)Werecordedplantstratawithanoculartubesuchthatonlystratathat intersectedwithcrosshairs intheoculartube were considered present (James amp Shugart 1970) While asinglestopcouldincludemultiplestratatypeseachstratumcouldonlyberepresentedonceperstopandthuseachsitecouldhaveamaximumofn=15occurrencesforeachstratumWeanalyzedplantstrata values as percentages Prior to all analyses we calculatedSpearmanrsquosrho(ρ)forallpairsofcovariatestobemodelledBecausenonewerestronglycorrelated(Spearmanrsquosρ lt 060)nocovariateswereredundantandallweresuitableformodelling
26emsp|emspHierarchical distance models
Weanalyzeddistancetransectdata(beecountsanddistances)usingHDS models implemented in the R package ldquounmarkedrdquo (Fiske ampChandler2011RCoreampTeam2018)Thepackageunmarkedfitslinearmodelsinamaximumlikelihoodframeworkandcanbecom‐bined with an Information‐Theoretic approach (Anderson 2007)forthepurposeofmodelselection(egusingAkaikersquosInformationCriterionAICBurnhamampAnderson2002)Hierarchicaldistancemodels allowed us to create and rank candidate models each ofwhich contained independent model components for detectionprobability (p) and expected animal abundance (density λ) HDSmodelsassume(a)subjectsareaccuratelyidentified(egnofalse‐presences)(b)thatallsubjectsonthetransect(distance=0m)aredetectedperfectly(p=10)(c)subjectsaredetectedattheiroriginallocation(iemovement isnot influencedbytheobserver) (d)dis‐tancesareaccuratelymeasuredand(e)detectionofeachindividualis independentofthedetectionofallotherindividuals(Thomasetal2010)Bumblebeesappeartoconstitutegoodcandidatesfordis‐tancesamplingastheycanbeeasilyidentified(togenus)inthefield(Micheneretal1994)areeasilyapproachedbyobservers(Wardetal2014)andremainrelativelystillduringpollinationsuchthataccu‐ratedistanceestimationscouldbemadeforeachworkerAlthoughdistances were measured in the field directly we binned detec‐tions as recommended by Buckland et al (2005) 0ndash1 1ndash2 2ndash33ndash4and4ndash5mMoreovertopreparedistance‐basedtransectdatawe truncated the outer 10of our data such that analyseswereconductedusingonly the closest 90ofBombus spp detections
emspensp emsp | emsp229McNEIL Et aL
asrecommendedfordistanceanalysesbyBucklandetal(2005)Bytruncating thedata in thiswayalldetectionswerelt5mfromtheobserver
Distance models provide robust estimates of abundance byadjusting animal counts by the probability of detection for givendistances (Buckland et al 2005) This is accomplished by fittingdetectiondistancedata to a ldquodetection functionrdquo that describes adecayindetectionprobabilityassubjectsarefurtherfromtheob‐server (Bucklandetal2005KeacuteryampRoyle2015)Toevaluateanappropriatedetectionfunctionweevaluatedmodelseachfitusingoneofthefollowingdetectionfunctions(a)exponential(b)hazardrateor(c)half‐normal(Bucklandetal2005)ThiswasdonepriortoallcovariatemodellingEachdetectionfunctionisusedtoestimatetheaverageprobabilityofdetectionwhichisthenusedtoadjustrawcountssuchthatdensitypredictionscanbemade(Bucklandetal2005)OncethemostappropriatedetectionfunctionwasselectedbasedonAICcrankitwasusedtomodeldetectionprobabilityanddensityinconsecutivemodelsWemodelleddetectionprobabilityintwotiersdetectiontier1(surveycovariatesondetection)andde‐tectiontier2(habitatcovariatesondetection)Becauseoursamplesizewasmodestweusedonlysingle‐covariatedetectionmodelstoavoidoverfittingHDSmodelsDetectiontier1includedunivariatemodels for (a) timeof day (b) surveyor (c) temperature (d) cloudcover(e)windindexand(f)anull(intercept‐only)modelDetectiontier 2 (fit independently of detection tier 1) included univariatemodelsfor(a)saplingcover(b)shrubcover(c)forbcover(d)grasscoverand(e)anullmodelWithinbothmodeltiersweusedaglobalhabitatmodel(iesapling+shrub+forb+grass)fordensitytoen‐sure thatvariation indensitywas reasonablywell explainedwhileassessingdetectionprobabilityWeconsideredcovariatestobein‐formativeiftheywerebothgt20AICclessthanthenullmodelandhadβcoefficient95confidenceintervalsthatdidnotincludezeroUsing the informative covariates fromdetection tiers1and2weconstructedasetofdensitymodels(habitatcovariatesondensity)thataccountedfor imperfectdetection (a)saplingcover (b)shrubcover (c) forbcover (d)grasscoverand (e)anullmodelThenullmodelcontainedonlyintercepttermsandtheinformativeparame‐tersfordetectionPriortomodellingallcontinuouscovariateswerestandardizedusingthescalefunctioninbaseRModelrankingwasdoneusing the ldquoaictabrdquo functionof thepackage ldquoAICcmodavgrdquoAllmodelswerefitassumingaPoissondistributioninldquogdistsamprdquoandmodelfitwasassessedbycalculatingavarianceinflationfactor(chatchatchatc)usingtheunmarkedfunctionldquofitstatsrdquo (KeacuteryampRoyle2015)Weconsideredallmodelslt20AICctobecompetingandequallysupportedbythedata(BurnhamampAnderson2002)
27emsp|emspPoisson generalized linear models
WeusedaPoissongeneralized linearmodels inR (using the ldquoglmrdquofunction)tomodelBombus sppabundancealongfixed‐radiustran‐sectsandnetcountsThisallowedustocomparehabitat‐abundancerelationshipsgeneratedfromHDSmodelstothosegeneratedfrommethodsthatdonotaccountfordetectionprobabilityAswithour
HDSmodels Poisson regressionmodels allowed us tomodel beecountsasafunctionofhabitatcovariates(a)saplingcover(b)shrubcover (c) forbcover (d)grasscover and (e) anull (intercept‐only)modelWemodelled our fixed‐radius transect counts by truncat‐ing allHDS‐transect databy2mof the transect line and treatingthedataasarawcount(HanleyAwbiampFranco2014Scheperetal 2015) which is a standard technique when conducting visualencounter surveys Net count data were modelled in a compara‐blemanner such that raw countsweremodelled as a function ofhabitat covariatesWedid not account for imperfect detection ineither of these models but rather modelled Bombus spp countarea interpretedasadensityWeagainusedan information‐theo‐reticapproach(Anderson2007)withmodelrankingbasedonAICc consideringmodelslt20AICctobeequallysupportedbythedata(BurnhamampAnderson2002)Wealsousedsingle‐covariatemodelstoavoidoverlycomplexmodelsandtheinclusionofuninformativeparameterswithintopmodels(Arnold2010)
3emsp |emspRESULTS
Wedetected194individualBombus sppwithin5mofwhich136werewithin2mof the transect lineDuringaerialnetcountswecapturedn = 201 BombussppworkersOfthebeescapturedduringaerial net countsover50wereB impatienswith the remainderbeingamixedcommunityoflesscommonspecieslikeB bimaculatus and B vagans
31emsp|emspDetection probability
Ofthreedetectionfunctionmodelsweranthebest‐rankedmodelincludedanexponentialdetectionfunctionwheredetectionprob‐abilitygt5mfromthetransectwasasymp0(Figure2)Usinganexponen‐tialdetection functionwe foundthatdetectionprobabilityvariedas a functionof time since1000 (theearliestpossible start time)
F I G U R E 2 emspFrequencyofdetections(greybarsrightaxis)forBombussppwithinregeneratingtimberharvestsDetectionprobability(leftaxis)declinedasafunctionofdistancefromtransectandwasfittoanexponentialdetectionfunction(blackline)Bombussppwereonlyrarelydetectedfurtherthan5mfromthetransectline
230emsp |emsp emspensp McNEIL Et aL
andobserverIDsuggestingthatthelatestsurveysofeachdayhadthe lowestdetectionprobability and thatobserverswereunequalin their ability to detectBombus spp (Table 1 Figure 3a) Amongmodels investigating the relationship between habitat covariatesand Bombus spp detection the model that included grass cover()wastheonlysupportedmodelandsuggestedthatBombussppweremorereadilydetectedatsiteswithmoregrasscover(Table1Figure3b)Allothercovariatesmodelledintiers1and2weregt20AICc less than the nullmodel and theβ 95 confidence intervalsoverlappedzero
32emsp|emspHabitat modelling
Models from all three analyses yielded discernable habitat asso‐ciationswithBombus sppabundance (Table2Figure4)All threeanalyses indicated thatBombus spp abundanceduring the surveyperiodwas negatively associatedwith per cent sapling cover andnotassociatedwithforbcover (Table2Figure4)The importanceofshrubcoverandgrasscoveraspredictorsofBombussppcountsandestimatedabundancevariedacrossmethods(Table2)HDSandtransectcountsrevealedsupportforshrubcoverasaninformativecovariatebeinggt20AICc less than thenull andhavingparameter
95confidence intervals thatdidnotoverlapzero (Table2)Onlynet counts suggested that grass cover was positively associatedwithBombus sppabundancewhileHDSsuggestedthatgrasscoverwasinsteadcorrelatedpositivelywithdetectionprobabilitybutnotabundance (Table 2 Figure 4) In contrast our net count analysissuggestednoeffectofshrubcoveronbeecountswiththeldquoshrubrdquomodel ranked lower than thenullmodeland the shrubparameter95confidenceintervalsoverlappingzero(Table2)Ourtop‐rankedHDSmodel(ldquosaplingrdquo)showedevidenceofminoroverdispersion(chatchatchatc=133)whilemostothermodelsdidnotappearoverdispersed (chatchatchatclt10 with a mean chatchatchatc=101acrossmodels inourfinalHDSmodelset)Weconsidered this an acceptable level of overdispersion and did notuse a variance inflation factor to adjust our parameter estimates(BurnhamampAnderson2002)
33emsp|emspDensity estimation
Inadditiontoexaminingabundanceasafunctionofhabitatamongthe three methods we compared their estimated mean densitiesof foragingBombus spp basedon intercept‐only abundancemod‐els(includingdetectioncovariatesforHDS)EstimatedBombusspp
Model name K AICc ΔAICc AICc Wt β estimate (95CI)
Surveycovariatesondetectionprobability
p(observer) 7 34893 000 078 058(021to095)
p(time) 7 35156 264 021 minus023(minus038tominus008)
p () 6 35829 936 001 ‐
p(wind) 7 35987 1094 000 minus016(minus044to013)
p(temp) 7 36064 1172 000 minus005(minus019to009)
Sitecovariatesondetectionprobability
p(grass) 7 35267 000 085 035(007to063)
p(forb) 7 35827 561 005 017(minus004to037)
p() 6 35829 562 005 ‐
p(shrub) 7 35965 699 003 minus013(minus035to009)
p (sapling) 7 36048 782 002 010(minus016to036)
NoteModelsareranked indescendingorderofAkaikersquos InformationCriterionadjustedforsmallsamplesize(AICc)Surveycovariatesincludedtimesincesurveystarttime(continuousldquotimerdquo)tem‐perature(continuous)cloudcover(overcastcontinuous)observer(categorical)andwindindex(categorical)Sitecovariatesincludedpercentcoverasmeasuredby50mradiusvegetationsurveysforvegetationstructuresaplingsshrubs forbsandgrassBothcandidatemodelsetsarerankedagainstanullintercept‐onlymodelBelowwereportnumberofmodelparameters(k)ΔAICcAICc weight(AICcWt)andβparameterestimates(95confidenceinterval)
TA B L E 1 emspHierarchicaldistancemodelsofdetectionprobabilityasafunctionofsurveycovariates(Tier1top)andsitecovariates(Tier2bottom)
F I G U R E 3 emspModelsofBombussppdetectionprobabilityasafunctionofsurveytime(left)percentgrasscover(centre)andobserver(right)whilealsobeingmostdetectableclosesttothetransect(all)
emspensp emsp | emsp231McNEIL Et aL
forager density within timber harvests was highest for the HDSmodels(192foragingworkersha95CI153ndash240)andlowestfornetcounts(21foragingworkersha95CI19ndash23Figure5)an89differencebetween the twomethodsTransect countsyielded in‐termediate estimates of density (40 foragingworkersha 95CI34ndash47)andwere80lowerthandensityestimatesfromHDSSite‐specific HDS modelled densities and netting count raw densitieswerecorrelated (Pearsonrsquos r = 031 p=003) though the relation‐shipwasnot11(Figure5)
4emsp |emspDISCUSSION
Ourstudyprovidesthefirstempiricalevidencethatdetectionprob‐abilitiesofBombus sppvaryinwaysthatcanaffectabundanceesti‐matesandinferencesabouthabitatrelationshipsObservationerrorcaused by imperfect detection is one of the central challenges ofecologicalmonitoringprograms(Thompson2002YoccozNicholsampBoulinier 2001)buthas yet tobewidely applied tomonitoringofmany invertebrates includingpollinators (but seeBendeletal2018Lofflandetal2017Mackenzie2003VanStrienTermaatGroenendijkMensingampKery 2010)Methods like distance sam‐plingwhileofferingapotential solution to this challenge are stillunder‐utilized in entomological research Meanwhile distance
samplingandsimilarmethodshavebeenastapleofvertebratewild‐liferesearchfordecades(Bucklandetal2005BurnhamAndersonampLaake1980Seber1986Thomasetal2002)andhavebeenex‐pandedtoestimatepopulationsizehabitat‐specificabundanceforindividualspeciesandcommunities(SillettChandlerRoyleKeacuteryampMorrison2012SollmannGardnerWilliamsGilbertampVeit2016)Althoughourstudyisnotthefirstestimateandaccountfordetec‐tionprobabilityofbumblebees(Lofflandetal2017)nostudybe‐foreourshasdescribedfactorsassociatedwithdetectionprobabilityanddonesoinaHDSframework
Wefoundthatdistancesamplingtransectswerebothasimpleandeffectivesurveymethodforestimatingdensityandhabitatre‐lationships (Buckland et al 2005) Hierarchical distance samplingmodelsareoneofthefewavailablemethodsthatallowresearcherstomodel detection‐adjusted abundancewithonly a single visit toeachsite(Bucklandetal2005KeacuteryampRoyle2015MacKenzieetal 2005)Themethodusesonlynon‐lethal samplingunlike trap‐pingnettingmethods(Tepedinoetal2015)whichisespeciallyde‐sirablewhen sampling for speciesof conservation concern or forcommonspecies in areaswherecapture‐based sampling isnot al‐lowedAdditionallyHDSmodelsarealsousefulbecausetheoutputisaneasily interpretedlatentstatedensitywithunits inldquoanimalsareardquo In our study HDS models generated estimates of foragingBombus sppworkerdensity
Model name K AICc ΔAICc AICc Wt β estimate (95CI)
Hierarchicaldistancesampling
λ(sapling) 6 33769 000 098 minus030(minus045tominus014)
λ(shrub) 6 34583 813 002 021(005to037)
λ() 5 3502 1251 000 ndash
λ(grass) 6 35041 1271 000 minus017(minus038to005)
λ(forb) 6 35282 1513 000 minus001(minus016to014)
Transectcounts
λ(sapling) 2 27763 000 096 minus144(minus220tominus069)
λ(shrub) 2 28448 685 003 085(025to144)
λ(grass) 2 2898 1217 000 minus093(minus214to028)
λ() 1 29007 1244 000 ‐
λ(forb) 2 29216 1454 000 0133(minus074to101)
Netcounts
λ(sapling) 2 36071 000 100 minus163(minus226tominus101)
λ(grass) 2 38438 2367 000 085(003to167)
λ(shrub) 2 38565 2494 000 041(minus009to090)
λ() 1 38608 2537 000 ndash
λ(forb) 2 38709 2638 000 039(minus031to109)
NoteModelsareranked indescendingorderofAkaikersquos InformationCriterionadjustedforsmallsamplesize(AICc)DistancetransectdataincludedBombussppdetectedfrom0to5malong66mtransectsTransectcounts includedBombus sppdetected from0ndash2malong66m transectsnetcountdatawerecountsofBombus sppwithin15mradiusplotsSitecovariatesincludedpercentcover asmeasured by 50m radius vegetation surveys for vegetation structure saplings shrubsforbsandgrassBelowwereportnumberofmodelparameters(k)AICcΔAICcAICc weight(AICc Wt)andeachcovariateβparameterestimateandβparameterestimates(95confidenceinterval)
TA B L E 2 emspHabitatmodelsderivedfromhierarchicaldistancemodels(top)fixed‐widthtransectmodels(centre)andlinearmodelsofnetcountdata(bottom)allfitusingaPoissondistribution
232emsp |emsp emspensp McNEIL Et aL
DespitebeingamongthelargestandmostconspicuousofNorthAmerican bees (Michener et al 1994) we found that detectionprobability of Bombus spp was imperfect and declined markedlywithdistancefromthesurveytransectwithalmostnodetectionsbeyond5mDetectionprobabilitiesinourstudywereinfluencedbysurvey‐specific(egtimeofday)andsite‐specific(eggrasscover)variableswithdetectionprobabilityhighestinthemorninginmid‐summerandinhabitatswithabundantgrasscoverWithinregener‐atingtimberharvestsinourstudyarealdquograssrdquocoverwastypicallylow‐growing monocotyledons like Carex pennsylvanica Abundantlow‐growing sedge allowed observers to view Bombus spp fromgreaterdistancesthanwhensitesweredominatedbytallsaplingsshrubs or forbs (egSolidago) Consequently studieswithin habi‐tatsdominatedbylowgrassorothershortvegetationmightfindde‐tectionprobabilityforBombusspptobereliableatdistancesgt5mAlthoughweareuncertainastowhyBombussppwerelessdetect‐ableduringsurveysconductedlaterintheafternoononeplausibleexplanationisthatlongershadowscastbylateafternoonlightmade
Bombussppmoredifficulttodetectwhenforagingin lowvegeta‐tionAdditionalworkexploringthedriversassociatedwithBombus sppdetectionwouldprovevaluabletomonitoringregimesaimedatsurveyingbumblebees
ThoughourstudyisnotacomprehensivehabitatassessmentforBombussppwithinregeneratingtimberharvestsofeasternforestsourresultsprovideaglimpseintothehabitatdynamicsofbumble‐beesinregeneratingforestsduringmid‐summerOurfindingsthatBombus sppwerepositivelyassociatedwithshrubsandnegativelyassociatedwithsaplingscanbeexplainedprimarilybyflowerphe‐nology during our survey window Regenerating saplings withinthe timber harvests we monitored were largely oaks hickoriesblackcherry (Prunus serotina)andredmaple (Acer rubrumWherryetal1979)Thesespeciesdonot flowerassmallsaplingsanddosoinearlyspringasmaturetrees(ieoutsidethesamplingperiodWherryetal1979)Incontrastseveralspeciesofshrubwereflow‐eringduringsamplingincludingblackhuckleberry(Gaylussacia bac‐cata)andhillsideblueberryIncontrastmostforbs(eggoldenrod
F I G U R E 4 emspModelledhabitatassociationsbetweenBombussppandstructuralvegetationfeatureswithinregeneratingtimberharvestsaspredictedbyhierarchicaldistancemodels(top)fixed‐width(4m)transectcounts(centre)andnetcounts(bottom)Variablesshownaresaplingcover(left)shrubcover(centre)andgrasscover(right)Solidlinesrepresentmodelpredictionswithdashedlinesas95confidenceintervalsRelationshipsmarkedwithanasteriskwerethosewithmodelsupport(iemoreinformativethananullmodelandβ95CInon‐overlappingzero)
F I G U R E 5 emspLeftBombusspppredictedmeandensityformodelsofnetcounts(ldquoncrdquo)transectcounts(ldquotcrdquo)andhierarchicaldistancesamplingmodels(ldquohdsrdquo)RightPredicteddensity(workersha)generatedfromourtop‐rankedhierarchicaldistancemodel(p [observer+time+grass]λ[sapling])regressedagainstcountdatafromBombus sppnetcounts
emspensp emsp | emsp233McNEIL Et aL
SolidagosppsnakerootAgeratina spp)hadnotbegunfloweringyetFutureworkshouldexplorehowBombussppmaytrackresourcesacrossagrowingseasontopersistwithineasternforestecosystems
Monitoringprograms forBombus spp andothernativepolli‐natorscanbeimprovedbyincorporatingstudydesignandmodel‐based approaches for minimizing detection error Although weincludedseveraldesign‐basedsolutionsforminimizingdetectionerror(egrestrictingsurveytimesonlysurveyinginfairweatherWard et al 2014) detection probability remained imperfectand varied due to time of day observer and vegetation coverConsequentlymethodsthatignoreddetectionprobabilitygener‐ated density estimates 80ndash89 lower than HDS Past studieshaveshowntheimportanceofusingdesign‐basedapproachestominimize false negativeswhen sampling bees (BuchananGibbsKomondyampSzendrei2017)Ourstudydemonstratesthevalueofusingbothdesign‐andmodel‐basedapproachesforreducingsam‐plingerrorscausedbyimperfectdetectionOtherstudysystemswith thick vegetation cover such as prairies and forested wet‐landsorobstructiveobjectssuchasurbanenvironmentsarealsolikely to underestimate bee abundance even if multiple design‐basedapproachesareusedWhiletraditionalsamplingtechniquesthat do not account for detection have numerous applicationsourstudyhighlightstheimportanceofincorporatingmodel‐basedapproachesforaccountingfordetectionprobabilitywithinnativebeesurveysparticularlywhenattemptingtoestimatebeeabun‐danceordensity
Althoughour results suggest thatHDS representsapromisingtoolformonitoringbumblebeesresearcherswishingtoemploythemethod should recognize its associated limitations For exampledistancemodelsassumethatallanimalsonthetransectlinearede‐tectedperfectlyAlthoughitislikelythisassumptionwasmetwithalargeinsectlikeBombussppthisassumptionmightbeviolatedwithsmallerinsectsMoreoversubjectsareassumedtobeuniformlydis‐tributedinamannerunaffectedbytheobserverWhileitispossiblethatBombussppwerefrightenedbyobserverswetookcaretonotethe locationof first detection forBombus spp apparently flushedandtheirloudflightmadeclosedetectionsalmostcertainWenotethat thismethodwouldnotworkwell for species‐level identifica‐tionbecauseobservationsaremadefromadistanceandsomebeegeneraareexceedinglydifficulttoidentifyevenwithamicroscope(Michener et al 1994)Misidentification of specieswould consti‐tuteafalsepositivewhichwouldviolateanassumptionofdistancesampling
Anotherconsiderationofthisstudydesignandmanymethodsofabundanceestimationisthatanimalsmayviolatetheclosureas‐sumptionInthecaseofBombussppthislikelyoccurredasforagersflew in‐ and out‐ of the effective survey area (~5m from the ob‐serverforHDS)WhilethismayconstituteaproblemforsomestudyobjectivesandmethodswehavenoreasontobelievethatBombus sppmovementwasnonrandomwithrespecttotheobserverandanaccuratedensitycouldthereforestillbemadewhenpassivecountingwasusedClosureviolationmaybeamoreimportantproblemwhenattempting tocalculatedensity fromanettingplotwhereanimals
mayentertheplotandbeunabletoleaveastheyarecapturedandhelduntil thesurveyhasfinished Insuchcasesmovementwouldbebiasedbyindividualsimmigratingintothemonitoredplotbutun‐abletoemigrateandmovementwouldbebiasedtowardstheplotAlthough net‐based sampling is often preferable for investigatingspecies‐specific habitat relationships the potential for movementbias highlights the need for cautious interpretation of net‐baseddensityestimatesforbeesSimilarlyresearchersshouldconsiderthepotentialfordouble‐countingsubjectsAlthoughBombussppinourstudywereapparentlyfewenoughandslowenoughtoavoidmostdouble‐countingthismaybeamoreimportantproblemtoconsiderformoreabundantinsectswithreduceddetectability(egHalictids)
Wealsoadvisecautionwith interpretationofhabitatrelation‐shipsreportedhereasourstudyshouldbe interpretedasasmallldquosnapshotrdquo in time and lacking species‐specific habitat relation‐ships(OlesenBascompteElberlingampJordano2008)Full‐seasonhabitat associations are temporally dynamic forBombus spp andvaryacrossspecies(Goulson1999JhaampKremen2013)Relativefloral resourceavailabilityofdifferentspecieschangesacrosstheseasonandfuturestudiesemployingthesemethodsatregularin‐tervals from early springwhen queens first emerge through lateautumnwould prove valuable In fact examination of queen beedensities would likely prove a better assessment of populationdensityandhabitatqualitythanworkerdensitywhenmonitoringorresearchingcolonialorganismssuchasbumblebeesestimatingthetruenumberofreproducingcoloniesisofmorevaluethanes‐timating the number of foragingworkers aswe have done hereConductingHDSduringthespringandearlysummerwhenqueensare theonly activebumblebee foragersmayprove auseful andnon‐lethalapproachtoestimating theabundanceof reproductiveindividualsandtheexpectednumbersummercoloniesforagivenarea However sampling queens would likely require additionalsamplingsitesorrepeatvisitbecausecountswouldbemuchlowerandHDSmodelsmayhavetroubleconvergingwithrelativelyfewsampling locations Caution should also be exercised with inter‐pretation ofBombus spp density estimates reported here as ourdensitieslikelyconsistofmultiplespeciesofBombus modelled and reportedasoneWealsorecommendfuturestudiesexplorehownon‐Bombusgenera(ormorphospeciesfunctionalgroups)performasthefocusofHDSmodelsAlthoughHDS isnotwithout limita‐tionwebelieveourstudyhighlightstheutilityofHDSmodelsforestimatingdensitiesandelucidatinghabitatassociationsofbumblebeeswhenindividualsaredetectedimperfectly
ACKNOWLEDG EMENTS
Wethank the following individuals andagencies for their supportandlandaccessSproulStateForestandMoshannonStateForestFunding was provided by the Indiana University of PennsylvaniaBUREfundandtheUnitedStatesDepartmentofAgricultureNaturalResources Conservation Service (68‐7482‐12‐502) through theConservationEffectsAssessmentProjectWeareverygrateful toJoanMilamandSamDroegefortheircommentsonearlyversions
234emsp |emsp emspensp McNEIL Et aL
of thismanuscriptWearealsoverygrateful to threeanonymousreviewers spend considerable time strengthening thismanuscriptFundersofourprojectdidnothaveanyinfluenceonthecontentofthesubmittedmanuscriptnordidtheyrequireapprovalofthefinalmanuscripttobepublishedAnyuseoftradefirmorproductnamesisfordescriptivepurposesonlyanddoesnotimplyendorsementbytheUSGovernment
AUTHORSrsquo CONTRIBUTIONS
DJMCRVOELMandJLLconceived researchDJMandELMcol‐lected field data DJM CRVO and ELM conducted statisticalanalysesDJMCRVOELMKRUMDEKADRand JLLwrote themanuscriptJLLsecuredfundingAllauthorsreadandapprovedthemanuscript
ORCID
Darin J McNeil httporcidorg0000‐0003‐4595‐8354
Clint R V Otto httporcidorg0000‐0002‐7582‐3525
Amanda D Rodewald httporcidorg0000‐0002‐6719‐6306
R E FE R E N C E S
Allen‐WardellGBernhardtPBitnerRBurquezABuchmannSCaneJhellipInouyeD(1998)Thepotentialconsequencesofpollina‐tordeclinesontheconservationofbiodiversityandstabilityoffoodcropyieldsConservation Biology128ndash17
AndersonDR(2007)Model based inference in the life sciences A primer on evidenceBerlinGermanySpringerScienceampBusinessMedia
Arnold T W (2010) Uninformative parameters and model selectionusingAkaikesInformationCriterionJournal of Wildlife Management741175ndash1178httpsdoiorg101111j1937‐28172010tb01236x
Ashman T L Knight TM Steets J A Amarasekare P BurdMCampbellDRhellipMorganMT (2004)Pollen limitationofplantreproductionEcologicalandevolutionarycausesandconsequencesEcology852408ndash2421httpsdoiorg10189003‐8024
BendelCRHovickTJLimbRFampHarmonJP(2018)Variationin grazing management practices supports diverse butterflycommunitiesacrossgrasslandworking landscapesJournal of Insect Conservation221ndash13httpsdoiorg101007s10841‐017‐0041‐9
BuchananALGibbsJKomondyLampSzendreiZ(2017)Beecom‐munityof commercial potato fields inMichigan andBombus impa‐tiensvisitationtoneonicotinoid‐treatedpotatoplantsInsects830httpsdoiorg103390insects8010030
BucklandSTAndersonDRBurnhamKPampLaake JL (2005)Distance samplingHobokenNJJohnWileyampSonsLtd
BurnhamKPampAndersonDR(2002)Model selection and multimodel inference A practical information‐theoretic approachBerlinGermanySpringerScienceampBusinessMedia
BurnhamKPAndersonDRampLaakeJL(1980)Estimationofden‐sity from line transect sampling of biological populationsWildlife Monographs723ndash202
Calderone N W (2012) Insect pollinated crops insect pollinatorsandUSagricultureTrendanalysisofaggregatedatafortheperiod1992ndash2009 PLoS ONE7 e37235 httpsdoiorg101371journalpone0037235
CameronSALozierJDStrangeJPKochJBCordesNSolterL F amp Griswold T L (2011) Patterns of widespread decline in
NorthAmericanbumblebeesProceedings of the National Academy of Sciences108662ndash667httpsdoiorg101073pnas1014743108
RCore Team (2018)R A language and environment for statistical com‐puting Vienna Austria R Foundation for Statistical ComputingRetrievedfromhttpswwwR‐projectorg
Environmental Systems Research Institute (2011) ArcGIS Desktop Release 10RedlandsCaliforniaESRI
Fiske IampChandlerRB (2011)UnmarkedAnRpackage for fittinghierarchicalmodelsofwildlifeoccurrenceandabundanceJournal of Statistical Software431ndash23
Garibaldi L A Steffan‐Dewenter I Winfree R Aizen M ABommarcoRCunninghamSAhellipBartomeusI(2013)Wildpolli‐natorsenhancefruitsetofcropsregardlessofhoneybeeabundanceScience3391608ndash1611httpsdoiorg101126science1230200
Goulson D (1999) Foraging strategies of insects for gathering nec‐tar and pollen and implications for plant ecology and evolutionPerspectives in Plant Ecology Evolution and Systematics2 185ndash209httpsdoiorg1010781433‐8319‐00070
GoulsonDLyeGCampDarvillB(2008)DeclineandconservationofbumblebeesAnnual Review of Entomology53191ndash208httpsdoiorg101146annurevento53103106093454
GoulsonDNicholls E Botiacuteas C amp Rotheray E L (2015) Bee de‐clines driven by combined stress from parasites pesticides andlack of flowers Science 347 1255957 httpsdoiorg101126science1255957
Hammond P S Berggren P Benke H Borchers D L Collet AHeide‐Joslashrgensen M P hellip Oslashien N (2002) Abundance of har‐bour porpoise and other cetaceans in the North Sea and adja‐cent waters Journal of Applied Ecology 39 361ndash376 httpsdoiorg101046j1365‐2664200200713x
HanleyMEAwbiAJampFrancoM(2014)GoingnativeFlowerusebybumblebeesinEnglishurbangardensAnnals of Botany113799ndash806httpsdoiorg101093aobmcu006
Hau E amp Von Renouard H (2006) The wind resource London UKElsevier
Hedley S L amp Buckland S T (2004) Spatial models for line tran‐sect sampling Journal of Agricultural Biological and Environmental Statistics9181ndash199httpsdoiorg1011981085711043578
JamesFCampShugartHHJr(1970)AquantitativemethodofhabitatdescriptionAudubon Field Notes24727ndash736
Jepsen S Evans E Thorp R Hatfield R amp Black S H (2003)Petition to list the rusty patched bumble bee Bombus affinis (Cresson) 1863 as an endangered species under the US Endangered Species Act Retrieved from httpwwwxercesorgwp‐ontentuploads 201301Bombus‐petitionpdf
Jha S amp Kremen C (2013) Resource diversity and landscape‐levelhomogeneitydrivenativebee foragingProceedings of the National Academy of Sciences 110 555ndash558 httpsdoiorg101073pnas1208682110
KaranthKUampSunquistME(1995)PreyselectionbytigerleopardanddholeintropicalforestsJournal of Animal Ecology64439ndash450httpsdoiorg1023075647
KeacuteryMampRoyleJA (2015)Applied Hierarchical Modeling in Ecology Analysis of distribution abundance and species richness in R and BUGS Volume 1 Prelude and Static ModelsCambridgeMAAcademicPress
KeacuteryM amp Schmidt B R (2008) Imperfect detection and its conse‐quencesformonitoringforconservationCommunity Ecology9207ndash216httpsdoiorg101556ComEc92008210
Kevan PG (1990)Pollination keystone process in sustainable globalproductivity InVIInternationalSymposiumonPollination288(pp103‐110)
Kremen CWilliams NM amp Thorp RW (2002) Crop pollinationfromnativebeesatriskfromagriculturalintensificationProceedings of the National Academy of Sciences99 16812ndash16816 httpsdoiorg101073pnas262413599
emspensp emsp | emsp235McNEIL Et aL
LofflandH L Polasik J S TingleyMW Elsey E A Loffland CLebuhnGampSiegelRB(2017)Bumblebeeuseofpost‐firechap‐arralinthecentralSierraNevadaThe Journal of Wildlife Management811084ndash1097httpsdoiorg101002jwmg21280
MackenzieD I (2006)Modelingtheprobabilityof resourceuseTheeffectofanddealingwithdetectingaspeciesimperfectlyJournal of Wildlife Management70367ndash374httpsdoiorg1021930022‐541X(2006)70[367MTPORU]20CO2
MacKenzieDINicholsJDLachmanGBDroegeSAndrewRoyleJampLangtimmCA(2002)Estimatingsiteoccupancyrateswhende‐tectionprobabilitiesarelessthanoneEcology832248ndash2255httpsdoiorg1018900012‐9658(2002)083[2248ESORWD]20CO2
MacKenzieDINicholsJDRoyleJAPollockKHBaileyLampHinesJE(2005)Occupancy estimation and modeling Inferring pat‐terns and dynamics of species occurrenceLondonUKElsevier
Mackenzie D I (2003) Assessing site occupancymodelling as a toolfor monitoring Mahoenui giant weta populations Department ofConservation17
Marques T A Thomas L Fancy S G amp Buckland S T (2007)Improvingestimatesofbirddensityusingmultiple‐covariatedistancesamplingThe Auk1241229ndash1243httpsdoiorg1016420004‐8038(2007)124[1229IEOBDU]20CO2
McCaskillGLMcWilliamsWHAlerichCAButlerBJCrockerS JDomkeGMhellipWestfall JA (2009)Pennsylvaniarsquos Forests 2009NewtownSquarePAUSDepartmentofAgricultureForestServiceNorthernResearchStation
MichenerCDMcGinleyRJampDanforthBN(1994)The Bee Genera of North and Central AmericaWashingtonDCSmithsonianInstitutePress
OlesenJMBascompteJElberlingHampJordanoP(2008)TemporaldynamicsinapollinationnetworkEcology891573ndash1582httpsdoiorg10189007‐04511
PerssonA S RundloumlfMCloughYampSmithHG (2015)Bumblebees show trait‐dependent vulnerability to landscape simplifica‐tion Biodiversity and Conservation 24 3469ndash3489 httpsdoiorg101007s10531‐015‐1008‐3
Potts SGVulliamyBDafniANeemanGampWillmer P (2003)Linking bees and flowers How do floral communities structurepollinator communities Ecology 84 2628ndash2642 httpsdoiorg10189002‐0136
PottsSGBiesmeijerJCKremenCNeumannPSchweigerOampKuninWE (2010)Globalpollinatordeclinestrends impactsanddriversTrends in ecology amp evolution25(6)345ndash353
Redhead JW Dreier S Bourke A F HeardM S JordanW CSumner S hellip Carvell C (2016) Effects of habitat compositionandlandscapestructureonworkerforagingdistancesoffivebum‐ble bee species Ecological Applications 26 726ndash739 httpsdoiorg10189015‐0546
Roulston T A H Smith S A amp Brewster A L (2007) A com‐parison of pan trap and intensive net sampling techniques fordocumenting a bee (Hymenoptera Apiformes) fauna Journal of the Kansas Entomological Society 80 179ndash181 httpsdoiorg1023170022‐8567(2007)80[179ACOPTA]20CO2
Royle J A Dawson D K amp Bates S (2004) Modeling abundanceeffects in distance sampling Ecology 85 1591ndash1597 httpsdoiorg10189003‐3127
Scheper J Bommarco R Holzschuh A Potts S G Riedinger VRoberts S P hellipWickens V J (2015) Local and landscape‐level
floral resources explain effects of wildflower strips on wild beesacrossfourEuropeancountriesJournal of Applied Ecology521165ndash1175httpsdoiorg1011111365‐266412479
SeberGA(1986)AreviewofestimatinganimalabundanceBiometrics42267ndash292httpsdoiorg1023072531049
ShultzCH(1999)The Geology of PennsylvaniaPennsylvaniaGeologicalSurveyHarrisburgPAPennsylvaniaGeologicalSurvey
Sillett T S Chandler R B Royle J A KeacuteryM ampMorrison S A(2012) Hierarchical distance‐sampling models to estimate popu‐lation size and habitat‐specific abundance of an island endemicEcological Applications22(7)1997ndash2006
SollmannRGardnerBWilliamsKAGilbertATampVeitRR(2016)AhierarchicaldistancesamplingmodeltoestimateabundanceandcovariateassociationsofspeciesandcommunitiesMethods in Ecology and Evolution7529ndash537httpsdoiorg1011112041‐210X12518
Tepedino V J Durham S Cameron S A amp Goodell K (2015)Documenting bee decline or squandering scarce resourcesConservation Biology 29 280ndash282 httpsdoiorg101111cobi12439
Thomas LBuckland S TBurnhamKPAndersonDR Laake JL Borchers D L amp Strindberg S (2002) Distance samplingEncyclopediaofenvironmetrics
Thomas L Buckland S T Rexstad EA Laake J L Strindberg SHedley S L hellipBurnham K P (2010)Distance softwareDesignand analysis of distance sampling surveys for estimating pop‐ulation size Journal of Applied Ecology 47 5ndash14 httpsdoiorg101111j1365‐2664200901737x
ThompsonWL (2002)TowardsreliablebirdsurveysAccountingforindividualspresentbutnotdetectedThe Auk11918ndash25httpsdoiorg1016420004‐8038(2002)119[0018TRBSAF]20CO2
VanStrienA JTermaatTGroenendijkDMensingVampKeryM(2010) Site‐occupancy models may offer new opportunities fordragonflymonitoringbasedondailyspecies listsBasic and Applied Ecology11495ndash503httpsdoiorg101016jbaae201005003
VilsackTampMcCarthyG(2015)National strategy to promote the health of honey bees and other pollinatorsWashingtonDCReport IssuedbytheWhiteHousethePollinatorHealthTaskForce
WardKCariveauDMayERoswellMVaughanMWilliamsNhellip Gill K (2014) Streamlined Bee Monitoring Protocol for Assessing Pollinator HabitatPortlandORTheXercesSocietyforInvertebrateConservation
WeatherUndergroundInc(2018)WeatherForecastandReports‐LongRangeandLocalWundergroundRetrievedfromhttpswwwwun‐dergroundcom
WherryET Fogg JM JrampWahlHA (1979)Atlas of the flora of Pennsylvania Philadelphia PA The Morris Arboretum of theUniversityofPennsylvania
YoccozNGNichols JDampBoulinierT (2001)Monitoringofbio‐logicaldiversityinspaceandtimeTrends Ecology and Evolution16446ndash453
How to cite this articleMcNeilDJOttoCRVMoserELetalDistancemodelsasatoolformodellingdetectionprobabilityanddensityofnativebumblebeesJ Appl Entomol 2019143225ndash235 httpsdoiorg101111jen12583
emspensp emsp | emsp227McNEIL Et aL
deciduous‐ormixedforest (80ndash100yearspost‐harvestMcCaskilletal2009)withoak(Quercus spp)hickory(Caryaspp)andeast‐ern hemlock (Tsuga canadensis) among the most common species(WherryFoggampWahl1979)Weconcentratedoureffortswithindeciduous forests of Sproul andMoshannon State Forestswhereoak silviculture aims to restore young forest age classes throughtimber harvest and regeneration Because silvicultural practiceswithinthesetwoStateForestsaimtorestorehabitatforforestwild‐lifewefocusedoursurveyeffortswithinregeneratingoakstands0ndash9yearspost‐managementDuringsurveysavarietyoffloweringplantswereavailabletoBombussppincludinglow‐growingshrubslike hillside blueberry (Vaccinium pallidum) as well as herbaceousforbs like eastern teaberry (Gaultheria procumbens) and commoncow‐wheat(Mellampyrum linerare)MosttallwoodyplantswerenotfloweringexceptforDevilrsquoswalkingstick (Aralia spinosa)whichwedetectedonlywithinafewofoursites
22emsp|emspSite selection and survey placement
We randomly selected 47 timber stands within Sproul andMoshannon State Forests that had been recently treated withoverstory removal (basal area 23ndash92 m2ha) We attemptedto maximize the distance between sites such that our averagedistance‐to‐nearest‐site was 1110m (SE 107m range 464ndash4516m)Thisreducedthelikelihoodofindividualsbeingdetectedatmultiplesites(Redheadetal2016)Timberharvestunitsaver‐aged2314ha(SD1862harange254ndash10392ha)insizeAsin‐glesurveypointwaslocatedwithineachharvestusingarandompoint generator tool inArcGIS102 (ESRI 2011)Weattemptedtominimizeedgeeffectsbyensuringpointswererelativelycon‐sistent in their placementwith respect to timberharvest edgessamplingwas restricted to areas at least80m from theedgeoftimberharvestsandourfinalsampleofsiteswasameandistanceof11867m(SE624m)
23emsp|emspTransect surveys
Ateachpointwe sampledBombus sppusing three survey types(a) distance transects (b) transect counts and (c) aerial nettingcounts Both distance transects and fixed‐width transect countsoccurred simultaneously along 66m transects oriented north‐to‐south and centred at eachpoint locationAlong each transectobserverswalked forwardat a constant rate (~1mmin) such thattheobserverarrivedatthetransectendafter30minPriortosur‐veyseachobserver(n=2)wastrainedindistanceestimationusingdummytransectsalongwhichbeesrsquodistanceswerephysicallymeas‐uredaftereachattemptedestimateusingameasuring tapeOnceallobserverswereconsistentlyestimatingdistanceswithinplusmn025mfield surveyswere conductedwith a2m longmeasuring stick forconstantreferenceWhilewalkingalongeachsurveytransect theobserverrecordedBombussppdetectionssuchthatafinalcount()wasgeneratedforeachsurveycoupledwiththedistances(plusmn025m)betweeneachBombus sppandthetransectWedidnotattempttoidentify speciesor sex forBombus spp detected in situ thereforecountswerelikelymultiplespeciesandsexesSurveydataforeachpointincludedaBombussppcountandtheircorrespondingdetec‐tion distancesWe discerned betweenBombus spp andXylocopa virginica byabdomenpubescence(MichenerMcGinleyampDanforth1994)DistanceswererecordedastheperpendiculardistancefromthetransecttoeachbeeandnotedasthedistanceatwhichthebeewasfirstdetectedWhilewalkingalongeachtransectobserversat‐temptedtokeeptrackofpreviouslydetectedBombusspptoavoiddouble‐counting individualsthatmightbemovingamongfloralre‐sources near the transectWe anecdotally observed this methodlargely avoided double‐counting as Bombus spp are generallylarge‐bodiedconspicuousinsectsandeasilyaudibleinflightAllrawcountsanddetectiondistancesconstitutedourldquodistancetransectrdquodata(a)andrawcountswithin2mofthetransectconstitutedourldquotransectcountrdquodata(b)
F I G U R E 1 emspSurveylocationswithinthePennsylvaniaWildswhereweconductedsurveysforBombussppwithinregeneratingtimberharvests
228emsp |emsp emspensp McNEIL Et aL
We followed standard bee survey methods to avoid commoncausesofdetection failure (Wardetal2014)Surveyswerecon‐ductedonlyinbrightlightconditionslowwindwarmdays(ge16degC)andonlyduringlatemorningandafternoon(1000ndash1700)ThoughweattemptedtousestudydesigntoreducethepotentialimpactsofthesefactorsonBombus sppdetectabilitywealso includedthemindetectionmodellingAtthetimeofeachsurveywerecorded(a)surveyorID(b)cloudcover(c)timeofdayand(d)BeaufortWindIndex Local temperature data were downloaded from WeatherUnderground from the KUNV weather station in State CollegePennsylvania (WeatherUnderground Inc2018)Cloudcoverwasestimatedinthefieldtothenearest25(0ndash100)BeaufortWindIndexwasmeasuredonanincrementalscalefrom0to5with0rep‐resentingnowind at all (ie smokewould theoretically risewith‐outdrift)and5representinghighwindssuchthatentiretreesswayinthewind(HauampVonRenouard2006)Weavoidedsurveyinginwindindicesgt3andthusconsideredtwocategoriesofwind0ndash1ldquolowrdquo2ndash3ldquomoderaterdquoinouranalysesAllsurveystookplacefrom10to25July2017
24emsp|emspNet counts
TomeasureBombussppabundancewithinfixed‐radiusnetcountswe created 15m radius count surveys centred around each pointlocation (thecentreofeachdistancetransect)Nettedbeecountstookplaceimmediatelyupontheconclusionoftransectsurveys(de‐scribedabove)Withineachfixed‐radiusplotasingleobserverspent30minseeking‐andattemptingtocaptureallBombussppdetectedwithahandnetWechosefixed‐radiusnetsamplingbecauseitisastandardsamplingtechniquefornativebees (Perssonetal2015PottsVulliamyDafniNersquoemanampWillmer2003RoulstonSmithampBrewster2007)andwouldthereforeserveasabasisforcomparisontoourabundanceestimatesgeneratedfromHDSForeachBombus sppdetectedtheobserverattemptedtocaptureeachbeeusingahandnet(collapsible15rdquodiameternet17rdquohandleBioquipProduct7115CP)andoncecapturedallbeeswereheldcaptiveforthere‐mainderofthesurveyForeachcapturedbeethetimerwasstoppedwhiletheobserverplaced it intoaplasticzipperbagandresumedimmediately thereafter Thismethod prevented us from recaptur‐inganddouble‐countingbeeswithinthesameplotAfter30minofsurvey timehadelapsedeachBombus sppwas removed from itsbagwith forceps photographed for anotherproject and releasedunharmedInthefewoccasionswhereBombussppwereobservedbutevadedcapturetheyweretreatedasallotherBombussppcap‐turedforthepurposesofthisstudy(ieincluded)
25emsp|emspHabitat surveys
Wesurveyedregeneratingvegetationstructurewithin timberhar‐vestunitsfrom15Juneto15July2017VegetationsurveyssharedtheircentroidwithBombussppsurveysVegetationdataquantifiedhabitatstructureofwoodystemsandherbaceousunderstoryratherthan plant composition All vegetation data were collected along
three50mradialtransectseachorientedat0deg120degand240degfrompoint centreAlong each transectwe recordedplant strata at 10ldquostopsrdquo(10mapartn=30netcountlocation)Vegetationstratare‐cordedateachstopconsistedofthepresenceabsenceofsaplingshrub forbandgrasssedgeSaplingswereyoungtreeslt10cm (indiameterbreastheight)Thissamplingregimegaveusadequateres‐olutiontoassessvegetationstructure(15stopssite)whileremain‐ingof comparable scale toourbee sampling transects (33m)Wefoundvegetationstructuretobehighlycorrelatedacrossscalesaslargeas100mandthereforebelieveour50mvegetationplotsrep‐resentedsiteconditionsreasonablywellShrubswerewoodyplantswithmultipleprimarystems(incontrasttosingle‐stemmedsaplings)Forbswerebroad‐leafeddicotyledonousplants(egSolidagospp)The plant category ldquograssrdquo included any monocotyledonous plant(grassessedgesetc)Werecordedplantstratawithanoculartubesuchthatonlystratathat intersectedwithcrosshairs intheoculartube were considered present (James amp Shugart 1970) While asinglestopcouldincludemultiplestratatypeseachstratumcouldonlyberepresentedonceperstopandthuseachsitecouldhaveamaximumofn=15occurrencesforeachstratumWeanalyzedplantstrata values as percentages Prior to all analyses we calculatedSpearmanrsquosrho(ρ)forallpairsofcovariatestobemodelledBecausenonewerestronglycorrelated(Spearmanrsquosρ lt 060)nocovariateswereredundantandallweresuitableformodelling
26emsp|emspHierarchical distance models
Weanalyzeddistancetransectdata(beecountsanddistances)usingHDS models implemented in the R package ldquounmarkedrdquo (Fiske ampChandler2011RCoreampTeam2018)Thepackageunmarkedfitslinearmodelsinamaximumlikelihoodframeworkandcanbecom‐bined with an Information‐Theoretic approach (Anderson 2007)forthepurposeofmodelselection(egusingAkaikersquosInformationCriterionAICBurnhamampAnderson2002)Hierarchicaldistancemodels allowed us to create and rank candidate models each ofwhich contained independent model components for detectionprobability (p) and expected animal abundance (density λ) HDSmodelsassume(a)subjectsareaccuratelyidentified(egnofalse‐presences)(b)thatallsubjectsonthetransect(distance=0m)aredetectedperfectly(p=10)(c)subjectsaredetectedattheiroriginallocation(iemovement isnot influencedbytheobserver) (d)dis‐tancesareaccuratelymeasuredand(e)detectionofeachindividualis independentofthedetectionofallotherindividuals(Thomasetal2010)Bumblebeesappeartoconstitutegoodcandidatesfordis‐tancesamplingastheycanbeeasilyidentified(togenus)inthefield(Micheneretal1994)areeasilyapproachedbyobservers(Wardetal2014)andremainrelativelystillduringpollinationsuchthataccu‐ratedistanceestimationscouldbemadeforeachworkerAlthoughdistances were measured in the field directly we binned detec‐tions as recommended by Buckland et al (2005) 0ndash1 1ndash2 2ndash33ndash4and4ndash5mMoreovertopreparedistance‐basedtransectdatawe truncated the outer 10of our data such that analyseswereconductedusingonly the closest 90ofBombus spp detections
emspensp emsp | emsp229McNEIL Et aL
asrecommendedfordistanceanalysesbyBucklandetal(2005)Bytruncating thedata in thiswayalldetectionswerelt5mfromtheobserver
Distance models provide robust estimates of abundance byadjusting animal counts by the probability of detection for givendistances (Buckland et al 2005) This is accomplished by fittingdetectiondistancedata to a ldquodetection functionrdquo that describes adecayindetectionprobabilityassubjectsarefurtherfromtheob‐server (Bucklandetal2005KeacuteryampRoyle2015)Toevaluateanappropriatedetectionfunctionweevaluatedmodelseachfitusingoneofthefollowingdetectionfunctions(a)exponential(b)hazardrateor(c)half‐normal(Bucklandetal2005)ThiswasdonepriortoallcovariatemodellingEachdetectionfunctionisusedtoestimatetheaverageprobabilityofdetectionwhichisthenusedtoadjustrawcountssuchthatdensitypredictionscanbemade(Bucklandetal2005)OncethemostappropriatedetectionfunctionwasselectedbasedonAICcrankitwasusedtomodeldetectionprobabilityanddensityinconsecutivemodelsWemodelleddetectionprobabilityintwotiersdetectiontier1(surveycovariatesondetection)andde‐tectiontier2(habitatcovariatesondetection)Becauseoursamplesizewasmodestweusedonlysingle‐covariatedetectionmodelstoavoidoverfittingHDSmodelsDetectiontier1includedunivariatemodels for (a) timeof day (b) surveyor (c) temperature (d) cloudcover(e)windindexand(f)anull(intercept‐only)modelDetectiontier 2 (fit independently of detection tier 1) included univariatemodelsfor(a)saplingcover(b)shrubcover(c)forbcover(d)grasscoverand(e)anullmodelWithinbothmodeltiersweusedaglobalhabitatmodel(iesapling+shrub+forb+grass)fordensitytoen‐sure thatvariation indensitywas reasonablywell explainedwhileassessingdetectionprobabilityWeconsideredcovariatestobein‐formativeiftheywerebothgt20AICclessthanthenullmodelandhadβcoefficient95confidenceintervalsthatdidnotincludezeroUsing the informative covariates fromdetection tiers1and2weconstructedasetofdensitymodels(habitatcovariatesondensity)thataccountedfor imperfectdetection (a)saplingcover (b)shrubcover (c) forbcover (d)grasscoverand (e)anullmodelThenullmodelcontainedonlyintercepttermsandtheinformativeparame‐tersfordetectionPriortomodellingallcontinuouscovariateswerestandardizedusingthescalefunctioninbaseRModelrankingwasdoneusing the ldquoaictabrdquo functionof thepackage ldquoAICcmodavgrdquoAllmodelswerefitassumingaPoissondistributioninldquogdistsamprdquoandmodelfitwasassessedbycalculatingavarianceinflationfactor(chatchatchatc)usingtheunmarkedfunctionldquofitstatsrdquo (KeacuteryampRoyle2015)Weconsideredallmodelslt20AICctobecompetingandequallysupportedbythedata(BurnhamampAnderson2002)
27emsp|emspPoisson generalized linear models
WeusedaPoissongeneralized linearmodels inR (using the ldquoglmrdquofunction)tomodelBombus sppabundancealongfixed‐radiustran‐sectsandnetcountsThisallowedustocomparehabitat‐abundancerelationshipsgeneratedfromHDSmodelstothosegeneratedfrommethodsthatdonotaccountfordetectionprobabilityAswithour
HDSmodels Poisson regressionmodels allowed us tomodel beecountsasafunctionofhabitatcovariates(a)saplingcover(b)shrubcover (c) forbcover (d)grasscover and (e) anull (intercept‐only)modelWemodelled our fixed‐radius transect counts by truncat‐ing allHDS‐transect databy2mof the transect line and treatingthedataasarawcount(HanleyAwbiampFranco2014Scheperetal 2015) which is a standard technique when conducting visualencounter surveys Net count data were modelled in a compara‐blemanner such that raw countsweremodelled as a function ofhabitat covariatesWedid not account for imperfect detection ineither of these models but rather modelled Bombus spp countarea interpretedasadensityWeagainusedan information‐theo‐reticapproach(Anderson2007)withmodelrankingbasedonAICc consideringmodelslt20AICctobeequallysupportedbythedata(BurnhamampAnderson2002)Wealsousedsingle‐covariatemodelstoavoidoverlycomplexmodelsandtheinclusionofuninformativeparameterswithintopmodels(Arnold2010)
3emsp |emspRESULTS
Wedetected194individualBombus sppwithin5mofwhich136werewithin2mof the transect lineDuringaerialnetcountswecapturedn = 201 BombussppworkersOfthebeescapturedduringaerial net countsover50wereB impatienswith the remainderbeingamixedcommunityoflesscommonspecieslikeB bimaculatus and B vagans
31emsp|emspDetection probability
Ofthreedetectionfunctionmodelsweranthebest‐rankedmodelincludedanexponentialdetectionfunctionwheredetectionprob‐abilitygt5mfromthetransectwasasymp0(Figure2)Usinganexponen‐tialdetection functionwe foundthatdetectionprobabilityvariedas a functionof time since1000 (theearliestpossible start time)
F I G U R E 2 emspFrequencyofdetections(greybarsrightaxis)forBombussppwithinregeneratingtimberharvestsDetectionprobability(leftaxis)declinedasafunctionofdistancefromtransectandwasfittoanexponentialdetectionfunction(blackline)Bombussppwereonlyrarelydetectedfurtherthan5mfromthetransectline
230emsp |emsp emspensp McNEIL Et aL
andobserverIDsuggestingthatthelatestsurveysofeachdayhadthe lowestdetectionprobability and thatobserverswereunequalin their ability to detectBombus spp (Table 1 Figure 3a) Amongmodels investigating the relationship between habitat covariatesand Bombus spp detection the model that included grass cover()wastheonlysupportedmodelandsuggestedthatBombussppweremorereadilydetectedatsiteswithmoregrasscover(Table1Figure3b)Allothercovariatesmodelledintiers1and2weregt20AICc less than the nullmodel and theβ 95 confidence intervalsoverlappedzero
32emsp|emspHabitat modelling
Models from all three analyses yielded discernable habitat asso‐ciationswithBombus sppabundance (Table2Figure4)All threeanalyses indicated thatBombus spp abundanceduring the surveyperiodwas negatively associatedwith per cent sapling cover andnotassociatedwithforbcover (Table2Figure4)The importanceofshrubcoverandgrasscoveraspredictorsofBombussppcountsandestimatedabundancevariedacrossmethods(Table2)HDSandtransectcountsrevealedsupportforshrubcoverasaninformativecovariatebeinggt20AICc less than thenull andhavingparameter
95confidence intervals thatdidnotoverlapzero (Table2)Onlynet counts suggested that grass cover was positively associatedwithBombus sppabundancewhileHDSsuggestedthatgrasscoverwasinsteadcorrelatedpositivelywithdetectionprobabilitybutnotabundance (Table 2 Figure 4) In contrast our net count analysissuggestednoeffectofshrubcoveronbeecountswiththeldquoshrubrdquomodel ranked lower than thenullmodeland the shrubparameter95confidenceintervalsoverlappingzero(Table2)Ourtop‐rankedHDSmodel(ldquosaplingrdquo)showedevidenceofminoroverdispersion(chatchatchatc=133)whilemostothermodelsdidnotappearoverdispersed (chatchatchatclt10 with a mean chatchatchatc=101acrossmodels inourfinalHDSmodelset)Weconsidered this an acceptable level of overdispersion and did notuse a variance inflation factor to adjust our parameter estimates(BurnhamampAnderson2002)
33emsp|emspDensity estimation
Inadditiontoexaminingabundanceasafunctionofhabitatamongthe three methods we compared their estimated mean densitiesof foragingBombus spp basedon intercept‐only abundancemod‐els(includingdetectioncovariatesforHDS)EstimatedBombusspp
Model name K AICc ΔAICc AICc Wt β estimate (95CI)
Surveycovariatesondetectionprobability
p(observer) 7 34893 000 078 058(021to095)
p(time) 7 35156 264 021 minus023(minus038tominus008)
p () 6 35829 936 001 ‐
p(wind) 7 35987 1094 000 minus016(minus044to013)
p(temp) 7 36064 1172 000 minus005(minus019to009)
Sitecovariatesondetectionprobability
p(grass) 7 35267 000 085 035(007to063)
p(forb) 7 35827 561 005 017(minus004to037)
p() 6 35829 562 005 ‐
p(shrub) 7 35965 699 003 minus013(minus035to009)
p (sapling) 7 36048 782 002 010(minus016to036)
NoteModelsareranked indescendingorderofAkaikersquos InformationCriterionadjustedforsmallsamplesize(AICc)Surveycovariatesincludedtimesincesurveystarttime(continuousldquotimerdquo)tem‐perature(continuous)cloudcover(overcastcontinuous)observer(categorical)andwindindex(categorical)Sitecovariatesincludedpercentcoverasmeasuredby50mradiusvegetationsurveysforvegetationstructuresaplingsshrubs forbsandgrassBothcandidatemodelsetsarerankedagainstanullintercept‐onlymodelBelowwereportnumberofmodelparameters(k)ΔAICcAICc weight(AICcWt)andβparameterestimates(95confidenceinterval)
TA B L E 1 emspHierarchicaldistancemodelsofdetectionprobabilityasafunctionofsurveycovariates(Tier1top)andsitecovariates(Tier2bottom)
F I G U R E 3 emspModelsofBombussppdetectionprobabilityasafunctionofsurveytime(left)percentgrasscover(centre)andobserver(right)whilealsobeingmostdetectableclosesttothetransect(all)
emspensp emsp | emsp231McNEIL Et aL
forager density within timber harvests was highest for the HDSmodels(192foragingworkersha95CI153ndash240)andlowestfornetcounts(21foragingworkersha95CI19ndash23Figure5)an89differencebetween the twomethodsTransect countsyielded in‐termediate estimates of density (40 foragingworkersha 95CI34ndash47)andwere80lowerthandensityestimatesfromHDSSite‐specific HDS modelled densities and netting count raw densitieswerecorrelated (Pearsonrsquos r = 031 p=003) though the relation‐shipwasnot11(Figure5)
4emsp |emspDISCUSSION
Ourstudyprovidesthefirstempiricalevidencethatdetectionprob‐abilitiesofBombus sppvaryinwaysthatcanaffectabundanceesti‐matesandinferencesabouthabitatrelationshipsObservationerrorcaused by imperfect detection is one of the central challenges ofecologicalmonitoringprograms(Thompson2002YoccozNicholsampBoulinier 2001)buthas yet tobewidely applied tomonitoringofmany invertebrates includingpollinators (but seeBendeletal2018Lofflandetal2017Mackenzie2003VanStrienTermaatGroenendijkMensingampKery 2010)Methods like distance sam‐plingwhileofferingapotential solution to this challenge are stillunder‐utilized in entomological research Meanwhile distance
samplingandsimilarmethodshavebeenastapleofvertebratewild‐liferesearchfordecades(Bucklandetal2005BurnhamAndersonampLaake1980Seber1986Thomasetal2002)andhavebeenex‐pandedtoestimatepopulationsizehabitat‐specificabundanceforindividualspeciesandcommunities(SillettChandlerRoyleKeacuteryampMorrison2012SollmannGardnerWilliamsGilbertampVeit2016)Althoughourstudyisnotthefirstestimateandaccountfordetec‐tionprobabilityofbumblebees(Lofflandetal2017)nostudybe‐foreourshasdescribedfactorsassociatedwithdetectionprobabilityanddonesoinaHDSframework
Wefoundthatdistancesamplingtransectswerebothasimpleandeffectivesurveymethodforestimatingdensityandhabitatre‐lationships (Buckland et al 2005) Hierarchical distance samplingmodelsareoneofthefewavailablemethodsthatallowresearcherstomodel detection‐adjusted abundancewithonly a single visit toeachsite(Bucklandetal2005KeacuteryampRoyle2015MacKenzieetal 2005)Themethodusesonlynon‐lethal samplingunlike trap‐pingnettingmethods(Tepedinoetal2015)whichisespeciallyde‐sirablewhen sampling for speciesof conservation concern or forcommonspecies in areaswherecapture‐based sampling isnot al‐lowedAdditionallyHDSmodelsarealsousefulbecausetheoutputisaneasily interpretedlatentstatedensitywithunits inldquoanimalsareardquo In our study HDS models generated estimates of foragingBombus sppworkerdensity
Model name K AICc ΔAICc AICc Wt β estimate (95CI)
Hierarchicaldistancesampling
λ(sapling) 6 33769 000 098 minus030(minus045tominus014)
λ(shrub) 6 34583 813 002 021(005to037)
λ() 5 3502 1251 000 ndash
λ(grass) 6 35041 1271 000 minus017(minus038to005)
λ(forb) 6 35282 1513 000 minus001(minus016to014)
Transectcounts
λ(sapling) 2 27763 000 096 minus144(minus220tominus069)
λ(shrub) 2 28448 685 003 085(025to144)
λ(grass) 2 2898 1217 000 minus093(minus214to028)
λ() 1 29007 1244 000 ‐
λ(forb) 2 29216 1454 000 0133(minus074to101)
Netcounts
λ(sapling) 2 36071 000 100 minus163(minus226tominus101)
λ(grass) 2 38438 2367 000 085(003to167)
λ(shrub) 2 38565 2494 000 041(minus009to090)
λ() 1 38608 2537 000 ndash
λ(forb) 2 38709 2638 000 039(minus031to109)
NoteModelsareranked indescendingorderofAkaikersquos InformationCriterionadjustedforsmallsamplesize(AICc)DistancetransectdataincludedBombussppdetectedfrom0to5malong66mtransectsTransectcounts includedBombus sppdetected from0ndash2malong66m transectsnetcountdatawerecountsofBombus sppwithin15mradiusplotsSitecovariatesincludedpercentcover asmeasured by 50m radius vegetation surveys for vegetation structure saplings shrubsforbsandgrassBelowwereportnumberofmodelparameters(k)AICcΔAICcAICc weight(AICc Wt)andeachcovariateβparameterestimateandβparameterestimates(95confidenceinterval)
TA B L E 2 emspHabitatmodelsderivedfromhierarchicaldistancemodels(top)fixed‐widthtransectmodels(centre)andlinearmodelsofnetcountdata(bottom)allfitusingaPoissondistribution
232emsp |emsp emspensp McNEIL Et aL
DespitebeingamongthelargestandmostconspicuousofNorthAmerican bees (Michener et al 1994) we found that detectionprobability of Bombus spp was imperfect and declined markedlywithdistancefromthesurveytransectwithalmostnodetectionsbeyond5mDetectionprobabilitiesinourstudywereinfluencedbysurvey‐specific(egtimeofday)andsite‐specific(eggrasscover)variableswithdetectionprobabilityhighestinthemorninginmid‐summerandinhabitatswithabundantgrasscoverWithinregener‐atingtimberharvestsinourstudyarealdquograssrdquocoverwastypicallylow‐growing monocotyledons like Carex pennsylvanica Abundantlow‐growing sedge allowed observers to view Bombus spp fromgreaterdistancesthanwhensitesweredominatedbytallsaplingsshrubs or forbs (egSolidago) Consequently studieswithin habi‐tatsdominatedbylowgrassorothershortvegetationmightfindde‐tectionprobabilityforBombusspptobereliableatdistancesgt5mAlthoughweareuncertainastowhyBombussppwerelessdetect‐ableduringsurveysconductedlaterintheafternoononeplausibleexplanationisthatlongershadowscastbylateafternoonlightmade
Bombussppmoredifficulttodetectwhenforagingin lowvegeta‐tionAdditionalworkexploringthedriversassociatedwithBombus sppdetectionwouldprovevaluabletomonitoringregimesaimedatsurveyingbumblebees
ThoughourstudyisnotacomprehensivehabitatassessmentforBombussppwithinregeneratingtimberharvestsofeasternforestsourresultsprovideaglimpseintothehabitatdynamicsofbumble‐beesinregeneratingforestsduringmid‐summerOurfindingsthatBombus sppwerepositivelyassociatedwithshrubsandnegativelyassociatedwithsaplingscanbeexplainedprimarilybyflowerphe‐nology during our survey window Regenerating saplings withinthe timber harvests we monitored were largely oaks hickoriesblackcherry (Prunus serotina)andredmaple (Acer rubrumWherryetal1979)Thesespeciesdonot flowerassmallsaplingsanddosoinearlyspringasmaturetrees(ieoutsidethesamplingperiodWherryetal1979)Incontrastseveralspeciesofshrubwereflow‐eringduringsamplingincludingblackhuckleberry(Gaylussacia bac‐cata)andhillsideblueberryIncontrastmostforbs(eggoldenrod
F I G U R E 4 emspModelledhabitatassociationsbetweenBombussppandstructuralvegetationfeatureswithinregeneratingtimberharvestsaspredictedbyhierarchicaldistancemodels(top)fixed‐width(4m)transectcounts(centre)andnetcounts(bottom)Variablesshownaresaplingcover(left)shrubcover(centre)andgrasscover(right)Solidlinesrepresentmodelpredictionswithdashedlinesas95confidenceintervalsRelationshipsmarkedwithanasteriskwerethosewithmodelsupport(iemoreinformativethananullmodelandβ95CInon‐overlappingzero)
F I G U R E 5 emspLeftBombusspppredictedmeandensityformodelsofnetcounts(ldquoncrdquo)transectcounts(ldquotcrdquo)andhierarchicaldistancesamplingmodels(ldquohdsrdquo)RightPredicteddensity(workersha)generatedfromourtop‐rankedhierarchicaldistancemodel(p [observer+time+grass]λ[sapling])regressedagainstcountdatafromBombus sppnetcounts
emspensp emsp | emsp233McNEIL Et aL
SolidagosppsnakerootAgeratina spp)hadnotbegunfloweringyetFutureworkshouldexplorehowBombussppmaytrackresourcesacrossagrowingseasontopersistwithineasternforestecosystems
Monitoringprograms forBombus spp andothernativepolli‐natorscanbeimprovedbyincorporatingstudydesignandmodel‐based approaches for minimizing detection error Although weincludedseveraldesign‐basedsolutionsforminimizingdetectionerror(egrestrictingsurveytimesonlysurveyinginfairweatherWard et al 2014) detection probability remained imperfectand varied due to time of day observer and vegetation coverConsequentlymethodsthatignoreddetectionprobabilitygener‐ated density estimates 80ndash89 lower than HDS Past studieshaveshowntheimportanceofusingdesign‐basedapproachestominimize false negativeswhen sampling bees (BuchananGibbsKomondyampSzendrei2017)Ourstudydemonstratesthevalueofusingbothdesign‐andmodel‐basedapproachesforreducingsam‐plingerrorscausedbyimperfectdetectionOtherstudysystemswith thick vegetation cover such as prairies and forested wet‐landsorobstructiveobjectssuchasurbanenvironmentsarealsolikely to underestimate bee abundance even if multiple design‐basedapproachesareusedWhiletraditionalsamplingtechniquesthat do not account for detection have numerous applicationsourstudyhighlightstheimportanceofincorporatingmodel‐basedapproachesforaccountingfordetectionprobabilitywithinnativebeesurveysparticularlywhenattemptingtoestimatebeeabun‐danceordensity
Althoughour results suggest thatHDS representsapromisingtoolformonitoringbumblebeesresearcherswishingtoemploythemethod should recognize its associated limitations For exampledistancemodelsassumethatallanimalsonthetransectlinearede‐tectedperfectlyAlthoughitislikelythisassumptionwasmetwithalargeinsectlikeBombussppthisassumptionmightbeviolatedwithsmallerinsectsMoreoversubjectsareassumedtobeuniformlydis‐tributedinamannerunaffectedbytheobserverWhileitispossiblethatBombussppwerefrightenedbyobserverswetookcaretonotethe locationof first detection forBombus spp apparently flushedandtheirloudflightmadeclosedetectionsalmostcertainWenotethat thismethodwouldnotworkwell for species‐level identifica‐tionbecauseobservationsaremadefromadistanceandsomebeegeneraareexceedinglydifficulttoidentifyevenwithamicroscope(Michener et al 1994)Misidentification of specieswould consti‐tuteafalsepositivewhichwouldviolateanassumptionofdistancesampling
Anotherconsiderationofthisstudydesignandmanymethodsofabundanceestimationisthatanimalsmayviolatetheclosureas‐sumptionInthecaseofBombussppthislikelyoccurredasforagersflew in‐ and out‐ of the effective survey area (~5m from the ob‐serverforHDS)WhilethismayconstituteaproblemforsomestudyobjectivesandmethodswehavenoreasontobelievethatBombus sppmovementwasnonrandomwithrespecttotheobserverandanaccuratedensitycouldthereforestillbemadewhenpassivecountingwasusedClosureviolationmaybeamoreimportantproblemwhenattempting tocalculatedensity fromanettingplotwhereanimals
mayentertheplotandbeunabletoleaveastheyarecapturedandhelduntil thesurveyhasfinished Insuchcasesmovementwouldbebiasedbyindividualsimmigratingintothemonitoredplotbutun‐abletoemigrateandmovementwouldbebiasedtowardstheplotAlthough net‐based sampling is often preferable for investigatingspecies‐specific habitat relationships the potential for movementbias highlights the need for cautious interpretation of net‐baseddensityestimatesforbeesSimilarlyresearchersshouldconsiderthepotentialfordouble‐countingsubjectsAlthoughBombussppinourstudywereapparentlyfewenoughandslowenoughtoavoidmostdouble‐countingthismaybeamoreimportantproblemtoconsiderformoreabundantinsectswithreduceddetectability(egHalictids)
Wealsoadvisecautionwith interpretationofhabitatrelation‐shipsreportedhereasourstudyshouldbe interpretedasasmallldquosnapshotrdquo in time and lacking species‐specific habitat relation‐ships(OlesenBascompteElberlingampJordano2008)Full‐seasonhabitat associations are temporally dynamic forBombus spp andvaryacrossspecies(Goulson1999JhaampKremen2013)Relativefloral resourceavailabilityofdifferentspecieschangesacrosstheseasonandfuturestudiesemployingthesemethodsatregularin‐tervals from early springwhen queens first emerge through lateautumnwould prove valuable In fact examination of queen beedensities would likely prove a better assessment of populationdensityandhabitatqualitythanworkerdensitywhenmonitoringorresearchingcolonialorganismssuchasbumblebeesestimatingthetruenumberofreproducingcoloniesisofmorevaluethanes‐timating the number of foragingworkers aswe have done hereConductingHDSduringthespringandearlysummerwhenqueensare theonly activebumblebee foragersmayprove auseful andnon‐lethalapproachtoestimating theabundanceof reproductiveindividualsandtheexpectednumbersummercoloniesforagivenarea However sampling queens would likely require additionalsamplingsitesorrepeatvisitbecausecountswouldbemuchlowerandHDSmodelsmayhavetroubleconvergingwithrelativelyfewsampling locations Caution should also be exercised with inter‐pretation ofBombus spp density estimates reported here as ourdensitieslikelyconsistofmultiplespeciesofBombus modelled and reportedasoneWealsorecommendfuturestudiesexplorehownon‐Bombusgenera(ormorphospeciesfunctionalgroups)performasthefocusofHDSmodelsAlthoughHDS isnotwithout limita‐tionwebelieveourstudyhighlightstheutilityofHDSmodelsforestimatingdensitiesandelucidatinghabitatassociationsofbumblebeeswhenindividualsaredetectedimperfectly
ACKNOWLEDG EMENTS
Wethank the following individuals andagencies for their supportandlandaccessSproulStateForestandMoshannonStateForestFunding was provided by the Indiana University of PennsylvaniaBUREfundandtheUnitedStatesDepartmentofAgricultureNaturalResources Conservation Service (68‐7482‐12‐502) through theConservationEffectsAssessmentProjectWeareverygrateful toJoanMilamandSamDroegefortheircommentsonearlyversions
234emsp |emsp emspensp McNEIL Et aL
of thismanuscriptWearealsoverygrateful to threeanonymousreviewers spend considerable time strengthening thismanuscriptFundersofourprojectdidnothaveanyinfluenceonthecontentofthesubmittedmanuscriptnordidtheyrequireapprovalofthefinalmanuscripttobepublishedAnyuseoftradefirmorproductnamesisfordescriptivepurposesonlyanddoesnotimplyendorsementbytheUSGovernment
AUTHORSrsquo CONTRIBUTIONS
DJMCRVOELMandJLLconceived researchDJMandELMcol‐lected field data DJM CRVO and ELM conducted statisticalanalysesDJMCRVOELMKRUMDEKADRand JLLwrote themanuscriptJLLsecuredfundingAllauthorsreadandapprovedthemanuscript
ORCID
Darin J McNeil httporcidorg0000‐0003‐4595‐8354
Clint R V Otto httporcidorg0000‐0002‐7582‐3525
Amanda D Rodewald httporcidorg0000‐0002‐6719‐6306
R E FE R E N C E S
Allen‐WardellGBernhardtPBitnerRBurquezABuchmannSCaneJhellipInouyeD(1998)Thepotentialconsequencesofpollina‐tordeclinesontheconservationofbiodiversityandstabilityoffoodcropyieldsConservation Biology128ndash17
AndersonDR(2007)Model based inference in the life sciences A primer on evidenceBerlinGermanySpringerScienceampBusinessMedia
Arnold T W (2010) Uninformative parameters and model selectionusingAkaikesInformationCriterionJournal of Wildlife Management741175ndash1178httpsdoiorg101111j1937‐28172010tb01236x
Ashman T L Knight TM Steets J A Amarasekare P BurdMCampbellDRhellipMorganMT (2004)Pollen limitationofplantreproductionEcologicalandevolutionarycausesandconsequencesEcology852408ndash2421httpsdoiorg10189003‐8024
BendelCRHovickTJLimbRFampHarmonJP(2018)Variationin grazing management practices supports diverse butterflycommunitiesacrossgrasslandworking landscapesJournal of Insect Conservation221ndash13httpsdoiorg101007s10841‐017‐0041‐9
BuchananALGibbsJKomondyLampSzendreiZ(2017)Beecom‐munityof commercial potato fields inMichigan andBombus impa‐tiensvisitationtoneonicotinoid‐treatedpotatoplantsInsects830httpsdoiorg103390insects8010030
BucklandSTAndersonDRBurnhamKPampLaake JL (2005)Distance samplingHobokenNJJohnWileyampSonsLtd
BurnhamKPampAndersonDR(2002)Model selection and multimodel inference A practical information‐theoretic approachBerlinGermanySpringerScienceampBusinessMedia
BurnhamKPAndersonDRampLaakeJL(1980)Estimationofden‐sity from line transect sampling of biological populationsWildlife Monographs723ndash202
Calderone N W (2012) Insect pollinated crops insect pollinatorsandUSagricultureTrendanalysisofaggregatedatafortheperiod1992ndash2009 PLoS ONE7 e37235 httpsdoiorg101371journalpone0037235
CameronSALozierJDStrangeJPKochJBCordesNSolterL F amp Griswold T L (2011) Patterns of widespread decline in
NorthAmericanbumblebeesProceedings of the National Academy of Sciences108662ndash667httpsdoiorg101073pnas1014743108
RCore Team (2018)R A language and environment for statistical com‐puting Vienna Austria R Foundation for Statistical ComputingRetrievedfromhttpswwwR‐projectorg
Environmental Systems Research Institute (2011) ArcGIS Desktop Release 10RedlandsCaliforniaESRI
Fiske IampChandlerRB (2011)UnmarkedAnRpackage for fittinghierarchicalmodelsofwildlifeoccurrenceandabundanceJournal of Statistical Software431ndash23
Garibaldi L A Steffan‐Dewenter I Winfree R Aizen M ABommarcoRCunninghamSAhellipBartomeusI(2013)Wildpolli‐natorsenhancefruitsetofcropsregardlessofhoneybeeabundanceScience3391608ndash1611httpsdoiorg101126science1230200
Goulson D (1999) Foraging strategies of insects for gathering nec‐tar and pollen and implications for plant ecology and evolutionPerspectives in Plant Ecology Evolution and Systematics2 185ndash209httpsdoiorg1010781433‐8319‐00070
GoulsonDLyeGCampDarvillB(2008)DeclineandconservationofbumblebeesAnnual Review of Entomology53191ndash208httpsdoiorg101146annurevento53103106093454
GoulsonDNicholls E Botiacuteas C amp Rotheray E L (2015) Bee de‐clines driven by combined stress from parasites pesticides andlack of flowers Science 347 1255957 httpsdoiorg101126science1255957
Hammond P S Berggren P Benke H Borchers D L Collet AHeide‐Joslashrgensen M P hellip Oslashien N (2002) Abundance of har‐bour porpoise and other cetaceans in the North Sea and adja‐cent waters Journal of Applied Ecology 39 361ndash376 httpsdoiorg101046j1365‐2664200200713x
HanleyMEAwbiAJampFrancoM(2014)GoingnativeFlowerusebybumblebeesinEnglishurbangardensAnnals of Botany113799ndash806httpsdoiorg101093aobmcu006
Hau E amp Von Renouard H (2006) The wind resource London UKElsevier
Hedley S L amp Buckland S T (2004) Spatial models for line tran‐sect sampling Journal of Agricultural Biological and Environmental Statistics9181ndash199httpsdoiorg1011981085711043578
JamesFCampShugartHHJr(1970)AquantitativemethodofhabitatdescriptionAudubon Field Notes24727ndash736
Jepsen S Evans E Thorp R Hatfield R amp Black S H (2003)Petition to list the rusty patched bumble bee Bombus affinis (Cresson) 1863 as an endangered species under the US Endangered Species Act Retrieved from httpwwwxercesorgwp‐ontentuploads 201301Bombus‐petitionpdf
Jha S amp Kremen C (2013) Resource diversity and landscape‐levelhomogeneitydrivenativebee foragingProceedings of the National Academy of Sciences 110 555ndash558 httpsdoiorg101073pnas1208682110
KaranthKUampSunquistME(1995)PreyselectionbytigerleopardanddholeintropicalforestsJournal of Animal Ecology64439ndash450httpsdoiorg1023075647
KeacuteryMampRoyleJA (2015)Applied Hierarchical Modeling in Ecology Analysis of distribution abundance and species richness in R and BUGS Volume 1 Prelude and Static ModelsCambridgeMAAcademicPress
KeacuteryM amp Schmidt B R (2008) Imperfect detection and its conse‐quencesformonitoringforconservationCommunity Ecology9207ndash216httpsdoiorg101556ComEc92008210
Kevan PG (1990)Pollination keystone process in sustainable globalproductivity InVIInternationalSymposiumonPollination288(pp103‐110)
Kremen CWilliams NM amp Thorp RW (2002) Crop pollinationfromnativebeesatriskfromagriculturalintensificationProceedings of the National Academy of Sciences99 16812ndash16816 httpsdoiorg101073pnas262413599
emspensp emsp | emsp235McNEIL Et aL
LofflandH L Polasik J S TingleyMW Elsey E A Loffland CLebuhnGampSiegelRB(2017)Bumblebeeuseofpost‐firechap‐arralinthecentralSierraNevadaThe Journal of Wildlife Management811084ndash1097httpsdoiorg101002jwmg21280
MackenzieD I (2006)Modelingtheprobabilityof resourceuseTheeffectofanddealingwithdetectingaspeciesimperfectlyJournal of Wildlife Management70367ndash374httpsdoiorg1021930022‐541X(2006)70[367MTPORU]20CO2
MacKenzieDINicholsJDLachmanGBDroegeSAndrewRoyleJampLangtimmCA(2002)Estimatingsiteoccupancyrateswhende‐tectionprobabilitiesarelessthanoneEcology832248ndash2255httpsdoiorg1018900012‐9658(2002)083[2248ESORWD]20CO2
MacKenzieDINicholsJDRoyleJAPollockKHBaileyLampHinesJE(2005)Occupancy estimation and modeling Inferring pat‐terns and dynamics of species occurrenceLondonUKElsevier
Mackenzie D I (2003) Assessing site occupancymodelling as a toolfor monitoring Mahoenui giant weta populations Department ofConservation17
Marques T A Thomas L Fancy S G amp Buckland S T (2007)Improvingestimatesofbirddensityusingmultiple‐covariatedistancesamplingThe Auk1241229ndash1243httpsdoiorg1016420004‐8038(2007)124[1229IEOBDU]20CO2
McCaskillGLMcWilliamsWHAlerichCAButlerBJCrockerS JDomkeGMhellipWestfall JA (2009)Pennsylvaniarsquos Forests 2009NewtownSquarePAUSDepartmentofAgricultureForestServiceNorthernResearchStation
MichenerCDMcGinleyRJampDanforthBN(1994)The Bee Genera of North and Central AmericaWashingtonDCSmithsonianInstitutePress
OlesenJMBascompteJElberlingHampJordanoP(2008)TemporaldynamicsinapollinationnetworkEcology891573ndash1582httpsdoiorg10189007‐04511
PerssonA S RundloumlfMCloughYampSmithHG (2015)Bumblebees show trait‐dependent vulnerability to landscape simplifica‐tion Biodiversity and Conservation 24 3469ndash3489 httpsdoiorg101007s10531‐015‐1008‐3
Potts SGVulliamyBDafniANeemanGampWillmer P (2003)Linking bees and flowers How do floral communities structurepollinator communities Ecology 84 2628ndash2642 httpsdoiorg10189002‐0136
PottsSGBiesmeijerJCKremenCNeumannPSchweigerOampKuninWE (2010)Globalpollinatordeclinestrends impactsanddriversTrends in ecology amp evolution25(6)345ndash353
Redhead JW Dreier S Bourke A F HeardM S JordanW CSumner S hellip Carvell C (2016) Effects of habitat compositionandlandscapestructureonworkerforagingdistancesoffivebum‐ble bee species Ecological Applications 26 726ndash739 httpsdoiorg10189015‐0546
Roulston T A H Smith S A amp Brewster A L (2007) A com‐parison of pan trap and intensive net sampling techniques fordocumenting a bee (Hymenoptera Apiformes) fauna Journal of the Kansas Entomological Society 80 179ndash181 httpsdoiorg1023170022‐8567(2007)80[179ACOPTA]20CO2
Royle J A Dawson D K amp Bates S (2004) Modeling abundanceeffects in distance sampling Ecology 85 1591ndash1597 httpsdoiorg10189003‐3127
Scheper J Bommarco R Holzschuh A Potts S G Riedinger VRoberts S P hellipWickens V J (2015) Local and landscape‐level
floral resources explain effects of wildflower strips on wild beesacrossfourEuropeancountriesJournal of Applied Ecology521165ndash1175httpsdoiorg1011111365‐266412479
SeberGA(1986)AreviewofestimatinganimalabundanceBiometrics42267ndash292httpsdoiorg1023072531049
ShultzCH(1999)The Geology of PennsylvaniaPennsylvaniaGeologicalSurveyHarrisburgPAPennsylvaniaGeologicalSurvey
Sillett T S Chandler R B Royle J A KeacuteryM ampMorrison S A(2012) Hierarchical distance‐sampling models to estimate popu‐lation size and habitat‐specific abundance of an island endemicEcological Applications22(7)1997ndash2006
SollmannRGardnerBWilliamsKAGilbertATampVeitRR(2016)AhierarchicaldistancesamplingmodeltoestimateabundanceandcovariateassociationsofspeciesandcommunitiesMethods in Ecology and Evolution7529ndash537httpsdoiorg1011112041‐210X12518
Tepedino V J Durham S Cameron S A amp Goodell K (2015)Documenting bee decline or squandering scarce resourcesConservation Biology 29 280ndash282 httpsdoiorg101111cobi12439
Thomas LBuckland S TBurnhamKPAndersonDR Laake JL Borchers D L amp Strindberg S (2002) Distance samplingEncyclopediaofenvironmetrics
Thomas L Buckland S T Rexstad EA Laake J L Strindberg SHedley S L hellipBurnham K P (2010)Distance softwareDesignand analysis of distance sampling surveys for estimating pop‐ulation size Journal of Applied Ecology 47 5ndash14 httpsdoiorg101111j1365‐2664200901737x
ThompsonWL (2002)TowardsreliablebirdsurveysAccountingforindividualspresentbutnotdetectedThe Auk11918ndash25httpsdoiorg1016420004‐8038(2002)119[0018TRBSAF]20CO2
VanStrienA JTermaatTGroenendijkDMensingVampKeryM(2010) Site‐occupancy models may offer new opportunities fordragonflymonitoringbasedondailyspecies listsBasic and Applied Ecology11495ndash503httpsdoiorg101016jbaae201005003
VilsackTampMcCarthyG(2015)National strategy to promote the health of honey bees and other pollinatorsWashingtonDCReport IssuedbytheWhiteHousethePollinatorHealthTaskForce
WardKCariveauDMayERoswellMVaughanMWilliamsNhellip Gill K (2014) Streamlined Bee Monitoring Protocol for Assessing Pollinator HabitatPortlandORTheXercesSocietyforInvertebrateConservation
WeatherUndergroundInc(2018)WeatherForecastandReports‐LongRangeandLocalWundergroundRetrievedfromhttpswwwwun‐dergroundcom
WherryET Fogg JM JrampWahlHA (1979)Atlas of the flora of Pennsylvania Philadelphia PA The Morris Arboretum of theUniversityofPennsylvania
YoccozNGNichols JDampBoulinierT (2001)Monitoringofbio‐logicaldiversityinspaceandtimeTrends Ecology and Evolution16446ndash453
How to cite this articleMcNeilDJOttoCRVMoserELetalDistancemodelsasatoolformodellingdetectionprobabilityanddensityofnativebumblebeesJ Appl Entomol 2019143225ndash235 httpsdoiorg101111jen12583
228emsp |emsp emspensp McNEIL Et aL
We followed standard bee survey methods to avoid commoncausesofdetection failure (Wardetal2014)Surveyswerecon‐ductedonlyinbrightlightconditionslowwindwarmdays(ge16degC)andonlyduringlatemorningandafternoon(1000ndash1700)ThoughweattemptedtousestudydesigntoreducethepotentialimpactsofthesefactorsonBombus sppdetectabilitywealso includedthemindetectionmodellingAtthetimeofeachsurveywerecorded(a)surveyorID(b)cloudcover(c)timeofdayand(d)BeaufortWindIndex Local temperature data were downloaded from WeatherUnderground from the KUNV weather station in State CollegePennsylvania (WeatherUnderground Inc2018)Cloudcoverwasestimatedinthefieldtothenearest25(0ndash100)BeaufortWindIndexwasmeasuredonanincrementalscalefrom0to5with0rep‐resentingnowind at all (ie smokewould theoretically risewith‐outdrift)and5representinghighwindssuchthatentiretreesswayinthewind(HauampVonRenouard2006)Weavoidedsurveyinginwindindicesgt3andthusconsideredtwocategoriesofwind0ndash1ldquolowrdquo2ndash3ldquomoderaterdquoinouranalysesAllsurveystookplacefrom10to25July2017
24emsp|emspNet counts
TomeasureBombussppabundancewithinfixed‐radiusnetcountswe created 15m radius count surveys centred around each pointlocation (thecentreofeachdistancetransect)Nettedbeecountstookplaceimmediatelyupontheconclusionoftransectsurveys(de‐scribedabove)Withineachfixed‐radiusplotasingleobserverspent30minseeking‐andattemptingtocaptureallBombussppdetectedwithahandnetWechosefixed‐radiusnetsamplingbecauseitisastandardsamplingtechniquefornativebees (Perssonetal2015PottsVulliamyDafniNersquoemanampWillmer2003RoulstonSmithampBrewster2007)andwouldthereforeserveasabasisforcomparisontoourabundanceestimatesgeneratedfromHDSForeachBombus sppdetectedtheobserverattemptedtocaptureeachbeeusingahandnet(collapsible15rdquodiameternet17rdquohandleBioquipProduct7115CP)andoncecapturedallbeeswereheldcaptiveforthere‐mainderofthesurveyForeachcapturedbeethetimerwasstoppedwhiletheobserverplaced it intoaplasticzipperbagandresumedimmediately thereafter Thismethod prevented us from recaptur‐inganddouble‐countingbeeswithinthesameplotAfter30minofsurvey timehadelapsedeachBombus sppwas removed from itsbagwith forceps photographed for anotherproject and releasedunharmedInthefewoccasionswhereBombussppwereobservedbutevadedcapturetheyweretreatedasallotherBombussppcap‐turedforthepurposesofthisstudy(ieincluded)
25emsp|emspHabitat surveys
Wesurveyedregeneratingvegetationstructurewithin timberhar‐vestunitsfrom15Juneto15July2017VegetationsurveyssharedtheircentroidwithBombussppsurveysVegetationdataquantifiedhabitatstructureofwoodystemsandherbaceousunderstoryratherthan plant composition All vegetation data were collected along
three50mradialtransectseachorientedat0deg120degand240degfrompoint centreAlong each transectwe recordedplant strata at 10ldquostopsrdquo(10mapartn=30netcountlocation)Vegetationstratare‐cordedateachstopconsistedofthepresenceabsenceofsaplingshrub forbandgrasssedgeSaplingswereyoungtreeslt10cm (indiameterbreastheight)Thissamplingregimegaveusadequateres‐olutiontoassessvegetationstructure(15stopssite)whileremain‐ingof comparable scale toourbee sampling transects (33m)Wefoundvegetationstructuretobehighlycorrelatedacrossscalesaslargeas100mandthereforebelieveour50mvegetationplotsrep‐resentedsiteconditionsreasonablywellShrubswerewoodyplantswithmultipleprimarystems(incontrasttosingle‐stemmedsaplings)Forbswerebroad‐leafeddicotyledonousplants(egSolidagospp)The plant category ldquograssrdquo included any monocotyledonous plant(grassessedgesetc)Werecordedplantstratawithanoculartubesuchthatonlystratathat intersectedwithcrosshairs intheoculartube were considered present (James amp Shugart 1970) While asinglestopcouldincludemultiplestratatypeseachstratumcouldonlyberepresentedonceperstopandthuseachsitecouldhaveamaximumofn=15occurrencesforeachstratumWeanalyzedplantstrata values as percentages Prior to all analyses we calculatedSpearmanrsquosrho(ρ)forallpairsofcovariatestobemodelledBecausenonewerestronglycorrelated(Spearmanrsquosρ lt 060)nocovariateswereredundantandallweresuitableformodelling
26emsp|emspHierarchical distance models
Weanalyzeddistancetransectdata(beecountsanddistances)usingHDS models implemented in the R package ldquounmarkedrdquo (Fiske ampChandler2011RCoreampTeam2018)Thepackageunmarkedfitslinearmodelsinamaximumlikelihoodframeworkandcanbecom‐bined with an Information‐Theoretic approach (Anderson 2007)forthepurposeofmodelselection(egusingAkaikersquosInformationCriterionAICBurnhamampAnderson2002)Hierarchicaldistancemodels allowed us to create and rank candidate models each ofwhich contained independent model components for detectionprobability (p) and expected animal abundance (density λ) HDSmodelsassume(a)subjectsareaccuratelyidentified(egnofalse‐presences)(b)thatallsubjectsonthetransect(distance=0m)aredetectedperfectly(p=10)(c)subjectsaredetectedattheiroriginallocation(iemovement isnot influencedbytheobserver) (d)dis‐tancesareaccuratelymeasuredand(e)detectionofeachindividualis independentofthedetectionofallotherindividuals(Thomasetal2010)Bumblebeesappeartoconstitutegoodcandidatesfordis‐tancesamplingastheycanbeeasilyidentified(togenus)inthefield(Micheneretal1994)areeasilyapproachedbyobservers(Wardetal2014)andremainrelativelystillduringpollinationsuchthataccu‐ratedistanceestimationscouldbemadeforeachworkerAlthoughdistances were measured in the field directly we binned detec‐tions as recommended by Buckland et al (2005) 0ndash1 1ndash2 2ndash33ndash4and4ndash5mMoreovertopreparedistance‐basedtransectdatawe truncated the outer 10of our data such that analyseswereconductedusingonly the closest 90ofBombus spp detections
emspensp emsp | emsp229McNEIL Et aL
asrecommendedfordistanceanalysesbyBucklandetal(2005)Bytruncating thedata in thiswayalldetectionswerelt5mfromtheobserver
Distance models provide robust estimates of abundance byadjusting animal counts by the probability of detection for givendistances (Buckland et al 2005) This is accomplished by fittingdetectiondistancedata to a ldquodetection functionrdquo that describes adecayindetectionprobabilityassubjectsarefurtherfromtheob‐server (Bucklandetal2005KeacuteryampRoyle2015)Toevaluateanappropriatedetectionfunctionweevaluatedmodelseachfitusingoneofthefollowingdetectionfunctions(a)exponential(b)hazardrateor(c)half‐normal(Bucklandetal2005)ThiswasdonepriortoallcovariatemodellingEachdetectionfunctionisusedtoestimatetheaverageprobabilityofdetectionwhichisthenusedtoadjustrawcountssuchthatdensitypredictionscanbemade(Bucklandetal2005)OncethemostappropriatedetectionfunctionwasselectedbasedonAICcrankitwasusedtomodeldetectionprobabilityanddensityinconsecutivemodelsWemodelleddetectionprobabilityintwotiersdetectiontier1(surveycovariatesondetection)andde‐tectiontier2(habitatcovariatesondetection)Becauseoursamplesizewasmodestweusedonlysingle‐covariatedetectionmodelstoavoidoverfittingHDSmodelsDetectiontier1includedunivariatemodels for (a) timeof day (b) surveyor (c) temperature (d) cloudcover(e)windindexand(f)anull(intercept‐only)modelDetectiontier 2 (fit independently of detection tier 1) included univariatemodelsfor(a)saplingcover(b)shrubcover(c)forbcover(d)grasscoverand(e)anullmodelWithinbothmodeltiersweusedaglobalhabitatmodel(iesapling+shrub+forb+grass)fordensitytoen‐sure thatvariation indensitywas reasonablywell explainedwhileassessingdetectionprobabilityWeconsideredcovariatestobein‐formativeiftheywerebothgt20AICclessthanthenullmodelandhadβcoefficient95confidenceintervalsthatdidnotincludezeroUsing the informative covariates fromdetection tiers1and2weconstructedasetofdensitymodels(habitatcovariatesondensity)thataccountedfor imperfectdetection (a)saplingcover (b)shrubcover (c) forbcover (d)grasscoverand (e)anullmodelThenullmodelcontainedonlyintercepttermsandtheinformativeparame‐tersfordetectionPriortomodellingallcontinuouscovariateswerestandardizedusingthescalefunctioninbaseRModelrankingwasdoneusing the ldquoaictabrdquo functionof thepackage ldquoAICcmodavgrdquoAllmodelswerefitassumingaPoissondistributioninldquogdistsamprdquoandmodelfitwasassessedbycalculatingavarianceinflationfactor(chatchatchatc)usingtheunmarkedfunctionldquofitstatsrdquo (KeacuteryampRoyle2015)Weconsideredallmodelslt20AICctobecompetingandequallysupportedbythedata(BurnhamampAnderson2002)
27emsp|emspPoisson generalized linear models
WeusedaPoissongeneralized linearmodels inR (using the ldquoglmrdquofunction)tomodelBombus sppabundancealongfixed‐radiustran‐sectsandnetcountsThisallowedustocomparehabitat‐abundancerelationshipsgeneratedfromHDSmodelstothosegeneratedfrommethodsthatdonotaccountfordetectionprobabilityAswithour
HDSmodels Poisson regressionmodels allowed us tomodel beecountsasafunctionofhabitatcovariates(a)saplingcover(b)shrubcover (c) forbcover (d)grasscover and (e) anull (intercept‐only)modelWemodelled our fixed‐radius transect counts by truncat‐ing allHDS‐transect databy2mof the transect line and treatingthedataasarawcount(HanleyAwbiampFranco2014Scheperetal 2015) which is a standard technique when conducting visualencounter surveys Net count data were modelled in a compara‐blemanner such that raw countsweremodelled as a function ofhabitat covariatesWedid not account for imperfect detection ineither of these models but rather modelled Bombus spp countarea interpretedasadensityWeagainusedan information‐theo‐reticapproach(Anderson2007)withmodelrankingbasedonAICc consideringmodelslt20AICctobeequallysupportedbythedata(BurnhamampAnderson2002)Wealsousedsingle‐covariatemodelstoavoidoverlycomplexmodelsandtheinclusionofuninformativeparameterswithintopmodels(Arnold2010)
3emsp |emspRESULTS
Wedetected194individualBombus sppwithin5mofwhich136werewithin2mof the transect lineDuringaerialnetcountswecapturedn = 201 BombussppworkersOfthebeescapturedduringaerial net countsover50wereB impatienswith the remainderbeingamixedcommunityoflesscommonspecieslikeB bimaculatus and B vagans
31emsp|emspDetection probability
Ofthreedetectionfunctionmodelsweranthebest‐rankedmodelincludedanexponentialdetectionfunctionwheredetectionprob‐abilitygt5mfromthetransectwasasymp0(Figure2)Usinganexponen‐tialdetection functionwe foundthatdetectionprobabilityvariedas a functionof time since1000 (theearliestpossible start time)
F I G U R E 2 emspFrequencyofdetections(greybarsrightaxis)forBombussppwithinregeneratingtimberharvestsDetectionprobability(leftaxis)declinedasafunctionofdistancefromtransectandwasfittoanexponentialdetectionfunction(blackline)Bombussppwereonlyrarelydetectedfurtherthan5mfromthetransectline
230emsp |emsp emspensp McNEIL Et aL
andobserverIDsuggestingthatthelatestsurveysofeachdayhadthe lowestdetectionprobability and thatobserverswereunequalin their ability to detectBombus spp (Table 1 Figure 3a) Amongmodels investigating the relationship between habitat covariatesand Bombus spp detection the model that included grass cover()wastheonlysupportedmodelandsuggestedthatBombussppweremorereadilydetectedatsiteswithmoregrasscover(Table1Figure3b)Allothercovariatesmodelledintiers1and2weregt20AICc less than the nullmodel and theβ 95 confidence intervalsoverlappedzero
32emsp|emspHabitat modelling
Models from all three analyses yielded discernable habitat asso‐ciationswithBombus sppabundance (Table2Figure4)All threeanalyses indicated thatBombus spp abundanceduring the surveyperiodwas negatively associatedwith per cent sapling cover andnotassociatedwithforbcover (Table2Figure4)The importanceofshrubcoverandgrasscoveraspredictorsofBombussppcountsandestimatedabundancevariedacrossmethods(Table2)HDSandtransectcountsrevealedsupportforshrubcoverasaninformativecovariatebeinggt20AICc less than thenull andhavingparameter
95confidence intervals thatdidnotoverlapzero (Table2)Onlynet counts suggested that grass cover was positively associatedwithBombus sppabundancewhileHDSsuggestedthatgrasscoverwasinsteadcorrelatedpositivelywithdetectionprobabilitybutnotabundance (Table 2 Figure 4) In contrast our net count analysissuggestednoeffectofshrubcoveronbeecountswiththeldquoshrubrdquomodel ranked lower than thenullmodeland the shrubparameter95confidenceintervalsoverlappingzero(Table2)Ourtop‐rankedHDSmodel(ldquosaplingrdquo)showedevidenceofminoroverdispersion(chatchatchatc=133)whilemostothermodelsdidnotappearoverdispersed (chatchatchatclt10 with a mean chatchatchatc=101acrossmodels inourfinalHDSmodelset)Weconsidered this an acceptable level of overdispersion and did notuse a variance inflation factor to adjust our parameter estimates(BurnhamampAnderson2002)
33emsp|emspDensity estimation
Inadditiontoexaminingabundanceasafunctionofhabitatamongthe three methods we compared their estimated mean densitiesof foragingBombus spp basedon intercept‐only abundancemod‐els(includingdetectioncovariatesforHDS)EstimatedBombusspp
Model name K AICc ΔAICc AICc Wt β estimate (95CI)
Surveycovariatesondetectionprobability
p(observer) 7 34893 000 078 058(021to095)
p(time) 7 35156 264 021 minus023(minus038tominus008)
p () 6 35829 936 001 ‐
p(wind) 7 35987 1094 000 minus016(minus044to013)
p(temp) 7 36064 1172 000 minus005(minus019to009)
Sitecovariatesondetectionprobability
p(grass) 7 35267 000 085 035(007to063)
p(forb) 7 35827 561 005 017(minus004to037)
p() 6 35829 562 005 ‐
p(shrub) 7 35965 699 003 minus013(minus035to009)
p (sapling) 7 36048 782 002 010(minus016to036)
NoteModelsareranked indescendingorderofAkaikersquos InformationCriterionadjustedforsmallsamplesize(AICc)Surveycovariatesincludedtimesincesurveystarttime(continuousldquotimerdquo)tem‐perature(continuous)cloudcover(overcastcontinuous)observer(categorical)andwindindex(categorical)Sitecovariatesincludedpercentcoverasmeasuredby50mradiusvegetationsurveysforvegetationstructuresaplingsshrubs forbsandgrassBothcandidatemodelsetsarerankedagainstanullintercept‐onlymodelBelowwereportnumberofmodelparameters(k)ΔAICcAICc weight(AICcWt)andβparameterestimates(95confidenceinterval)
TA B L E 1 emspHierarchicaldistancemodelsofdetectionprobabilityasafunctionofsurveycovariates(Tier1top)andsitecovariates(Tier2bottom)
F I G U R E 3 emspModelsofBombussppdetectionprobabilityasafunctionofsurveytime(left)percentgrasscover(centre)andobserver(right)whilealsobeingmostdetectableclosesttothetransect(all)
emspensp emsp | emsp231McNEIL Et aL
forager density within timber harvests was highest for the HDSmodels(192foragingworkersha95CI153ndash240)andlowestfornetcounts(21foragingworkersha95CI19ndash23Figure5)an89differencebetween the twomethodsTransect countsyielded in‐termediate estimates of density (40 foragingworkersha 95CI34ndash47)andwere80lowerthandensityestimatesfromHDSSite‐specific HDS modelled densities and netting count raw densitieswerecorrelated (Pearsonrsquos r = 031 p=003) though the relation‐shipwasnot11(Figure5)
4emsp |emspDISCUSSION
Ourstudyprovidesthefirstempiricalevidencethatdetectionprob‐abilitiesofBombus sppvaryinwaysthatcanaffectabundanceesti‐matesandinferencesabouthabitatrelationshipsObservationerrorcaused by imperfect detection is one of the central challenges ofecologicalmonitoringprograms(Thompson2002YoccozNicholsampBoulinier 2001)buthas yet tobewidely applied tomonitoringofmany invertebrates includingpollinators (but seeBendeletal2018Lofflandetal2017Mackenzie2003VanStrienTermaatGroenendijkMensingampKery 2010)Methods like distance sam‐plingwhileofferingapotential solution to this challenge are stillunder‐utilized in entomological research Meanwhile distance
samplingandsimilarmethodshavebeenastapleofvertebratewild‐liferesearchfordecades(Bucklandetal2005BurnhamAndersonampLaake1980Seber1986Thomasetal2002)andhavebeenex‐pandedtoestimatepopulationsizehabitat‐specificabundanceforindividualspeciesandcommunities(SillettChandlerRoyleKeacuteryampMorrison2012SollmannGardnerWilliamsGilbertampVeit2016)Althoughourstudyisnotthefirstestimateandaccountfordetec‐tionprobabilityofbumblebees(Lofflandetal2017)nostudybe‐foreourshasdescribedfactorsassociatedwithdetectionprobabilityanddonesoinaHDSframework
Wefoundthatdistancesamplingtransectswerebothasimpleandeffectivesurveymethodforestimatingdensityandhabitatre‐lationships (Buckland et al 2005) Hierarchical distance samplingmodelsareoneofthefewavailablemethodsthatallowresearcherstomodel detection‐adjusted abundancewithonly a single visit toeachsite(Bucklandetal2005KeacuteryampRoyle2015MacKenzieetal 2005)Themethodusesonlynon‐lethal samplingunlike trap‐pingnettingmethods(Tepedinoetal2015)whichisespeciallyde‐sirablewhen sampling for speciesof conservation concern or forcommonspecies in areaswherecapture‐based sampling isnot al‐lowedAdditionallyHDSmodelsarealsousefulbecausetheoutputisaneasily interpretedlatentstatedensitywithunits inldquoanimalsareardquo In our study HDS models generated estimates of foragingBombus sppworkerdensity
Model name K AICc ΔAICc AICc Wt β estimate (95CI)
Hierarchicaldistancesampling
λ(sapling) 6 33769 000 098 minus030(minus045tominus014)
λ(shrub) 6 34583 813 002 021(005to037)
λ() 5 3502 1251 000 ndash
λ(grass) 6 35041 1271 000 minus017(minus038to005)
λ(forb) 6 35282 1513 000 minus001(minus016to014)
Transectcounts
λ(sapling) 2 27763 000 096 minus144(minus220tominus069)
λ(shrub) 2 28448 685 003 085(025to144)
λ(grass) 2 2898 1217 000 minus093(minus214to028)
λ() 1 29007 1244 000 ‐
λ(forb) 2 29216 1454 000 0133(minus074to101)
Netcounts
λ(sapling) 2 36071 000 100 minus163(minus226tominus101)
λ(grass) 2 38438 2367 000 085(003to167)
λ(shrub) 2 38565 2494 000 041(minus009to090)
λ() 1 38608 2537 000 ndash
λ(forb) 2 38709 2638 000 039(minus031to109)
NoteModelsareranked indescendingorderofAkaikersquos InformationCriterionadjustedforsmallsamplesize(AICc)DistancetransectdataincludedBombussppdetectedfrom0to5malong66mtransectsTransectcounts includedBombus sppdetected from0ndash2malong66m transectsnetcountdatawerecountsofBombus sppwithin15mradiusplotsSitecovariatesincludedpercentcover asmeasured by 50m radius vegetation surveys for vegetation structure saplings shrubsforbsandgrassBelowwereportnumberofmodelparameters(k)AICcΔAICcAICc weight(AICc Wt)andeachcovariateβparameterestimateandβparameterestimates(95confidenceinterval)
TA B L E 2 emspHabitatmodelsderivedfromhierarchicaldistancemodels(top)fixed‐widthtransectmodels(centre)andlinearmodelsofnetcountdata(bottom)allfitusingaPoissondistribution
232emsp |emsp emspensp McNEIL Et aL
DespitebeingamongthelargestandmostconspicuousofNorthAmerican bees (Michener et al 1994) we found that detectionprobability of Bombus spp was imperfect and declined markedlywithdistancefromthesurveytransectwithalmostnodetectionsbeyond5mDetectionprobabilitiesinourstudywereinfluencedbysurvey‐specific(egtimeofday)andsite‐specific(eggrasscover)variableswithdetectionprobabilityhighestinthemorninginmid‐summerandinhabitatswithabundantgrasscoverWithinregener‐atingtimberharvestsinourstudyarealdquograssrdquocoverwastypicallylow‐growing monocotyledons like Carex pennsylvanica Abundantlow‐growing sedge allowed observers to view Bombus spp fromgreaterdistancesthanwhensitesweredominatedbytallsaplingsshrubs or forbs (egSolidago) Consequently studieswithin habi‐tatsdominatedbylowgrassorothershortvegetationmightfindde‐tectionprobabilityforBombusspptobereliableatdistancesgt5mAlthoughweareuncertainastowhyBombussppwerelessdetect‐ableduringsurveysconductedlaterintheafternoononeplausibleexplanationisthatlongershadowscastbylateafternoonlightmade
Bombussppmoredifficulttodetectwhenforagingin lowvegeta‐tionAdditionalworkexploringthedriversassociatedwithBombus sppdetectionwouldprovevaluabletomonitoringregimesaimedatsurveyingbumblebees
ThoughourstudyisnotacomprehensivehabitatassessmentforBombussppwithinregeneratingtimberharvestsofeasternforestsourresultsprovideaglimpseintothehabitatdynamicsofbumble‐beesinregeneratingforestsduringmid‐summerOurfindingsthatBombus sppwerepositivelyassociatedwithshrubsandnegativelyassociatedwithsaplingscanbeexplainedprimarilybyflowerphe‐nology during our survey window Regenerating saplings withinthe timber harvests we monitored were largely oaks hickoriesblackcherry (Prunus serotina)andredmaple (Acer rubrumWherryetal1979)Thesespeciesdonot flowerassmallsaplingsanddosoinearlyspringasmaturetrees(ieoutsidethesamplingperiodWherryetal1979)Incontrastseveralspeciesofshrubwereflow‐eringduringsamplingincludingblackhuckleberry(Gaylussacia bac‐cata)andhillsideblueberryIncontrastmostforbs(eggoldenrod
F I G U R E 4 emspModelledhabitatassociationsbetweenBombussppandstructuralvegetationfeatureswithinregeneratingtimberharvestsaspredictedbyhierarchicaldistancemodels(top)fixed‐width(4m)transectcounts(centre)andnetcounts(bottom)Variablesshownaresaplingcover(left)shrubcover(centre)andgrasscover(right)Solidlinesrepresentmodelpredictionswithdashedlinesas95confidenceintervalsRelationshipsmarkedwithanasteriskwerethosewithmodelsupport(iemoreinformativethananullmodelandβ95CInon‐overlappingzero)
F I G U R E 5 emspLeftBombusspppredictedmeandensityformodelsofnetcounts(ldquoncrdquo)transectcounts(ldquotcrdquo)andhierarchicaldistancesamplingmodels(ldquohdsrdquo)RightPredicteddensity(workersha)generatedfromourtop‐rankedhierarchicaldistancemodel(p [observer+time+grass]λ[sapling])regressedagainstcountdatafromBombus sppnetcounts
emspensp emsp | emsp233McNEIL Et aL
SolidagosppsnakerootAgeratina spp)hadnotbegunfloweringyetFutureworkshouldexplorehowBombussppmaytrackresourcesacrossagrowingseasontopersistwithineasternforestecosystems
Monitoringprograms forBombus spp andothernativepolli‐natorscanbeimprovedbyincorporatingstudydesignandmodel‐based approaches for minimizing detection error Although weincludedseveraldesign‐basedsolutionsforminimizingdetectionerror(egrestrictingsurveytimesonlysurveyinginfairweatherWard et al 2014) detection probability remained imperfectand varied due to time of day observer and vegetation coverConsequentlymethodsthatignoreddetectionprobabilitygener‐ated density estimates 80ndash89 lower than HDS Past studieshaveshowntheimportanceofusingdesign‐basedapproachestominimize false negativeswhen sampling bees (BuchananGibbsKomondyampSzendrei2017)Ourstudydemonstratesthevalueofusingbothdesign‐andmodel‐basedapproachesforreducingsam‐plingerrorscausedbyimperfectdetectionOtherstudysystemswith thick vegetation cover such as prairies and forested wet‐landsorobstructiveobjectssuchasurbanenvironmentsarealsolikely to underestimate bee abundance even if multiple design‐basedapproachesareusedWhiletraditionalsamplingtechniquesthat do not account for detection have numerous applicationsourstudyhighlightstheimportanceofincorporatingmodel‐basedapproachesforaccountingfordetectionprobabilitywithinnativebeesurveysparticularlywhenattemptingtoestimatebeeabun‐danceordensity
Althoughour results suggest thatHDS representsapromisingtoolformonitoringbumblebeesresearcherswishingtoemploythemethod should recognize its associated limitations For exampledistancemodelsassumethatallanimalsonthetransectlinearede‐tectedperfectlyAlthoughitislikelythisassumptionwasmetwithalargeinsectlikeBombussppthisassumptionmightbeviolatedwithsmallerinsectsMoreoversubjectsareassumedtobeuniformlydis‐tributedinamannerunaffectedbytheobserverWhileitispossiblethatBombussppwerefrightenedbyobserverswetookcaretonotethe locationof first detection forBombus spp apparently flushedandtheirloudflightmadeclosedetectionsalmostcertainWenotethat thismethodwouldnotworkwell for species‐level identifica‐tionbecauseobservationsaremadefromadistanceandsomebeegeneraareexceedinglydifficulttoidentifyevenwithamicroscope(Michener et al 1994)Misidentification of specieswould consti‐tuteafalsepositivewhichwouldviolateanassumptionofdistancesampling
Anotherconsiderationofthisstudydesignandmanymethodsofabundanceestimationisthatanimalsmayviolatetheclosureas‐sumptionInthecaseofBombussppthislikelyoccurredasforagersflew in‐ and out‐ of the effective survey area (~5m from the ob‐serverforHDS)WhilethismayconstituteaproblemforsomestudyobjectivesandmethodswehavenoreasontobelievethatBombus sppmovementwasnonrandomwithrespecttotheobserverandanaccuratedensitycouldthereforestillbemadewhenpassivecountingwasusedClosureviolationmaybeamoreimportantproblemwhenattempting tocalculatedensity fromanettingplotwhereanimals
mayentertheplotandbeunabletoleaveastheyarecapturedandhelduntil thesurveyhasfinished Insuchcasesmovementwouldbebiasedbyindividualsimmigratingintothemonitoredplotbutun‐abletoemigrateandmovementwouldbebiasedtowardstheplotAlthough net‐based sampling is often preferable for investigatingspecies‐specific habitat relationships the potential for movementbias highlights the need for cautious interpretation of net‐baseddensityestimatesforbeesSimilarlyresearchersshouldconsiderthepotentialfordouble‐countingsubjectsAlthoughBombussppinourstudywereapparentlyfewenoughandslowenoughtoavoidmostdouble‐countingthismaybeamoreimportantproblemtoconsiderformoreabundantinsectswithreduceddetectability(egHalictids)
Wealsoadvisecautionwith interpretationofhabitatrelation‐shipsreportedhereasourstudyshouldbe interpretedasasmallldquosnapshotrdquo in time and lacking species‐specific habitat relation‐ships(OlesenBascompteElberlingampJordano2008)Full‐seasonhabitat associations are temporally dynamic forBombus spp andvaryacrossspecies(Goulson1999JhaampKremen2013)Relativefloral resourceavailabilityofdifferentspecieschangesacrosstheseasonandfuturestudiesemployingthesemethodsatregularin‐tervals from early springwhen queens first emerge through lateautumnwould prove valuable In fact examination of queen beedensities would likely prove a better assessment of populationdensityandhabitatqualitythanworkerdensitywhenmonitoringorresearchingcolonialorganismssuchasbumblebeesestimatingthetruenumberofreproducingcoloniesisofmorevaluethanes‐timating the number of foragingworkers aswe have done hereConductingHDSduringthespringandearlysummerwhenqueensare theonly activebumblebee foragersmayprove auseful andnon‐lethalapproachtoestimating theabundanceof reproductiveindividualsandtheexpectednumbersummercoloniesforagivenarea However sampling queens would likely require additionalsamplingsitesorrepeatvisitbecausecountswouldbemuchlowerandHDSmodelsmayhavetroubleconvergingwithrelativelyfewsampling locations Caution should also be exercised with inter‐pretation ofBombus spp density estimates reported here as ourdensitieslikelyconsistofmultiplespeciesofBombus modelled and reportedasoneWealsorecommendfuturestudiesexplorehownon‐Bombusgenera(ormorphospeciesfunctionalgroups)performasthefocusofHDSmodelsAlthoughHDS isnotwithout limita‐tionwebelieveourstudyhighlightstheutilityofHDSmodelsforestimatingdensitiesandelucidatinghabitatassociationsofbumblebeeswhenindividualsaredetectedimperfectly
ACKNOWLEDG EMENTS
Wethank the following individuals andagencies for their supportandlandaccessSproulStateForestandMoshannonStateForestFunding was provided by the Indiana University of PennsylvaniaBUREfundandtheUnitedStatesDepartmentofAgricultureNaturalResources Conservation Service (68‐7482‐12‐502) through theConservationEffectsAssessmentProjectWeareverygrateful toJoanMilamandSamDroegefortheircommentsonearlyversions
234emsp |emsp emspensp McNEIL Et aL
of thismanuscriptWearealsoverygrateful to threeanonymousreviewers spend considerable time strengthening thismanuscriptFundersofourprojectdidnothaveanyinfluenceonthecontentofthesubmittedmanuscriptnordidtheyrequireapprovalofthefinalmanuscripttobepublishedAnyuseoftradefirmorproductnamesisfordescriptivepurposesonlyanddoesnotimplyendorsementbytheUSGovernment
AUTHORSrsquo CONTRIBUTIONS
DJMCRVOELMandJLLconceived researchDJMandELMcol‐lected field data DJM CRVO and ELM conducted statisticalanalysesDJMCRVOELMKRUMDEKADRand JLLwrote themanuscriptJLLsecuredfundingAllauthorsreadandapprovedthemanuscript
ORCID
Darin J McNeil httporcidorg0000‐0003‐4595‐8354
Clint R V Otto httporcidorg0000‐0002‐7582‐3525
Amanda D Rodewald httporcidorg0000‐0002‐6719‐6306
R E FE R E N C E S
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AndersonDR(2007)Model based inference in the life sciences A primer on evidenceBerlinGermanySpringerScienceampBusinessMedia
Arnold T W (2010) Uninformative parameters and model selectionusingAkaikesInformationCriterionJournal of Wildlife Management741175ndash1178httpsdoiorg101111j1937‐28172010tb01236x
Ashman T L Knight TM Steets J A Amarasekare P BurdMCampbellDRhellipMorganMT (2004)Pollen limitationofplantreproductionEcologicalandevolutionarycausesandconsequencesEcology852408ndash2421httpsdoiorg10189003‐8024
BendelCRHovickTJLimbRFampHarmonJP(2018)Variationin grazing management practices supports diverse butterflycommunitiesacrossgrasslandworking landscapesJournal of Insect Conservation221ndash13httpsdoiorg101007s10841‐017‐0041‐9
BuchananALGibbsJKomondyLampSzendreiZ(2017)Beecom‐munityof commercial potato fields inMichigan andBombus impa‐tiensvisitationtoneonicotinoid‐treatedpotatoplantsInsects830httpsdoiorg103390insects8010030
BucklandSTAndersonDRBurnhamKPampLaake JL (2005)Distance samplingHobokenNJJohnWileyampSonsLtd
BurnhamKPampAndersonDR(2002)Model selection and multimodel inference A practical information‐theoretic approachBerlinGermanySpringerScienceampBusinessMedia
BurnhamKPAndersonDRampLaakeJL(1980)Estimationofden‐sity from line transect sampling of biological populationsWildlife Monographs723ndash202
Calderone N W (2012) Insect pollinated crops insect pollinatorsandUSagricultureTrendanalysisofaggregatedatafortheperiod1992ndash2009 PLoS ONE7 e37235 httpsdoiorg101371journalpone0037235
CameronSALozierJDStrangeJPKochJBCordesNSolterL F amp Griswold T L (2011) Patterns of widespread decline in
NorthAmericanbumblebeesProceedings of the National Academy of Sciences108662ndash667httpsdoiorg101073pnas1014743108
RCore Team (2018)R A language and environment for statistical com‐puting Vienna Austria R Foundation for Statistical ComputingRetrievedfromhttpswwwR‐projectorg
Environmental Systems Research Institute (2011) ArcGIS Desktop Release 10RedlandsCaliforniaESRI
Fiske IampChandlerRB (2011)UnmarkedAnRpackage for fittinghierarchicalmodelsofwildlifeoccurrenceandabundanceJournal of Statistical Software431ndash23
Garibaldi L A Steffan‐Dewenter I Winfree R Aizen M ABommarcoRCunninghamSAhellipBartomeusI(2013)Wildpolli‐natorsenhancefruitsetofcropsregardlessofhoneybeeabundanceScience3391608ndash1611httpsdoiorg101126science1230200
Goulson D (1999) Foraging strategies of insects for gathering nec‐tar and pollen and implications for plant ecology and evolutionPerspectives in Plant Ecology Evolution and Systematics2 185ndash209httpsdoiorg1010781433‐8319‐00070
GoulsonDLyeGCampDarvillB(2008)DeclineandconservationofbumblebeesAnnual Review of Entomology53191ndash208httpsdoiorg101146annurevento53103106093454
GoulsonDNicholls E Botiacuteas C amp Rotheray E L (2015) Bee de‐clines driven by combined stress from parasites pesticides andlack of flowers Science 347 1255957 httpsdoiorg101126science1255957
Hammond P S Berggren P Benke H Borchers D L Collet AHeide‐Joslashrgensen M P hellip Oslashien N (2002) Abundance of har‐bour porpoise and other cetaceans in the North Sea and adja‐cent waters Journal of Applied Ecology 39 361ndash376 httpsdoiorg101046j1365‐2664200200713x
HanleyMEAwbiAJampFrancoM(2014)GoingnativeFlowerusebybumblebeesinEnglishurbangardensAnnals of Botany113799ndash806httpsdoiorg101093aobmcu006
Hau E amp Von Renouard H (2006) The wind resource London UKElsevier
Hedley S L amp Buckland S T (2004) Spatial models for line tran‐sect sampling Journal of Agricultural Biological and Environmental Statistics9181ndash199httpsdoiorg1011981085711043578
JamesFCampShugartHHJr(1970)AquantitativemethodofhabitatdescriptionAudubon Field Notes24727ndash736
Jepsen S Evans E Thorp R Hatfield R amp Black S H (2003)Petition to list the rusty patched bumble bee Bombus affinis (Cresson) 1863 as an endangered species under the US Endangered Species Act Retrieved from httpwwwxercesorgwp‐ontentuploads 201301Bombus‐petitionpdf
Jha S amp Kremen C (2013) Resource diversity and landscape‐levelhomogeneitydrivenativebee foragingProceedings of the National Academy of Sciences 110 555ndash558 httpsdoiorg101073pnas1208682110
KaranthKUampSunquistME(1995)PreyselectionbytigerleopardanddholeintropicalforestsJournal of Animal Ecology64439ndash450httpsdoiorg1023075647
KeacuteryMampRoyleJA (2015)Applied Hierarchical Modeling in Ecology Analysis of distribution abundance and species richness in R and BUGS Volume 1 Prelude and Static ModelsCambridgeMAAcademicPress
KeacuteryM amp Schmidt B R (2008) Imperfect detection and its conse‐quencesformonitoringforconservationCommunity Ecology9207ndash216httpsdoiorg101556ComEc92008210
Kevan PG (1990)Pollination keystone process in sustainable globalproductivity InVIInternationalSymposiumonPollination288(pp103‐110)
Kremen CWilliams NM amp Thorp RW (2002) Crop pollinationfromnativebeesatriskfromagriculturalintensificationProceedings of the National Academy of Sciences99 16812ndash16816 httpsdoiorg101073pnas262413599
emspensp emsp | emsp235McNEIL Et aL
LofflandH L Polasik J S TingleyMW Elsey E A Loffland CLebuhnGampSiegelRB(2017)Bumblebeeuseofpost‐firechap‐arralinthecentralSierraNevadaThe Journal of Wildlife Management811084ndash1097httpsdoiorg101002jwmg21280
MackenzieD I (2006)Modelingtheprobabilityof resourceuseTheeffectofanddealingwithdetectingaspeciesimperfectlyJournal of Wildlife Management70367ndash374httpsdoiorg1021930022‐541X(2006)70[367MTPORU]20CO2
MacKenzieDINicholsJDLachmanGBDroegeSAndrewRoyleJampLangtimmCA(2002)Estimatingsiteoccupancyrateswhende‐tectionprobabilitiesarelessthanoneEcology832248ndash2255httpsdoiorg1018900012‐9658(2002)083[2248ESORWD]20CO2
MacKenzieDINicholsJDRoyleJAPollockKHBaileyLampHinesJE(2005)Occupancy estimation and modeling Inferring pat‐terns and dynamics of species occurrenceLondonUKElsevier
Mackenzie D I (2003) Assessing site occupancymodelling as a toolfor monitoring Mahoenui giant weta populations Department ofConservation17
Marques T A Thomas L Fancy S G amp Buckland S T (2007)Improvingestimatesofbirddensityusingmultiple‐covariatedistancesamplingThe Auk1241229ndash1243httpsdoiorg1016420004‐8038(2007)124[1229IEOBDU]20CO2
McCaskillGLMcWilliamsWHAlerichCAButlerBJCrockerS JDomkeGMhellipWestfall JA (2009)Pennsylvaniarsquos Forests 2009NewtownSquarePAUSDepartmentofAgricultureForestServiceNorthernResearchStation
MichenerCDMcGinleyRJampDanforthBN(1994)The Bee Genera of North and Central AmericaWashingtonDCSmithsonianInstitutePress
OlesenJMBascompteJElberlingHampJordanoP(2008)TemporaldynamicsinapollinationnetworkEcology891573ndash1582httpsdoiorg10189007‐04511
PerssonA S RundloumlfMCloughYampSmithHG (2015)Bumblebees show trait‐dependent vulnerability to landscape simplifica‐tion Biodiversity and Conservation 24 3469ndash3489 httpsdoiorg101007s10531‐015‐1008‐3
Potts SGVulliamyBDafniANeemanGampWillmer P (2003)Linking bees and flowers How do floral communities structurepollinator communities Ecology 84 2628ndash2642 httpsdoiorg10189002‐0136
PottsSGBiesmeijerJCKremenCNeumannPSchweigerOampKuninWE (2010)Globalpollinatordeclinestrends impactsanddriversTrends in ecology amp evolution25(6)345ndash353
Redhead JW Dreier S Bourke A F HeardM S JordanW CSumner S hellip Carvell C (2016) Effects of habitat compositionandlandscapestructureonworkerforagingdistancesoffivebum‐ble bee species Ecological Applications 26 726ndash739 httpsdoiorg10189015‐0546
Roulston T A H Smith S A amp Brewster A L (2007) A com‐parison of pan trap and intensive net sampling techniques fordocumenting a bee (Hymenoptera Apiformes) fauna Journal of the Kansas Entomological Society 80 179ndash181 httpsdoiorg1023170022‐8567(2007)80[179ACOPTA]20CO2
Royle J A Dawson D K amp Bates S (2004) Modeling abundanceeffects in distance sampling Ecology 85 1591ndash1597 httpsdoiorg10189003‐3127
Scheper J Bommarco R Holzschuh A Potts S G Riedinger VRoberts S P hellipWickens V J (2015) Local and landscape‐level
floral resources explain effects of wildflower strips on wild beesacrossfourEuropeancountriesJournal of Applied Ecology521165ndash1175httpsdoiorg1011111365‐266412479
SeberGA(1986)AreviewofestimatinganimalabundanceBiometrics42267ndash292httpsdoiorg1023072531049
ShultzCH(1999)The Geology of PennsylvaniaPennsylvaniaGeologicalSurveyHarrisburgPAPennsylvaniaGeologicalSurvey
Sillett T S Chandler R B Royle J A KeacuteryM ampMorrison S A(2012) Hierarchical distance‐sampling models to estimate popu‐lation size and habitat‐specific abundance of an island endemicEcological Applications22(7)1997ndash2006
SollmannRGardnerBWilliamsKAGilbertATampVeitRR(2016)AhierarchicaldistancesamplingmodeltoestimateabundanceandcovariateassociationsofspeciesandcommunitiesMethods in Ecology and Evolution7529ndash537httpsdoiorg1011112041‐210X12518
Tepedino V J Durham S Cameron S A amp Goodell K (2015)Documenting bee decline or squandering scarce resourcesConservation Biology 29 280ndash282 httpsdoiorg101111cobi12439
Thomas LBuckland S TBurnhamKPAndersonDR Laake JL Borchers D L amp Strindberg S (2002) Distance samplingEncyclopediaofenvironmetrics
Thomas L Buckland S T Rexstad EA Laake J L Strindberg SHedley S L hellipBurnham K P (2010)Distance softwareDesignand analysis of distance sampling surveys for estimating pop‐ulation size Journal of Applied Ecology 47 5ndash14 httpsdoiorg101111j1365‐2664200901737x
ThompsonWL (2002)TowardsreliablebirdsurveysAccountingforindividualspresentbutnotdetectedThe Auk11918ndash25httpsdoiorg1016420004‐8038(2002)119[0018TRBSAF]20CO2
VanStrienA JTermaatTGroenendijkDMensingVampKeryM(2010) Site‐occupancy models may offer new opportunities fordragonflymonitoringbasedondailyspecies listsBasic and Applied Ecology11495ndash503httpsdoiorg101016jbaae201005003
VilsackTampMcCarthyG(2015)National strategy to promote the health of honey bees and other pollinatorsWashingtonDCReport IssuedbytheWhiteHousethePollinatorHealthTaskForce
WardKCariveauDMayERoswellMVaughanMWilliamsNhellip Gill K (2014) Streamlined Bee Monitoring Protocol for Assessing Pollinator HabitatPortlandORTheXercesSocietyforInvertebrateConservation
WeatherUndergroundInc(2018)WeatherForecastandReports‐LongRangeandLocalWundergroundRetrievedfromhttpswwwwun‐dergroundcom
WherryET Fogg JM JrampWahlHA (1979)Atlas of the flora of Pennsylvania Philadelphia PA The Morris Arboretum of theUniversityofPennsylvania
YoccozNGNichols JDampBoulinierT (2001)Monitoringofbio‐logicaldiversityinspaceandtimeTrends Ecology and Evolution16446ndash453
How to cite this articleMcNeilDJOttoCRVMoserELetalDistancemodelsasatoolformodellingdetectionprobabilityanddensityofnativebumblebeesJ Appl Entomol 2019143225ndash235 httpsdoiorg101111jen12583
emspensp emsp | emsp229McNEIL Et aL
asrecommendedfordistanceanalysesbyBucklandetal(2005)Bytruncating thedata in thiswayalldetectionswerelt5mfromtheobserver
Distance models provide robust estimates of abundance byadjusting animal counts by the probability of detection for givendistances (Buckland et al 2005) This is accomplished by fittingdetectiondistancedata to a ldquodetection functionrdquo that describes adecayindetectionprobabilityassubjectsarefurtherfromtheob‐server (Bucklandetal2005KeacuteryampRoyle2015)Toevaluateanappropriatedetectionfunctionweevaluatedmodelseachfitusingoneofthefollowingdetectionfunctions(a)exponential(b)hazardrateor(c)half‐normal(Bucklandetal2005)ThiswasdonepriortoallcovariatemodellingEachdetectionfunctionisusedtoestimatetheaverageprobabilityofdetectionwhichisthenusedtoadjustrawcountssuchthatdensitypredictionscanbemade(Bucklandetal2005)OncethemostappropriatedetectionfunctionwasselectedbasedonAICcrankitwasusedtomodeldetectionprobabilityanddensityinconsecutivemodelsWemodelleddetectionprobabilityintwotiersdetectiontier1(surveycovariatesondetection)andde‐tectiontier2(habitatcovariatesondetection)Becauseoursamplesizewasmodestweusedonlysingle‐covariatedetectionmodelstoavoidoverfittingHDSmodelsDetectiontier1includedunivariatemodels for (a) timeof day (b) surveyor (c) temperature (d) cloudcover(e)windindexand(f)anull(intercept‐only)modelDetectiontier 2 (fit independently of detection tier 1) included univariatemodelsfor(a)saplingcover(b)shrubcover(c)forbcover(d)grasscoverand(e)anullmodelWithinbothmodeltiersweusedaglobalhabitatmodel(iesapling+shrub+forb+grass)fordensitytoen‐sure thatvariation indensitywas reasonablywell explainedwhileassessingdetectionprobabilityWeconsideredcovariatestobein‐formativeiftheywerebothgt20AICclessthanthenullmodelandhadβcoefficient95confidenceintervalsthatdidnotincludezeroUsing the informative covariates fromdetection tiers1and2weconstructedasetofdensitymodels(habitatcovariatesondensity)thataccountedfor imperfectdetection (a)saplingcover (b)shrubcover (c) forbcover (d)grasscoverand (e)anullmodelThenullmodelcontainedonlyintercepttermsandtheinformativeparame‐tersfordetectionPriortomodellingallcontinuouscovariateswerestandardizedusingthescalefunctioninbaseRModelrankingwasdoneusing the ldquoaictabrdquo functionof thepackage ldquoAICcmodavgrdquoAllmodelswerefitassumingaPoissondistributioninldquogdistsamprdquoandmodelfitwasassessedbycalculatingavarianceinflationfactor(chatchatchatc)usingtheunmarkedfunctionldquofitstatsrdquo (KeacuteryampRoyle2015)Weconsideredallmodelslt20AICctobecompetingandequallysupportedbythedata(BurnhamampAnderson2002)
27emsp|emspPoisson generalized linear models
WeusedaPoissongeneralized linearmodels inR (using the ldquoglmrdquofunction)tomodelBombus sppabundancealongfixed‐radiustran‐sectsandnetcountsThisallowedustocomparehabitat‐abundancerelationshipsgeneratedfromHDSmodelstothosegeneratedfrommethodsthatdonotaccountfordetectionprobabilityAswithour
HDSmodels Poisson regressionmodels allowed us tomodel beecountsasafunctionofhabitatcovariates(a)saplingcover(b)shrubcover (c) forbcover (d)grasscover and (e) anull (intercept‐only)modelWemodelled our fixed‐radius transect counts by truncat‐ing allHDS‐transect databy2mof the transect line and treatingthedataasarawcount(HanleyAwbiampFranco2014Scheperetal 2015) which is a standard technique when conducting visualencounter surveys Net count data were modelled in a compara‐blemanner such that raw countsweremodelled as a function ofhabitat covariatesWedid not account for imperfect detection ineither of these models but rather modelled Bombus spp countarea interpretedasadensityWeagainusedan information‐theo‐reticapproach(Anderson2007)withmodelrankingbasedonAICc consideringmodelslt20AICctobeequallysupportedbythedata(BurnhamampAnderson2002)Wealsousedsingle‐covariatemodelstoavoidoverlycomplexmodelsandtheinclusionofuninformativeparameterswithintopmodels(Arnold2010)
3emsp |emspRESULTS
Wedetected194individualBombus sppwithin5mofwhich136werewithin2mof the transect lineDuringaerialnetcountswecapturedn = 201 BombussppworkersOfthebeescapturedduringaerial net countsover50wereB impatienswith the remainderbeingamixedcommunityoflesscommonspecieslikeB bimaculatus and B vagans
31emsp|emspDetection probability
Ofthreedetectionfunctionmodelsweranthebest‐rankedmodelincludedanexponentialdetectionfunctionwheredetectionprob‐abilitygt5mfromthetransectwasasymp0(Figure2)Usinganexponen‐tialdetection functionwe foundthatdetectionprobabilityvariedas a functionof time since1000 (theearliestpossible start time)
F I G U R E 2 emspFrequencyofdetections(greybarsrightaxis)forBombussppwithinregeneratingtimberharvestsDetectionprobability(leftaxis)declinedasafunctionofdistancefromtransectandwasfittoanexponentialdetectionfunction(blackline)Bombussppwereonlyrarelydetectedfurtherthan5mfromthetransectline
230emsp |emsp emspensp McNEIL Et aL
andobserverIDsuggestingthatthelatestsurveysofeachdayhadthe lowestdetectionprobability and thatobserverswereunequalin their ability to detectBombus spp (Table 1 Figure 3a) Amongmodels investigating the relationship between habitat covariatesand Bombus spp detection the model that included grass cover()wastheonlysupportedmodelandsuggestedthatBombussppweremorereadilydetectedatsiteswithmoregrasscover(Table1Figure3b)Allothercovariatesmodelledintiers1and2weregt20AICc less than the nullmodel and theβ 95 confidence intervalsoverlappedzero
32emsp|emspHabitat modelling
Models from all three analyses yielded discernable habitat asso‐ciationswithBombus sppabundance (Table2Figure4)All threeanalyses indicated thatBombus spp abundanceduring the surveyperiodwas negatively associatedwith per cent sapling cover andnotassociatedwithforbcover (Table2Figure4)The importanceofshrubcoverandgrasscoveraspredictorsofBombussppcountsandestimatedabundancevariedacrossmethods(Table2)HDSandtransectcountsrevealedsupportforshrubcoverasaninformativecovariatebeinggt20AICc less than thenull andhavingparameter
95confidence intervals thatdidnotoverlapzero (Table2)Onlynet counts suggested that grass cover was positively associatedwithBombus sppabundancewhileHDSsuggestedthatgrasscoverwasinsteadcorrelatedpositivelywithdetectionprobabilitybutnotabundance (Table 2 Figure 4) In contrast our net count analysissuggestednoeffectofshrubcoveronbeecountswiththeldquoshrubrdquomodel ranked lower than thenullmodeland the shrubparameter95confidenceintervalsoverlappingzero(Table2)Ourtop‐rankedHDSmodel(ldquosaplingrdquo)showedevidenceofminoroverdispersion(chatchatchatc=133)whilemostothermodelsdidnotappearoverdispersed (chatchatchatclt10 with a mean chatchatchatc=101acrossmodels inourfinalHDSmodelset)Weconsidered this an acceptable level of overdispersion and did notuse a variance inflation factor to adjust our parameter estimates(BurnhamampAnderson2002)
33emsp|emspDensity estimation
Inadditiontoexaminingabundanceasafunctionofhabitatamongthe three methods we compared their estimated mean densitiesof foragingBombus spp basedon intercept‐only abundancemod‐els(includingdetectioncovariatesforHDS)EstimatedBombusspp
Model name K AICc ΔAICc AICc Wt β estimate (95CI)
Surveycovariatesondetectionprobability
p(observer) 7 34893 000 078 058(021to095)
p(time) 7 35156 264 021 minus023(minus038tominus008)
p () 6 35829 936 001 ‐
p(wind) 7 35987 1094 000 minus016(minus044to013)
p(temp) 7 36064 1172 000 minus005(minus019to009)
Sitecovariatesondetectionprobability
p(grass) 7 35267 000 085 035(007to063)
p(forb) 7 35827 561 005 017(minus004to037)
p() 6 35829 562 005 ‐
p(shrub) 7 35965 699 003 minus013(minus035to009)
p (sapling) 7 36048 782 002 010(minus016to036)
NoteModelsareranked indescendingorderofAkaikersquos InformationCriterionadjustedforsmallsamplesize(AICc)Surveycovariatesincludedtimesincesurveystarttime(continuousldquotimerdquo)tem‐perature(continuous)cloudcover(overcastcontinuous)observer(categorical)andwindindex(categorical)Sitecovariatesincludedpercentcoverasmeasuredby50mradiusvegetationsurveysforvegetationstructuresaplingsshrubs forbsandgrassBothcandidatemodelsetsarerankedagainstanullintercept‐onlymodelBelowwereportnumberofmodelparameters(k)ΔAICcAICc weight(AICcWt)andβparameterestimates(95confidenceinterval)
TA B L E 1 emspHierarchicaldistancemodelsofdetectionprobabilityasafunctionofsurveycovariates(Tier1top)andsitecovariates(Tier2bottom)
F I G U R E 3 emspModelsofBombussppdetectionprobabilityasafunctionofsurveytime(left)percentgrasscover(centre)andobserver(right)whilealsobeingmostdetectableclosesttothetransect(all)
emspensp emsp | emsp231McNEIL Et aL
forager density within timber harvests was highest for the HDSmodels(192foragingworkersha95CI153ndash240)andlowestfornetcounts(21foragingworkersha95CI19ndash23Figure5)an89differencebetween the twomethodsTransect countsyielded in‐termediate estimates of density (40 foragingworkersha 95CI34ndash47)andwere80lowerthandensityestimatesfromHDSSite‐specific HDS modelled densities and netting count raw densitieswerecorrelated (Pearsonrsquos r = 031 p=003) though the relation‐shipwasnot11(Figure5)
4emsp |emspDISCUSSION
Ourstudyprovidesthefirstempiricalevidencethatdetectionprob‐abilitiesofBombus sppvaryinwaysthatcanaffectabundanceesti‐matesandinferencesabouthabitatrelationshipsObservationerrorcaused by imperfect detection is one of the central challenges ofecologicalmonitoringprograms(Thompson2002YoccozNicholsampBoulinier 2001)buthas yet tobewidely applied tomonitoringofmany invertebrates includingpollinators (but seeBendeletal2018Lofflandetal2017Mackenzie2003VanStrienTermaatGroenendijkMensingampKery 2010)Methods like distance sam‐plingwhileofferingapotential solution to this challenge are stillunder‐utilized in entomological research Meanwhile distance
samplingandsimilarmethodshavebeenastapleofvertebratewild‐liferesearchfordecades(Bucklandetal2005BurnhamAndersonampLaake1980Seber1986Thomasetal2002)andhavebeenex‐pandedtoestimatepopulationsizehabitat‐specificabundanceforindividualspeciesandcommunities(SillettChandlerRoyleKeacuteryampMorrison2012SollmannGardnerWilliamsGilbertampVeit2016)Althoughourstudyisnotthefirstestimateandaccountfordetec‐tionprobabilityofbumblebees(Lofflandetal2017)nostudybe‐foreourshasdescribedfactorsassociatedwithdetectionprobabilityanddonesoinaHDSframework
Wefoundthatdistancesamplingtransectswerebothasimpleandeffectivesurveymethodforestimatingdensityandhabitatre‐lationships (Buckland et al 2005) Hierarchical distance samplingmodelsareoneofthefewavailablemethodsthatallowresearcherstomodel detection‐adjusted abundancewithonly a single visit toeachsite(Bucklandetal2005KeacuteryampRoyle2015MacKenzieetal 2005)Themethodusesonlynon‐lethal samplingunlike trap‐pingnettingmethods(Tepedinoetal2015)whichisespeciallyde‐sirablewhen sampling for speciesof conservation concern or forcommonspecies in areaswherecapture‐based sampling isnot al‐lowedAdditionallyHDSmodelsarealsousefulbecausetheoutputisaneasily interpretedlatentstatedensitywithunits inldquoanimalsareardquo In our study HDS models generated estimates of foragingBombus sppworkerdensity
Model name K AICc ΔAICc AICc Wt β estimate (95CI)
Hierarchicaldistancesampling
λ(sapling) 6 33769 000 098 minus030(minus045tominus014)
λ(shrub) 6 34583 813 002 021(005to037)
λ() 5 3502 1251 000 ndash
λ(grass) 6 35041 1271 000 minus017(minus038to005)
λ(forb) 6 35282 1513 000 minus001(minus016to014)
Transectcounts
λ(sapling) 2 27763 000 096 minus144(minus220tominus069)
λ(shrub) 2 28448 685 003 085(025to144)
λ(grass) 2 2898 1217 000 minus093(minus214to028)
λ() 1 29007 1244 000 ‐
λ(forb) 2 29216 1454 000 0133(minus074to101)
Netcounts
λ(sapling) 2 36071 000 100 minus163(minus226tominus101)
λ(grass) 2 38438 2367 000 085(003to167)
λ(shrub) 2 38565 2494 000 041(minus009to090)
λ() 1 38608 2537 000 ndash
λ(forb) 2 38709 2638 000 039(minus031to109)
NoteModelsareranked indescendingorderofAkaikersquos InformationCriterionadjustedforsmallsamplesize(AICc)DistancetransectdataincludedBombussppdetectedfrom0to5malong66mtransectsTransectcounts includedBombus sppdetected from0ndash2malong66m transectsnetcountdatawerecountsofBombus sppwithin15mradiusplotsSitecovariatesincludedpercentcover asmeasured by 50m radius vegetation surveys for vegetation structure saplings shrubsforbsandgrassBelowwereportnumberofmodelparameters(k)AICcΔAICcAICc weight(AICc Wt)andeachcovariateβparameterestimateandβparameterestimates(95confidenceinterval)
TA B L E 2 emspHabitatmodelsderivedfromhierarchicaldistancemodels(top)fixed‐widthtransectmodels(centre)andlinearmodelsofnetcountdata(bottom)allfitusingaPoissondistribution
232emsp |emsp emspensp McNEIL Et aL
DespitebeingamongthelargestandmostconspicuousofNorthAmerican bees (Michener et al 1994) we found that detectionprobability of Bombus spp was imperfect and declined markedlywithdistancefromthesurveytransectwithalmostnodetectionsbeyond5mDetectionprobabilitiesinourstudywereinfluencedbysurvey‐specific(egtimeofday)andsite‐specific(eggrasscover)variableswithdetectionprobabilityhighestinthemorninginmid‐summerandinhabitatswithabundantgrasscoverWithinregener‐atingtimberharvestsinourstudyarealdquograssrdquocoverwastypicallylow‐growing monocotyledons like Carex pennsylvanica Abundantlow‐growing sedge allowed observers to view Bombus spp fromgreaterdistancesthanwhensitesweredominatedbytallsaplingsshrubs or forbs (egSolidago) Consequently studieswithin habi‐tatsdominatedbylowgrassorothershortvegetationmightfindde‐tectionprobabilityforBombusspptobereliableatdistancesgt5mAlthoughweareuncertainastowhyBombussppwerelessdetect‐ableduringsurveysconductedlaterintheafternoononeplausibleexplanationisthatlongershadowscastbylateafternoonlightmade
Bombussppmoredifficulttodetectwhenforagingin lowvegeta‐tionAdditionalworkexploringthedriversassociatedwithBombus sppdetectionwouldprovevaluabletomonitoringregimesaimedatsurveyingbumblebees
ThoughourstudyisnotacomprehensivehabitatassessmentforBombussppwithinregeneratingtimberharvestsofeasternforestsourresultsprovideaglimpseintothehabitatdynamicsofbumble‐beesinregeneratingforestsduringmid‐summerOurfindingsthatBombus sppwerepositivelyassociatedwithshrubsandnegativelyassociatedwithsaplingscanbeexplainedprimarilybyflowerphe‐nology during our survey window Regenerating saplings withinthe timber harvests we monitored were largely oaks hickoriesblackcherry (Prunus serotina)andredmaple (Acer rubrumWherryetal1979)Thesespeciesdonot flowerassmallsaplingsanddosoinearlyspringasmaturetrees(ieoutsidethesamplingperiodWherryetal1979)Incontrastseveralspeciesofshrubwereflow‐eringduringsamplingincludingblackhuckleberry(Gaylussacia bac‐cata)andhillsideblueberryIncontrastmostforbs(eggoldenrod
F I G U R E 4 emspModelledhabitatassociationsbetweenBombussppandstructuralvegetationfeatureswithinregeneratingtimberharvestsaspredictedbyhierarchicaldistancemodels(top)fixed‐width(4m)transectcounts(centre)andnetcounts(bottom)Variablesshownaresaplingcover(left)shrubcover(centre)andgrasscover(right)Solidlinesrepresentmodelpredictionswithdashedlinesas95confidenceintervalsRelationshipsmarkedwithanasteriskwerethosewithmodelsupport(iemoreinformativethananullmodelandβ95CInon‐overlappingzero)
F I G U R E 5 emspLeftBombusspppredictedmeandensityformodelsofnetcounts(ldquoncrdquo)transectcounts(ldquotcrdquo)andhierarchicaldistancesamplingmodels(ldquohdsrdquo)RightPredicteddensity(workersha)generatedfromourtop‐rankedhierarchicaldistancemodel(p [observer+time+grass]λ[sapling])regressedagainstcountdatafromBombus sppnetcounts
emspensp emsp | emsp233McNEIL Et aL
SolidagosppsnakerootAgeratina spp)hadnotbegunfloweringyetFutureworkshouldexplorehowBombussppmaytrackresourcesacrossagrowingseasontopersistwithineasternforestecosystems
Monitoringprograms forBombus spp andothernativepolli‐natorscanbeimprovedbyincorporatingstudydesignandmodel‐based approaches for minimizing detection error Although weincludedseveraldesign‐basedsolutionsforminimizingdetectionerror(egrestrictingsurveytimesonlysurveyinginfairweatherWard et al 2014) detection probability remained imperfectand varied due to time of day observer and vegetation coverConsequentlymethodsthatignoreddetectionprobabilitygener‐ated density estimates 80ndash89 lower than HDS Past studieshaveshowntheimportanceofusingdesign‐basedapproachestominimize false negativeswhen sampling bees (BuchananGibbsKomondyampSzendrei2017)Ourstudydemonstratesthevalueofusingbothdesign‐andmodel‐basedapproachesforreducingsam‐plingerrorscausedbyimperfectdetectionOtherstudysystemswith thick vegetation cover such as prairies and forested wet‐landsorobstructiveobjectssuchasurbanenvironmentsarealsolikely to underestimate bee abundance even if multiple design‐basedapproachesareusedWhiletraditionalsamplingtechniquesthat do not account for detection have numerous applicationsourstudyhighlightstheimportanceofincorporatingmodel‐basedapproachesforaccountingfordetectionprobabilitywithinnativebeesurveysparticularlywhenattemptingtoestimatebeeabun‐danceordensity
Althoughour results suggest thatHDS representsapromisingtoolformonitoringbumblebeesresearcherswishingtoemploythemethod should recognize its associated limitations For exampledistancemodelsassumethatallanimalsonthetransectlinearede‐tectedperfectlyAlthoughitislikelythisassumptionwasmetwithalargeinsectlikeBombussppthisassumptionmightbeviolatedwithsmallerinsectsMoreoversubjectsareassumedtobeuniformlydis‐tributedinamannerunaffectedbytheobserverWhileitispossiblethatBombussppwerefrightenedbyobserverswetookcaretonotethe locationof first detection forBombus spp apparently flushedandtheirloudflightmadeclosedetectionsalmostcertainWenotethat thismethodwouldnotworkwell for species‐level identifica‐tionbecauseobservationsaremadefromadistanceandsomebeegeneraareexceedinglydifficulttoidentifyevenwithamicroscope(Michener et al 1994)Misidentification of specieswould consti‐tuteafalsepositivewhichwouldviolateanassumptionofdistancesampling
Anotherconsiderationofthisstudydesignandmanymethodsofabundanceestimationisthatanimalsmayviolatetheclosureas‐sumptionInthecaseofBombussppthislikelyoccurredasforagersflew in‐ and out‐ of the effective survey area (~5m from the ob‐serverforHDS)WhilethismayconstituteaproblemforsomestudyobjectivesandmethodswehavenoreasontobelievethatBombus sppmovementwasnonrandomwithrespecttotheobserverandanaccuratedensitycouldthereforestillbemadewhenpassivecountingwasusedClosureviolationmaybeamoreimportantproblemwhenattempting tocalculatedensity fromanettingplotwhereanimals
mayentertheplotandbeunabletoleaveastheyarecapturedandhelduntil thesurveyhasfinished Insuchcasesmovementwouldbebiasedbyindividualsimmigratingintothemonitoredplotbutun‐abletoemigrateandmovementwouldbebiasedtowardstheplotAlthough net‐based sampling is often preferable for investigatingspecies‐specific habitat relationships the potential for movementbias highlights the need for cautious interpretation of net‐baseddensityestimatesforbeesSimilarlyresearchersshouldconsiderthepotentialfordouble‐countingsubjectsAlthoughBombussppinourstudywereapparentlyfewenoughandslowenoughtoavoidmostdouble‐countingthismaybeamoreimportantproblemtoconsiderformoreabundantinsectswithreduceddetectability(egHalictids)
Wealsoadvisecautionwith interpretationofhabitatrelation‐shipsreportedhereasourstudyshouldbe interpretedasasmallldquosnapshotrdquo in time and lacking species‐specific habitat relation‐ships(OlesenBascompteElberlingampJordano2008)Full‐seasonhabitat associations are temporally dynamic forBombus spp andvaryacrossspecies(Goulson1999JhaampKremen2013)Relativefloral resourceavailabilityofdifferentspecieschangesacrosstheseasonandfuturestudiesemployingthesemethodsatregularin‐tervals from early springwhen queens first emerge through lateautumnwould prove valuable In fact examination of queen beedensities would likely prove a better assessment of populationdensityandhabitatqualitythanworkerdensitywhenmonitoringorresearchingcolonialorganismssuchasbumblebeesestimatingthetruenumberofreproducingcoloniesisofmorevaluethanes‐timating the number of foragingworkers aswe have done hereConductingHDSduringthespringandearlysummerwhenqueensare theonly activebumblebee foragersmayprove auseful andnon‐lethalapproachtoestimating theabundanceof reproductiveindividualsandtheexpectednumbersummercoloniesforagivenarea However sampling queens would likely require additionalsamplingsitesorrepeatvisitbecausecountswouldbemuchlowerandHDSmodelsmayhavetroubleconvergingwithrelativelyfewsampling locations Caution should also be exercised with inter‐pretation ofBombus spp density estimates reported here as ourdensitieslikelyconsistofmultiplespeciesofBombus modelled and reportedasoneWealsorecommendfuturestudiesexplorehownon‐Bombusgenera(ormorphospeciesfunctionalgroups)performasthefocusofHDSmodelsAlthoughHDS isnotwithout limita‐tionwebelieveourstudyhighlightstheutilityofHDSmodelsforestimatingdensitiesandelucidatinghabitatassociationsofbumblebeeswhenindividualsaredetectedimperfectly
ACKNOWLEDG EMENTS
Wethank the following individuals andagencies for their supportandlandaccessSproulStateForestandMoshannonStateForestFunding was provided by the Indiana University of PennsylvaniaBUREfundandtheUnitedStatesDepartmentofAgricultureNaturalResources Conservation Service (68‐7482‐12‐502) through theConservationEffectsAssessmentProjectWeareverygrateful toJoanMilamandSamDroegefortheircommentsonearlyversions
234emsp |emsp emspensp McNEIL Et aL
of thismanuscriptWearealsoverygrateful to threeanonymousreviewers spend considerable time strengthening thismanuscriptFundersofourprojectdidnothaveanyinfluenceonthecontentofthesubmittedmanuscriptnordidtheyrequireapprovalofthefinalmanuscripttobepublishedAnyuseoftradefirmorproductnamesisfordescriptivepurposesonlyanddoesnotimplyendorsementbytheUSGovernment
AUTHORSrsquo CONTRIBUTIONS
DJMCRVOELMandJLLconceived researchDJMandELMcol‐lected field data DJM CRVO and ELM conducted statisticalanalysesDJMCRVOELMKRUMDEKADRand JLLwrote themanuscriptJLLsecuredfundingAllauthorsreadandapprovedthemanuscript
ORCID
Darin J McNeil httporcidorg0000‐0003‐4595‐8354
Clint R V Otto httporcidorg0000‐0002‐7582‐3525
Amanda D Rodewald httporcidorg0000‐0002‐6719‐6306
R E FE R E N C E S
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AndersonDR(2007)Model based inference in the life sciences A primer on evidenceBerlinGermanySpringerScienceampBusinessMedia
Arnold T W (2010) Uninformative parameters and model selectionusingAkaikesInformationCriterionJournal of Wildlife Management741175ndash1178httpsdoiorg101111j1937‐28172010tb01236x
Ashman T L Knight TM Steets J A Amarasekare P BurdMCampbellDRhellipMorganMT (2004)Pollen limitationofplantreproductionEcologicalandevolutionarycausesandconsequencesEcology852408ndash2421httpsdoiorg10189003‐8024
BendelCRHovickTJLimbRFampHarmonJP(2018)Variationin grazing management practices supports diverse butterflycommunitiesacrossgrasslandworking landscapesJournal of Insect Conservation221ndash13httpsdoiorg101007s10841‐017‐0041‐9
BuchananALGibbsJKomondyLampSzendreiZ(2017)Beecom‐munityof commercial potato fields inMichigan andBombus impa‐tiensvisitationtoneonicotinoid‐treatedpotatoplantsInsects830httpsdoiorg103390insects8010030
BucklandSTAndersonDRBurnhamKPampLaake JL (2005)Distance samplingHobokenNJJohnWileyampSonsLtd
BurnhamKPampAndersonDR(2002)Model selection and multimodel inference A practical information‐theoretic approachBerlinGermanySpringerScienceampBusinessMedia
BurnhamKPAndersonDRampLaakeJL(1980)Estimationofden‐sity from line transect sampling of biological populationsWildlife Monographs723ndash202
Calderone N W (2012) Insect pollinated crops insect pollinatorsandUSagricultureTrendanalysisofaggregatedatafortheperiod1992ndash2009 PLoS ONE7 e37235 httpsdoiorg101371journalpone0037235
CameronSALozierJDStrangeJPKochJBCordesNSolterL F amp Griswold T L (2011) Patterns of widespread decline in
NorthAmericanbumblebeesProceedings of the National Academy of Sciences108662ndash667httpsdoiorg101073pnas1014743108
RCore Team (2018)R A language and environment for statistical com‐puting Vienna Austria R Foundation for Statistical ComputingRetrievedfromhttpswwwR‐projectorg
Environmental Systems Research Institute (2011) ArcGIS Desktop Release 10RedlandsCaliforniaESRI
Fiske IampChandlerRB (2011)UnmarkedAnRpackage for fittinghierarchicalmodelsofwildlifeoccurrenceandabundanceJournal of Statistical Software431ndash23
Garibaldi L A Steffan‐Dewenter I Winfree R Aizen M ABommarcoRCunninghamSAhellipBartomeusI(2013)Wildpolli‐natorsenhancefruitsetofcropsregardlessofhoneybeeabundanceScience3391608ndash1611httpsdoiorg101126science1230200
Goulson D (1999) Foraging strategies of insects for gathering nec‐tar and pollen and implications for plant ecology and evolutionPerspectives in Plant Ecology Evolution and Systematics2 185ndash209httpsdoiorg1010781433‐8319‐00070
GoulsonDLyeGCampDarvillB(2008)DeclineandconservationofbumblebeesAnnual Review of Entomology53191ndash208httpsdoiorg101146annurevento53103106093454
GoulsonDNicholls E Botiacuteas C amp Rotheray E L (2015) Bee de‐clines driven by combined stress from parasites pesticides andlack of flowers Science 347 1255957 httpsdoiorg101126science1255957
Hammond P S Berggren P Benke H Borchers D L Collet AHeide‐Joslashrgensen M P hellip Oslashien N (2002) Abundance of har‐bour porpoise and other cetaceans in the North Sea and adja‐cent waters Journal of Applied Ecology 39 361ndash376 httpsdoiorg101046j1365‐2664200200713x
HanleyMEAwbiAJampFrancoM(2014)GoingnativeFlowerusebybumblebeesinEnglishurbangardensAnnals of Botany113799ndash806httpsdoiorg101093aobmcu006
Hau E amp Von Renouard H (2006) The wind resource London UKElsevier
Hedley S L amp Buckland S T (2004) Spatial models for line tran‐sect sampling Journal of Agricultural Biological and Environmental Statistics9181ndash199httpsdoiorg1011981085711043578
JamesFCampShugartHHJr(1970)AquantitativemethodofhabitatdescriptionAudubon Field Notes24727ndash736
Jepsen S Evans E Thorp R Hatfield R amp Black S H (2003)Petition to list the rusty patched bumble bee Bombus affinis (Cresson) 1863 as an endangered species under the US Endangered Species Act Retrieved from httpwwwxercesorgwp‐ontentuploads 201301Bombus‐petitionpdf
Jha S amp Kremen C (2013) Resource diversity and landscape‐levelhomogeneitydrivenativebee foragingProceedings of the National Academy of Sciences 110 555ndash558 httpsdoiorg101073pnas1208682110
KaranthKUampSunquistME(1995)PreyselectionbytigerleopardanddholeintropicalforestsJournal of Animal Ecology64439ndash450httpsdoiorg1023075647
KeacuteryMampRoyleJA (2015)Applied Hierarchical Modeling in Ecology Analysis of distribution abundance and species richness in R and BUGS Volume 1 Prelude and Static ModelsCambridgeMAAcademicPress
KeacuteryM amp Schmidt B R (2008) Imperfect detection and its conse‐quencesformonitoringforconservationCommunity Ecology9207ndash216httpsdoiorg101556ComEc92008210
Kevan PG (1990)Pollination keystone process in sustainable globalproductivity InVIInternationalSymposiumonPollination288(pp103‐110)
Kremen CWilliams NM amp Thorp RW (2002) Crop pollinationfromnativebeesatriskfromagriculturalintensificationProceedings of the National Academy of Sciences99 16812ndash16816 httpsdoiorg101073pnas262413599
emspensp emsp | emsp235McNEIL Et aL
LofflandH L Polasik J S TingleyMW Elsey E A Loffland CLebuhnGampSiegelRB(2017)Bumblebeeuseofpost‐firechap‐arralinthecentralSierraNevadaThe Journal of Wildlife Management811084ndash1097httpsdoiorg101002jwmg21280
MackenzieD I (2006)Modelingtheprobabilityof resourceuseTheeffectofanddealingwithdetectingaspeciesimperfectlyJournal of Wildlife Management70367ndash374httpsdoiorg1021930022‐541X(2006)70[367MTPORU]20CO2
MacKenzieDINicholsJDLachmanGBDroegeSAndrewRoyleJampLangtimmCA(2002)Estimatingsiteoccupancyrateswhende‐tectionprobabilitiesarelessthanoneEcology832248ndash2255httpsdoiorg1018900012‐9658(2002)083[2248ESORWD]20CO2
MacKenzieDINicholsJDRoyleJAPollockKHBaileyLampHinesJE(2005)Occupancy estimation and modeling Inferring pat‐terns and dynamics of species occurrenceLondonUKElsevier
Mackenzie D I (2003) Assessing site occupancymodelling as a toolfor monitoring Mahoenui giant weta populations Department ofConservation17
Marques T A Thomas L Fancy S G amp Buckland S T (2007)Improvingestimatesofbirddensityusingmultiple‐covariatedistancesamplingThe Auk1241229ndash1243httpsdoiorg1016420004‐8038(2007)124[1229IEOBDU]20CO2
McCaskillGLMcWilliamsWHAlerichCAButlerBJCrockerS JDomkeGMhellipWestfall JA (2009)Pennsylvaniarsquos Forests 2009NewtownSquarePAUSDepartmentofAgricultureForestServiceNorthernResearchStation
MichenerCDMcGinleyRJampDanforthBN(1994)The Bee Genera of North and Central AmericaWashingtonDCSmithsonianInstitutePress
OlesenJMBascompteJElberlingHampJordanoP(2008)TemporaldynamicsinapollinationnetworkEcology891573ndash1582httpsdoiorg10189007‐04511
PerssonA S RundloumlfMCloughYampSmithHG (2015)Bumblebees show trait‐dependent vulnerability to landscape simplifica‐tion Biodiversity and Conservation 24 3469ndash3489 httpsdoiorg101007s10531‐015‐1008‐3
Potts SGVulliamyBDafniANeemanGampWillmer P (2003)Linking bees and flowers How do floral communities structurepollinator communities Ecology 84 2628ndash2642 httpsdoiorg10189002‐0136
PottsSGBiesmeijerJCKremenCNeumannPSchweigerOampKuninWE (2010)Globalpollinatordeclinestrends impactsanddriversTrends in ecology amp evolution25(6)345ndash353
Redhead JW Dreier S Bourke A F HeardM S JordanW CSumner S hellip Carvell C (2016) Effects of habitat compositionandlandscapestructureonworkerforagingdistancesoffivebum‐ble bee species Ecological Applications 26 726ndash739 httpsdoiorg10189015‐0546
Roulston T A H Smith S A amp Brewster A L (2007) A com‐parison of pan trap and intensive net sampling techniques fordocumenting a bee (Hymenoptera Apiformes) fauna Journal of the Kansas Entomological Society 80 179ndash181 httpsdoiorg1023170022‐8567(2007)80[179ACOPTA]20CO2
Royle J A Dawson D K amp Bates S (2004) Modeling abundanceeffects in distance sampling Ecology 85 1591ndash1597 httpsdoiorg10189003‐3127
Scheper J Bommarco R Holzschuh A Potts S G Riedinger VRoberts S P hellipWickens V J (2015) Local and landscape‐level
floral resources explain effects of wildflower strips on wild beesacrossfourEuropeancountriesJournal of Applied Ecology521165ndash1175httpsdoiorg1011111365‐266412479
SeberGA(1986)AreviewofestimatinganimalabundanceBiometrics42267ndash292httpsdoiorg1023072531049
ShultzCH(1999)The Geology of PennsylvaniaPennsylvaniaGeologicalSurveyHarrisburgPAPennsylvaniaGeologicalSurvey
Sillett T S Chandler R B Royle J A KeacuteryM ampMorrison S A(2012) Hierarchical distance‐sampling models to estimate popu‐lation size and habitat‐specific abundance of an island endemicEcological Applications22(7)1997ndash2006
SollmannRGardnerBWilliamsKAGilbertATampVeitRR(2016)AhierarchicaldistancesamplingmodeltoestimateabundanceandcovariateassociationsofspeciesandcommunitiesMethods in Ecology and Evolution7529ndash537httpsdoiorg1011112041‐210X12518
Tepedino V J Durham S Cameron S A amp Goodell K (2015)Documenting bee decline or squandering scarce resourcesConservation Biology 29 280ndash282 httpsdoiorg101111cobi12439
Thomas LBuckland S TBurnhamKPAndersonDR Laake JL Borchers D L amp Strindberg S (2002) Distance samplingEncyclopediaofenvironmetrics
Thomas L Buckland S T Rexstad EA Laake J L Strindberg SHedley S L hellipBurnham K P (2010)Distance softwareDesignand analysis of distance sampling surveys for estimating pop‐ulation size Journal of Applied Ecology 47 5ndash14 httpsdoiorg101111j1365‐2664200901737x
ThompsonWL (2002)TowardsreliablebirdsurveysAccountingforindividualspresentbutnotdetectedThe Auk11918ndash25httpsdoiorg1016420004‐8038(2002)119[0018TRBSAF]20CO2
VanStrienA JTermaatTGroenendijkDMensingVampKeryM(2010) Site‐occupancy models may offer new opportunities fordragonflymonitoringbasedondailyspecies listsBasic and Applied Ecology11495ndash503httpsdoiorg101016jbaae201005003
VilsackTampMcCarthyG(2015)National strategy to promote the health of honey bees and other pollinatorsWashingtonDCReport IssuedbytheWhiteHousethePollinatorHealthTaskForce
WardKCariveauDMayERoswellMVaughanMWilliamsNhellip Gill K (2014) Streamlined Bee Monitoring Protocol for Assessing Pollinator HabitatPortlandORTheXercesSocietyforInvertebrateConservation
WeatherUndergroundInc(2018)WeatherForecastandReports‐LongRangeandLocalWundergroundRetrievedfromhttpswwwwun‐dergroundcom
WherryET Fogg JM JrampWahlHA (1979)Atlas of the flora of Pennsylvania Philadelphia PA The Morris Arboretum of theUniversityofPennsylvania
YoccozNGNichols JDampBoulinierT (2001)Monitoringofbio‐logicaldiversityinspaceandtimeTrends Ecology and Evolution16446ndash453
How to cite this articleMcNeilDJOttoCRVMoserELetalDistancemodelsasatoolformodellingdetectionprobabilityanddensityofnativebumblebeesJ Appl Entomol 2019143225ndash235 httpsdoiorg101111jen12583
230emsp |emsp emspensp McNEIL Et aL
andobserverIDsuggestingthatthelatestsurveysofeachdayhadthe lowestdetectionprobability and thatobserverswereunequalin their ability to detectBombus spp (Table 1 Figure 3a) Amongmodels investigating the relationship between habitat covariatesand Bombus spp detection the model that included grass cover()wastheonlysupportedmodelandsuggestedthatBombussppweremorereadilydetectedatsiteswithmoregrasscover(Table1Figure3b)Allothercovariatesmodelledintiers1and2weregt20AICc less than the nullmodel and theβ 95 confidence intervalsoverlappedzero
32emsp|emspHabitat modelling
Models from all three analyses yielded discernable habitat asso‐ciationswithBombus sppabundance (Table2Figure4)All threeanalyses indicated thatBombus spp abundanceduring the surveyperiodwas negatively associatedwith per cent sapling cover andnotassociatedwithforbcover (Table2Figure4)The importanceofshrubcoverandgrasscoveraspredictorsofBombussppcountsandestimatedabundancevariedacrossmethods(Table2)HDSandtransectcountsrevealedsupportforshrubcoverasaninformativecovariatebeinggt20AICc less than thenull andhavingparameter
95confidence intervals thatdidnotoverlapzero (Table2)Onlynet counts suggested that grass cover was positively associatedwithBombus sppabundancewhileHDSsuggestedthatgrasscoverwasinsteadcorrelatedpositivelywithdetectionprobabilitybutnotabundance (Table 2 Figure 4) In contrast our net count analysissuggestednoeffectofshrubcoveronbeecountswiththeldquoshrubrdquomodel ranked lower than thenullmodeland the shrubparameter95confidenceintervalsoverlappingzero(Table2)Ourtop‐rankedHDSmodel(ldquosaplingrdquo)showedevidenceofminoroverdispersion(chatchatchatc=133)whilemostothermodelsdidnotappearoverdispersed (chatchatchatclt10 with a mean chatchatchatc=101acrossmodels inourfinalHDSmodelset)Weconsidered this an acceptable level of overdispersion and did notuse a variance inflation factor to adjust our parameter estimates(BurnhamampAnderson2002)
33emsp|emspDensity estimation
Inadditiontoexaminingabundanceasafunctionofhabitatamongthe three methods we compared their estimated mean densitiesof foragingBombus spp basedon intercept‐only abundancemod‐els(includingdetectioncovariatesforHDS)EstimatedBombusspp
Model name K AICc ΔAICc AICc Wt β estimate (95CI)
Surveycovariatesondetectionprobability
p(observer) 7 34893 000 078 058(021to095)
p(time) 7 35156 264 021 minus023(minus038tominus008)
p () 6 35829 936 001 ‐
p(wind) 7 35987 1094 000 minus016(minus044to013)
p(temp) 7 36064 1172 000 minus005(minus019to009)
Sitecovariatesondetectionprobability
p(grass) 7 35267 000 085 035(007to063)
p(forb) 7 35827 561 005 017(minus004to037)
p() 6 35829 562 005 ‐
p(shrub) 7 35965 699 003 minus013(minus035to009)
p (sapling) 7 36048 782 002 010(minus016to036)
NoteModelsareranked indescendingorderofAkaikersquos InformationCriterionadjustedforsmallsamplesize(AICc)Surveycovariatesincludedtimesincesurveystarttime(continuousldquotimerdquo)tem‐perature(continuous)cloudcover(overcastcontinuous)observer(categorical)andwindindex(categorical)Sitecovariatesincludedpercentcoverasmeasuredby50mradiusvegetationsurveysforvegetationstructuresaplingsshrubs forbsandgrassBothcandidatemodelsetsarerankedagainstanullintercept‐onlymodelBelowwereportnumberofmodelparameters(k)ΔAICcAICc weight(AICcWt)andβparameterestimates(95confidenceinterval)
TA B L E 1 emspHierarchicaldistancemodelsofdetectionprobabilityasafunctionofsurveycovariates(Tier1top)andsitecovariates(Tier2bottom)
F I G U R E 3 emspModelsofBombussppdetectionprobabilityasafunctionofsurveytime(left)percentgrasscover(centre)andobserver(right)whilealsobeingmostdetectableclosesttothetransect(all)
emspensp emsp | emsp231McNEIL Et aL
forager density within timber harvests was highest for the HDSmodels(192foragingworkersha95CI153ndash240)andlowestfornetcounts(21foragingworkersha95CI19ndash23Figure5)an89differencebetween the twomethodsTransect countsyielded in‐termediate estimates of density (40 foragingworkersha 95CI34ndash47)andwere80lowerthandensityestimatesfromHDSSite‐specific HDS modelled densities and netting count raw densitieswerecorrelated (Pearsonrsquos r = 031 p=003) though the relation‐shipwasnot11(Figure5)
4emsp |emspDISCUSSION
Ourstudyprovidesthefirstempiricalevidencethatdetectionprob‐abilitiesofBombus sppvaryinwaysthatcanaffectabundanceesti‐matesandinferencesabouthabitatrelationshipsObservationerrorcaused by imperfect detection is one of the central challenges ofecologicalmonitoringprograms(Thompson2002YoccozNicholsampBoulinier 2001)buthas yet tobewidely applied tomonitoringofmany invertebrates includingpollinators (but seeBendeletal2018Lofflandetal2017Mackenzie2003VanStrienTermaatGroenendijkMensingampKery 2010)Methods like distance sam‐plingwhileofferingapotential solution to this challenge are stillunder‐utilized in entomological research Meanwhile distance
samplingandsimilarmethodshavebeenastapleofvertebratewild‐liferesearchfordecades(Bucklandetal2005BurnhamAndersonampLaake1980Seber1986Thomasetal2002)andhavebeenex‐pandedtoestimatepopulationsizehabitat‐specificabundanceforindividualspeciesandcommunities(SillettChandlerRoyleKeacuteryampMorrison2012SollmannGardnerWilliamsGilbertampVeit2016)Althoughourstudyisnotthefirstestimateandaccountfordetec‐tionprobabilityofbumblebees(Lofflandetal2017)nostudybe‐foreourshasdescribedfactorsassociatedwithdetectionprobabilityanddonesoinaHDSframework
Wefoundthatdistancesamplingtransectswerebothasimpleandeffectivesurveymethodforestimatingdensityandhabitatre‐lationships (Buckland et al 2005) Hierarchical distance samplingmodelsareoneofthefewavailablemethodsthatallowresearcherstomodel detection‐adjusted abundancewithonly a single visit toeachsite(Bucklandetal2005KeacuteryampRoyle2015MacKenzieetal 2005)Themethodusesonlynon‐lethal samplingunlike trap‐pingnettingmethods(Tepedinoetal2015)whichisespeciallyde‐sirablewhen sampling for speciesof conservation concern or forcommonspecies in areaswherecapture‐based sampling isnot al‐lowedAdditionallyHDSmodelsarealsousefulbecausetheoutputisaneasily interpretedlatentstatedensitywithunits inldquoanimalsareardquo In our study HDS models generated estimates of foragingBombus sppworkerdensity
Model name K AICc ΔAICc AICc Wt β estimate (95CI)
Hierarchicaldistancesampling
λ(sapling) 6 33769 000 098 minus030(minus045tominus014)
λ(shrub) 6 34583 813 002 021(005to037)
λ() 5 3502 1251 000 ndash
λ(grass) 6 35041 1271 000 minus017(minus038to005)
λ(forb) 6 35282 1513 000 minus001(minus016to014)
Transectcounts
λ(sapling) 2 27763 000 096 minus144(minus220tominus069)
λ(shrub) 2 28448 685 003 085(025to144)
λ(grass) 2 2898 1217 000 minus093(minus214to028)
λ() 1 29007 1244 000 ‐
λ(forb) 2 29216 1454 000 0133(minus074to101)
Netcounts
λ(sapling) 2 36071 000 100 minus163(minus226tominus101)
λ(grass) 2 38438 2367 000 085(003to167)
λ(shrub) 2 38565 2494 000 041(minus009to090)
λ() 1 38608 2537 000 ndash
λ(forb) 2 38709 2638 000 039(minus031to109)
NoteModelsareranked indescendingorderofAkaikersquos InformationCriterionadjustedforsmallsamplesize(AICc)DistancetransectdataincludedBombussppdetectedfrom0to5malong66mtransectsTransectcounts includedBombus sppdetected from0ndash2malong66m transectsnetcountdatawerecountsofBombus sppwithin15mradiusplotsSitecovariatesincludedpercentcover asmeasured by 50m radius vegetation surveys for vegetation structure saplings shrubsforbsandgrassBelowwereportnumberofmodelparameters(k)AICcΔAICcAICc weight(AICc Wt)andeachcovariateβparameterestimateandβparameterestimates(95confidenceinterval)
TA B L E 2 emspHabitatmodelsderivedfromhierarchicaldistancemodels(top)fixed‐widthtransectmodels(centre)andlinearmodelsofnetcountdata(bottom)allfitusingaPoissondistribution
232emsp |emsp emspensp McNEIL Et aL
DespitebeingamongthelargestandmostconspicuousofNorthAmerican bees (Michener et al 1994) we found that detectionprobability of Bombus spp was imperfect and declined markedlywithdistancefromthesurveytransectwithalmostnodetectionsbeyond5mDetectionprobabilitiesinourstudywereinfluencedbysurvey‐specific(egtimeofday)andsite‐specific(eggrasscover)variableswithdetectionprobabilityhighestinthemorninginmid‐summerandinhabitatswithabundantgrasscoverWithinregener‐atingtimberharvestsinourstudyarealdquograssrdquocoverwastypicallylow‐growing monocotyledons like Carex pennsylvanica Abundantlow‐growing sedge allowed observers to view Bombus spp fromgreaterdistancesthanwhensitesweredominatedbytallsaplingsshrubs or forbs (egSolidago) Consequently studieswithin habi‐tatsdominatedbylowgrassorothershortvegetationmightfindde‐tectionprobabilityforBombusspptobereliableatdistancesgt5mAlthoughweareuncertainastowhyBombussppwerelessdetect‐ableduringsurveysconductedlaterintheafternoononeplausibleexplanationisthatlongershadowscastbylateafternoonlightmade
Bombussppmoredifficulttodetectwhenforagingin lowvegeta‐tionAdditionalworkexploringthedriversassociatedwithBombus sppdetectionwouldprovevaluabletomonitoringregimesaimedatsurveyingbumblebees
ThoughourstudyisnotacomprehensivehabitatassessmentforBombussppwithinregeneratingtimberharvestsofeasternforestsourresultsprovideaglimpseintothehabitatdynamicsofbumble‐beesinregeneratingforestsduringmid‐summerOurfindingsthatBombus sppwerepositivelyassociatedwithshrubsandnegativelyassociatedwithsaplingscanbeexplainedprimarilybyflowerphe‐nology during our survey window Regenerating saplings withinthe timber harvests we monitored were largely oaks hickoriesblackcherry (Prunus serotina)andredmaple (Acer rubrumWherryetal1979)Thesespeciesdonot flowerassmallsaplingsanddosoinearlyspringasmaturetrees(ieoutsidethesamplingperiodWherryetal1979)Incontrastseveralspeciesofshrubwereflow‐eringduringsamplingincludingblackhuckleberry(Gaylussacia bac‐cata)andhillsideblueberryIncontrastmostforbs(eggoldenrod
F I G U R E 4 emspModelledhabitatassociationsbetweenBombussppandstructuralvegetationfeatureswithinregeneratingtimberharvestsaspredictedbyhierarchicaldistancemodels(top)fixed‐width(4m)transectcounts(centre)andnetcounts(bottom)Variablesshownaresaplingcover(left)shrubcover(centre)andgrasscover(right)Solidlinesrepresentmodelpredictionswithdashedlinesas95confidenceintervalsRelationshipsmarkedwithanasteriskwerethosewithmodelsupport(iemoreinformativethananullmodelandβ95CInon‐overlappingzero)
F I G U R E 5 emspLeftBombusspppredictedmeandensityformodelsofnetcounts(ldquoncrdquo)transectcounts(ldquotcrdquo)andhierarchicaldistancesamplingmodels(ldquohdsrdquo)RightPredicteddensity(workersha)generatedfromourtop‐rankedhierarchicaldistancemodel(p [observer+time+grass]λ[sapling])regressedagainstcountdatafromBombus sppnetcounts
emspensp emsp | emsp233McNEIL Et aL
SolidagosppsnakerootAgeratina spp)hadnotbegunfloweringyetFutureworkshouldexplorehowBombussppmaytrackresourcesacrossagrowingseasontopersistwithineasternforestecosystems
Monitoringprograms forBombus spp andothernativepolli‐natorscanbeimprovedbyincorporatingstudydesignandmodel‐based approaches for minimizing detection error Although weincludedseveraldesign‐basedsolutionsforminimizingdetectionerror(egrestrictingsurveytimesonlysurveyinginfairweatherWard et al 2014) detection probability remained imperfectand varied due to time of day observer and vegetation coverConsequentlymethodsthatignoreddetectionprobabilitygener‐ated density estimates 80ndash89 lower than HDS Past studieshaveshowntheimportanceofusingdesign‐basedapproachestominimize false negativeswhen sampling bees (BuchananGibbsKomondyampSzendrei2017)Ourstudydemonstratesthevalueofusingbothdesign‐andmodel‐basedapproachesforreducingsam‐plingerrorscausedbyimperfectdetectionOtherstudysystemswith thick vegetation cover such as prairies and forested wet‐landsorobstructiveobjectssuchasurbanenvironmentsarealsolikely to underestimate bee abundance even if multiple design‐basedapproachesareusedWhiletraditionalsamplingtechniquesthat do not account for detection have numerous applicationsourstudyhighlightstheimportanceofincorporatingmodel‐basedapproachesforaccountingfordetectionprobabilitywithinnativebeesurveysparticularlywhenattemptingtoestimatebeeabun‐danceordensity
Althoughour results suggest thatHDS representsapromisingtoolformonitoringbumblebeesresearcherswishingtoemploythemethod should recognize its associated limitations For exampledistancemodelsassumethatallanimalsonthetransectlinearede‐tectedperfectlyAlthoughitislikelythisassumptionwasmetwithalargeinsectlikeBombussppthisassumptionmightbeviolatedwithsmallerinsectsMoreoversubjectsareassumedtobeuniformlydis‐tributedinamannerunaffectedbytheobserverWhileitispossiblethatBombussppwerefrightenedbyobserverswetookcaretonotethe locationof first detection forBombus spp apparently flushedandtheirloudflightmadeclosedetectionsalmostcertainWenotethat thismethodwouldnotworkwell for species‐level identifica‐tionbecauseobservationsaremadefromadistanceandsomebeegeneraareexceedinglydifficulttoidentifyevenwithamicroscope(Michener et al 1994)Misidentification of specieswould consti‐tuteafalsepositivewhichwouldviolateanassumptionofdistancesampling
Anotherconsiderationofthisstudydesignandmanymethodsofabundanceestimationisthatanimalsmayviolatetheclosureas‐sumptionInthecaseofBombussppthislikelyoccurredasforagersflew in‐ and out‐ of the effective survey area (~5m from the ob‐serverforHDS)WhilethismayconstituteaproblemforsomestudyobjectivesandmethodswehavenoreasontobelievethatBombus sppmovementwasnonrandomwithrespecttotheobserverandanaccuratedensitycouldthereforestillbemadewhenpassivecountingwasusedClosureviolationmaybeamoreimportantproblemwhenattempting tocalculatedensity fromanettingplotwhereanimals
mayentertheplotandbeunabletoleaveastheyarecapturedandhelduntil thesurveyhasfinished Insuchcasesmovementwouldbebiasedbyindividualsimmigratingintothemonitoredplotbutun‐abletoemigrateandmovementwouldbebiasedtowardstheplotAlthough net‐based sampling is often preferable for investigatingspecies‐specific habitat relationships the potential for movementbias highlights the need for cautious interpretation of net‐baseddensityestimatesforbeesSimilarlyresearchersshouldconsiderthepotentialfordouble‐countingsubjectsAlthoughBombussppinourstudywereapparentlyfewenoughandslowenoughtoavoidmostdouble‐countingthismaybeamoreimportantproblemtoconsiderformoreabundantinsectswithreduceddetectability(egHalictids)
Wealsoadvisecautionwith interpretationofhabitatrelation‐shipsreportedhereasourstudyshouldbe interpretedasasmallldquosnapshotrdquo in time and lacking species‐specific habitat relation‐ships(OlesenBascompteElberlingampJordano2008)Full‐seasonhabitat associations are temporally dynamic forBombus spp andvaryacrossspecies(Goulson1999JhaampKremen2013)Relativefloral resourceavailabilityofdifferentspecieschangesacrosstheseasonandfuturestudiesemployingthesemethodsatregularin‐tervals from early springwhen queens first emerge through lateautumnwould prove valuable In fact examination of queen beedensities would likely prove a better assessment of populationdensityandhabitatqualitythanworkerdensitywhenmonitoringorresearchingcolonialorganismssuchasbumblebeesestimatingthetruenumberofreproducingcoloniesisofmorevaluethanes‐timating the number of foragingworkers aswe have done hereConductingHDSduringthespringandearlysummerwhenqueensare theonly activebumblebee foragersmayprove auseful andnon‐lethalapproachtoestimating theabundanceof reproductiveindividualsandtheexpectednumbersummercoloniesforagivenarea However sampling queens would likely require additionalsamplingsitesorrepeatvisitbecausecountswouldbemuchlowerandHDSmodelsmayhavetroubleconvergingwithrelativelyfewsampling locations Caution should also be exercised with inter‐pretation ofBombus spp density estimates reported here as ourdensitieslikelyconsistofmultiplespeciesofBombus modelled and reportedasoneWealsorecommendfuturestudiesexplorehownon‐Bombusgenera(ormorphospeciesfunctionalgroups)performasthefocusofHDSmodelsAlthoughHDS isnotwithout limita‐tionwebelieveourstudyhighlightstheutilityofHDSmodelsforestimatingdensitiesandelucidatinghabitatassociationsofbumblebeeswhenindividualsaredetectedimperfectly
ACKNOWLEDG EMENTS
Wethank the following individuals andagencies for their supportandlandaccessSproulStateForestandMoshannonStateForestFunding was provided by the Indiana University of PennsylvaniaBUREfundandtheUnitedStatesDepartmentofAgricultureNaturalResources Conservation Service (68‐7482‐12‐502) through theConservationEffectsAssessmentProjectWeareverygrateful toJoanMilamandSamDroegefortheircommentsonearlyversions
234emsp |emsp emspensp McNEIL Et aL
of thismanuscriptWearealsoverygrateful to threeanonymousreviewers spend considerable time strengthening thismanuscriptFundersofourprojectdidnothaveanyinfluenceonthecontentofthesubmittedmanuscriptnordidtheyrequireapprovalofthefinalmanuscripttobepublishedAnyuseoftradefirmorproductnamesisfordescriptivepurposesonlyanddoesnotimplyendorsementbytheUSGovernment
AUTHORSrsquo CONTRIBUTIONS
DJMCRVOELMandJLLconceived researchDJMandELMcol‐lected field data DJM CRVO and ELM conducted statisticalanalysesDJMCRVOELMKRUMDEKADRand JLLwrote themanuscriptJLLsecuredfundingAllauthorsreadandapprovedthemanuscript
ORCID
Darin J McNeil httporcidorg0000‐0003‐4595‐8354
Clint R V Otto httporcidorg0000‐0002‐7582‐3525
Amanda D Rodewald httporcidorg0000‐0002‐6719‐6306
R E FE R E N C E S
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AndersonDR(2007)Model based inference in the life sciences A primer on evidenceBerlinGermanySpringerScienceampBusinessMedia
Arnold T W (2010) Uninformative parameters and model selectionusingAkaikesInformationCriterionJournal of Wildlife Management741175ndash1178httpsdoiorg101111j1937‐28172010tb01236x
Ashman T L Knight TM Steets J A Amarasekare P BurdMCampbellDRhellipMorganMT (2004)Pollen limitationofplantreproductionEcologicalandevolutionarycausesandconsequencesEcology852408ndash2421httpsdoiorg10189003‐8024
BendelCRHovickTJLimbRFampHarmonJP(2018)Variationin grazing management practices supports diverse butterflycommunitiesacrossgrasslandworking landscapesJournal of Insect Conservation221ndash13httpsdoiorg101007s10841‐017‐0041‐9
BuchananALGibbsJKomondyLampSzendreiZ(2017)Beecom‐munityof commercial potato fields inMichigan andBombus impa‐tiensvisitationtoneonicotinoid‐treatedpotatoplantsInsects830httpsdoiorg103390insects8010030
BucklandSTAndersonDRBurnhamKPampLaake JL (2005)Distance samplingHobokenNJJohnWileyampSonsLtd
BurnhamKPampAndersonDR(2002)Model selection and multimodel inference A practical information‐theoretic approachBerlinGermanySpringerScienceampBusinessMedia
BurnhamKPAndersonDRampLaakeJL(1980)Estimationofden‐sity from line transect sampling of biological populationsWildlife Monographs723ndash202
Calderone N W (2012) Insect pollinated crops insect pollinatorsandUSagricultureTrendanalysisofaggregatedatafortheperiod1992ndash2009 PLoS ONE7 e37235 httpsdoiorg101371journalpone0037235
CameronSALozierJDStrangeJPKochJBCordesNSolterL F amp Griswold T L (2011) Patterns of widespread decline in
NorthAmericanbumblebeesProceedings of the National Academy of Sciences108662ndash667httpsdoiorg101073pnas1014743108
RCore Team (2018)R A language and environment for statistical com‐puting Vienna Austria R Foundation for Statistical ComputingRetrievedfromhttpswwwR‐projectorg
Environmental Systems Research Institute (2011) ArcGIS Desktop Release 10RedlandsCaliforniaESRI
Fiske IampChandlerRB (2011)UnmarkedAnRpackage for fittinghierarchicalmodelsofwildlifeoccurrenceandabundanceJournal of Statistical Software431ndash23
Garibaldi L A Steffan‐Dewenter I Winfree R Aizen M ABommarcoRCunninghamSAhellipBartomeusI(2013)Wildpolli‐natorsenhancefruitsetofcropsregardlessofhoneybeeabundanceScience3391608ndash1611httpsdoiorg101126science1230200
Goulson D (1999) Foraging strategies of insects for gathering nec‐tar and pollen and implications for plant ecology and evolutionPerspectives in Plant Ecology Evolution and Systematics2 185ndash209httpsdoiorg1010781433‐8319‐00070
GoulsonDLyeGCampDarvillB(2008)DeclineandconservationofbumblebeesAnnual Review of Entomology53191ndash208httpsdoiorg101146annurevento53103106093454
GoulsonDNicholls E Botiacuteas C amp Rotheray E L (2015) Bee de‐clines driven by combined stress from parasites pesticides andlack of flowers Science 347 1255957 httpsdoiorg101126science1255957
Hammond P S Berggren P Benke H Borchers D L Collet AHeide‐Joslashrgensen M P hellip Oslashien N (2002) Abundance of har‐bour porpoise and other cetaceans in the North Sea and adja‐cent waters Journal of Applied Ecology 39 361ndash376 httpsdoiorg101046j1365‐2664200200713x
HanleyMEAwbiAJampFrancoM(2014)GoingnativeFlowerusebybumblebeesinEnglishurbangardensAnnals of Botany113799ndash806httpsdoiorg101093aobmcu006
Hau E amp Von Renouard H (2006) The wind resource London UKElsevier
Hedley S L amp Buckland S T (2004) Spatial models for line tran‐sect sampling Journal of Agricultural Biological and Environmental Statistics9181ndash199httpsdoiorg1011981085711043578
JamesFCampShugartHHJr(1970)AquantitativemethodofhabitatdescriptionAudubon Field Notes24727ndash736
Jepsen S Evans E Thorp R Hatfield R amp Black S H (2003)Petition to list the rusty patched bumble bee Bombus affinis (Cresson) 1863 as an endangered species under the US Endangered Species Act Retrieved from httpwwwxercesorgwp‐ontentuploads 201301Bombus‐petitionpdf
Jha S amp Kremen C (2013) Resource diversity and landscape‐levelhomogeneitydrivenativebee foragingProceedings of the National Academy of Sciences 110 555ndash558 httpsdoiorg101073pnas1208682110
KaranthKUampSunquistME(1995)PreyselectionbytigerleopardanddholeintropicalforestsJournal of Animal Ecology64439ndash450httpsdoiorg1023075647
KeacuteryMampRoyleJA (2015)Applied Hierarchical Modeling in Ecology Analysis of distribution abundance and species richness in R and BUGS Volume 1 Prelude and Static ModelsCambridgeMAAcademicPress
KeacuteryM amp Schmidt B R (2008) Imperfect detection and its conse‐quencesformonitoringforconservationCommunity Ecology9207ndash216httpsdoiorg101556ComEc92008210
Kevan PG (1990)Pollination keystone process in sustainable globalproductivity InVIInternationalSymposiumonPollination288(pp103‐110)
Kremen CWilliams NM amp Thorp RW (2002) Crop pollinationfromnativebeesatriskfromagriculturalintensificationProceedings of the National Academy of Sciences99 16812ndash16816 httpsdoiorg101073pnas262413599
emspensp emsp | emsp235McNEIL Et aL
LofflandH L Polasik J S TingleyMW Elsey E A Loffland CLebuhnGampSiegelRB(2017)Bumblebeeuseofpost‐firechap‐arralinthecentralSierraNevadaThe Journal of Wildlife Management811084ndash1097httpsdoiorg101002jwmg21280
MackenzieD I (2006)Modelingtheprobabilityof resourceuseTheeffectofanddealingwithdetectingaspeciesimperfectlyJournal of Wildlife Management70367ndash374httpsdoiorg1021930022‐541X(2006)70[367MTPORU]20CO2
MacKenzieDINicholsJDLachmanGBDroegeSAndrewRoyleJampLangtimmCA(2002)Estimatingsiteoccupancyrateswhende‐tectionprobabilitiesarelessthanoneEcology832248ndash2255httpsdoiorg1018900012‐9658(2002)083[2248ESORWD]20CO2
MacKenzieDINicholsJDRoyleJAPollockKHBaileyLampHinesJE(2005)Occupancy estimation and modeling Inferring pat‐terns and dynamics of species occurrenceLondonUKElsevier
Mackenzie D I (2003) Assessing site occupancymodelling as a toolfor monitoring Mahoenui giant weta populations Department ofConservation17
Marques T A Thomas L Fancy S G amp Buckland S T (2007)Improvingestimatesofbirddensityusingmultiple‐covariatedistancesamplingThe Auk1241229ndash1243httpsdoiorg1016420004‐8038(2007)124[1229IEOBDU]20CO2
McCaskillGLMcWilliamsWHAlerichCAButlerBJCrockerS JDomkeGMhellipWestfall JA (2009)Pennsylvaniarsquos Forests 2009NewtownSquarePAUSDepartmentofAgricultureForestServiceNorthernResearchStation
MichenerCDMcGinleyRJampDanforthBN(1994)The Bee Genera of North and Central AmericaWashingtonDCSmithsonianInstitutePress
OlesenJMBascompteJElberlingHampJordanoP(2008)TemporaldynamicsinapollinationnetworkEcology891573ndash1582httpsdoiorg10189007‐04511
PerssonA S RundloumlfMCloughYampSmithHG (2015)Bumblebees show trait‐dependent vulnerability to landscape simplifica‐tion Biodiversity and Conservation 24 3469ndash3489 httpsdoiorg101007s10531‐015‐1008‐3
Potts SGVulliamyBDafniANeemanGampWillmer P (2003)Linking bees and flowers How do floral communities structurepollinator communities Ecology 84 2628ndash2642 httpsdoiorg10189002‐0136
PottsSGBiesmeijerJCKremenCNeumannPSchweigerOampKuninWE (2010)Globalpollinatordeclinestrends impactsanddriversTrends in ecology amp evolution25(6)345ndash353
Redhead JW Dreier S Bourke A F HeardM S JordanW CSumner S hellip Carvell C (2016) Effects of habitat compositionandlandscapestructureonworkerforagingdistancesoffivebum‐ble bee species Ecological Applications 26 726ndash739 httpsdoiorg10189015‐0546
Roulston T A H Smith S A amp Brewster A L (2007) A com‐parison of pan trap and intensive net sampling techniques fordocumenting a bee (Hymenoptera Apiformes) fauna Journal of the Kansas Entomological Society 80 179ndash181 httpsdoiorg1023170022‐8567(2007)80[179ACOPTA]20CO2
Royle J A Dawson D K amp Bates S (2004) Modeling abundanceeffects in distance sampling Ecology 85 1591ndash1597 httpsdoiorg10189003‐3127
Scheper J Bommarco R Holzschuh A Potts S G Riedinger VRoberts S P hellipWickens V J (2015) Local and landscape‐level
floral resources explain effects of wildflower strips on wild beesacrossfourEuropeancountriesJournal of Applied Ecology521165ndash1175httpsdoiorg1011111365‐266412479
SeberGA(1986)AreviewofestimatinganimalabundanceBiometrics42267ndash292httpsdoiorg1023072531049
ShultzCH(1999)The Geology of PennsylvaniaPennsylvaniaGeologicalSurveyHarrisburgPAPennsylvaniaGeologicalSurvey
Sillett T S Chandler R B Royle J A KeacuteryM ampMorrison S A(2012) Hierarchical distance‐sampling models to estimate popu‐lation size and habitat‐specific abundance of an island endemicEcological Applications22(7)1997ndash2006
SollmannRGardnerBWilliamsKAGilbertATampVeitRR(2016)AhierarchicaldistancesamplingmodeltoestimateabundanceandcovariateassociationsofspeciesandcommunitiesMethods in Ecology and Evolution7529ndash537httpsdoiorg1011112041‐210X12518
Tepedino V J Durham S Cameron S A amp Goodell K (2015)Documenting bee decline or squandering scarce resourcesConservation Biology 29 280ndash282 httpsdoiorg101111cobi12439
Thomas LBuckland S TBurnhamKPAndersonDR Laake JL Borchers D L amp Strindberg S (2002) Distance samplingEncyclopediaofenvironmetrics
Thomas L Buckland S T Rexstad EA Laake J L Strindberg SHedley S L hellipBurnham K P (2010)Distance softwareDesignand analysis of distance sampling surveys for estimating pop‐ulation size Journal of Applied Ecology 47 5ndash14 httpsdoiorg101111j1365‐2664200901737x
ThompsonWL (2002)TowardsreliablebirdsurveysAccountingforindividualspresentbutnotdetectedThe Auk11918ndash25httpsdoiorg1016420004‐8038(2002)119[0018TRBSAF]20CO2
VanStrienA JTermaatTGroenendijkDMensingVampKeryM(2010) Site‐occupancy models may offer new opportunities fordragonflymonitoringbasedondailyspecies listsBasic and Applied Ecology11495ndash503httpsdoiorg101016jbaae201005003
VilsackTampMcCarthyG(2015)National strategy to promote the health of honey bees and other pollinatorsWashingtonDCReport IssuedbytheWhiteHousethePollinatorHealthTaskForce
WardKCariveauDMayERoswellMVaughanMWilliamsNhellip Gill K (2014) Streamlined Bee Monitoring Protocol for Assessing Pollinator HabitatPortlandORTheXercesSocietyforInvertebrateConservation
WeatherUndergroundInc(2018)WeatherForecastandReports‐LongRangeandLocalWundergroundRetrievedfromhttpswwwwun‐dergroundcom
WherryET Fogg JM JrampWahlHA (1979)Atlas of the flora of Pennsylvania Philadelphia PA The Morris Arboretum of theUniversityofPennsylvania
YoccozNGNichols JDampBoulinierT (2001)Monitoringofbio‐logicaldiversityinspaceandtimeTrends Ecology and Evolution16446ndash453
How to cite this articleMcNeilDJOttoCRVMoserELetalDistancemodelsasatoolformodellingdetectionprobabilityanddensityofnativebumblebeesJ Appl Entomol 2019143225ndash235 httpsdoiorg101111jen12583
emspensp emsp | emsp231McNEIL Et aL
forager density within timber harvests was highest for the HDSmodels(192foragingworkersha95CI153ndash240)andlowestfornetcounts(21foragingworkersha95CI19ndash23Figure5)an89differencebetween the twomethodsTransect countsyielded in‐termediate estimates of density (40 foragingworkersha 95CI34ndash47)andwere80lowerthandensityestimatesfromHDSSite‐specific HDS modelled densities and netting count raw densitieswerecorrelated (Pearsonrsquos r = 031 p=003) though the relation‐shipwasnot11(Figure5)
4emsp |emspDISCUSSION
Ourstudyprovidesthefirstempiricalevidencethatdetectionprob‐abilitiesofBombus sppvaryinwaysthatcanaffectabundanceesti‐matesandinferencesabouthabitatrelationshipsObservationerrorcaused by imperfect detection is one of the central challenges ofecologicalmonitoringprograms(Thompson2002YoccozNicholsampBoulinier 2001)buthas yet tobewidely applied tomonitoringofmany invertebrates includingpollinators (but seeBendeletal2018Lofflandetal2017Mackenzie2003VanStrienTermaatGroenendijkMensingampKery 2010)Methods like distance sam‐plingwhileofferingapotential solution to this challenge are stillunder‐utilized in entomological research Meanwhile distance
samplingandsimilarmethodshavebeenastapleofvertebratewild‐liferesearchfordecades(Bucklandetal2005BurnhamAndersonampLaake1980Seber1986Thomasetal2002)andhavebeenex‐pandedtoestimatepopulationsizehabitat‐specificabundanceforindividualspeciesandcommunities(SillettChandlerRoyleKeacuteryampMorrison2012SollmannGardnerWilliamsGilbertampVeit2016)Althoughourstudyisnotthefirstestimateandaccountfordetec‐tionprobabilityofbumblebees(Lofflandetal2017)nostudybe‐foreourshasdescribedfactorsassociatedwithdetectionprobabilityanddonesoinaHDSframework
Wefoundthatdistancesamplingtransectswerebothasimpleandeffectivesurveymethodforestimatingdensityandhabitatre‐lationships (Buckland et al 2005) Hierarchical distance samplingmodelsareoneofthefewavailablemethodsthatallowresearcherstomodel detection‐adjusted abundancewithonly a single visit toeachsite(Bucklandetal2005KeacuteryampRoyle2015MacKenzieetal 2005)Themethodusesonlynon‐lethal samplingunlike trap‐pingnettingmethods(Tepedinoetal2015)whichisespeciallyde‐sirablewhen sampling for speciesof conservation concern or forcommonspecies in areaswherecapture‐based sampling isnot al‐lowedAdditionallyHDSmodelsarealsousefulbecausetheoutputisaneasily interpretedlatentstatedensitywithunits inldquoanimalsareardquo In our study HDS models generated estimates of foragingBombus sppworkerdensity
Model name K AICc ΔAICc AICc Wt β estimate (95CI)
Hierarchicaldistancesampling
λ(sapling) 6 33769 000 098 minus030(minus045tominus014)
λ(shrub) 6 34583 813 002 021(005to037)
λ() 5 3502 1251 000 ndash
λ(grass) 6 35041 1271 000 minus017(minus038to005)
λ(forb) 6 35282 1513 000 minus001(minus016to014)
Transectcounts
λ(sapling) 2 27763 000 096 minus144(minus220tominus069)
λ(shrub) 2 28448 685 003 085(025to144)
λ(grass) 2 2898 1217 000 minus093(minus214to028)
λ() 1 29007 1244 000 ‐
λ(forb) 2 29216 1454 000 0133(minus074to101)
Netcounts
λ(sapling) 2 36071 000 100 minus163(minus226tominus101)
λ(grass) 2 38438 2367 000 085(003to167)
λ(shrub) 2 38565 2494 000 041(minus009to090)
λ() 1 38608 2537 000 ndash
λ(forb) 2 38709 2638 000 039(minus031to109)
NoteModelsareranked indescendingorderofAkaikersquos InformationCriterionadjustedforsmallsamplesize(AICc)DistancetransectdataincludedBombussppdetectedfrom0to5malong66mtransectsTransectcounts includedBombus sppdetected from0ndash2malong66m transectsnetcountdatawerecountsofBombus sppwithin15mradiusplotsSitecovariatesincludedpercentcover asmeasured by 50m radius vegetation surveys for vegetation structure saplings shrubsforbsandgrassBelowwereportnumberofmodelparameters(k)AICcΔAICcAICc weight(AICc Wt)andeachcovariateβparameterestimateandβparameterestimates(95confidenceinterval)
TA B L E 2 emspHabitatmodelsderivedfromhierarchicaldistancemodels(top)fixed‐widthtransectmodels(centre)andlinearmodelsofnetcountdata(bottom)allfitusingaPoissondistribution
232emsp |emsp emspensp McNEIL Et aL
DespitebeingamongthelargestandmostconspicuousofNorthAmerican bees (Michener et al 1994) we found that detectionprobability of Bombus spp was imperfect and declined markedlywithdistancefromthesurveytransectwithalmostnodetectionsbeyond5mDetectionprobabilitiesinourstudywereinfluencedbysurvey‐specific(egtimeofday)andsite‐specific(eggrasscover)variableswithdetectionprobabilityhighestinthemorninginmid‐summerandinhabitatswithabundantgrasscoverWithinregener‐atingtimberharvestsinourstudyarealdquograssrdquocoverwastypicallylow‐growing monocotyledons like Carex pennsylvanica Abundantlow‐growing sedge allowed observers to view Bombus spp fromgreaterdistancesthanwhensitesweredominatedbytallsaplingsshrubs or forbs (egSolidago) Consequently studieswithin habi‐tatsdominatedbylowgrassorothershortvegetationmightfindde‐tectionprobabilityforBombusspptobereliableatdistancesgt5mAlthoughweareuncertainastowhyBombussppwerelessdetect‐ableduringsurveysconductedlaterintheafternoononeplausibleexplanationisthatlongershadowscastbylateafternoonlightmade
Bombussppmoredifficulttodetectwhenforagingin lowvegeta‐tionAdditionalworkexploringthedriversassociatedwithBombus sppdetectionwouldprovevaluabletomonitoringregimesaimedatsurveyingbumblebees
ThoughourstudyisnotacomprehensivehabitatassessmentforBombussppwithinregeneratingtimberharvestsofeasternforestsourresultsprovideaglimpseintothehabitatdynamicsofbumble‐beesinregeneratingforestsduringmid‐summerOurfindingsthatBombus sppwerepositivelyassociatedwithshrubsandnegativelyassociatedwithsaplingscanbeexplainedprimarilybyflowerphe‐nology during our survey window Regenerating saplings withinthe timber harvests we monitored were largely oaks hickoriesblackcherry (Prunus serotina)andredmaple (Acer rubrumWherryetal1979)Thesespeciesdonot flowerassmallsaplingsanddosoinearlyspringasmaturetrees(ieoutsidethesamplingperiodWherryetal1979)Incontrastseveralspeciesofshrubwereflow‐eringduringsamplingincludingblackhuckleberry(Gaylussacia bac‐cata)andhillsideblueberryIncontrastmostforbs(eggoldenrod
F I G U R E 4 emspModelledhabitatassociationsbetweenBombussppandstructuralvegetationfeatureswithinregeneratingtimberharvestsaspredictedbyhierarchicaldistancemodels(top)fixed‐width(4m)transectcounts(centre)andnetcounts(bottom)Variablesshownaresaplingcover(left)shrubcover(centre)andgrasscover(right)Solidlinesrepresentmodelpredictionswithdashedlinesas95confidenceintervalsRelationshipsmarkedwithanasteriskwerethosewithmodelsupport(iemoreinformativethananullmodelandβ95CInon‐overlappingzero)
F I G U R E 5 emspLeftBombusspppredictedmeandensityformodelsofnetcounts(ldquoncrdquo)transectcounts(ldquotcrdquo)andhierarchicaldistancesamplingmodels(ldquohdsrdquo)RightPredicteddensity(workersha)generatedfromourtop‐rankedhierarchicaldistancemodel(p [observer+time+grass]λ[sapling])regressedagainstcountdatafromBombus sppnetcounts
emspensp emsp | emsp233McNEIL Et aL
SolidagosppsnakerootAgeratina spp)hadnotbegunfloweringyetFutureworkshouldexplorehowBombussppmaytrackresourcesacrossagrowingseasontopersistwithineasternforestecosystems
Monitoringprograms forBombus spp andothernativepolli‐natorscanbeimprovedbyincorporatingstudydesignandmodel‐based approaches for minimizing detection error Although weincludedseveraldesign‐basedsolutionsforminimizingdetectionerror(egrestrictingsurveytimesonlysurveyinginfairweatherWard et al 2014) detection probability remained imperfectand varied due to time of day observer and vegetation coverConsequentlymethodsthatignoreddetectionprobabilitygener‐ated density estimates 80ndash89 lower than HDS Past studieshaveshowntheimportanceofusingdesign‐basedapproachestominimize false negativeswhen sampling bees (BuchananGibbsKomondyampSzendrei2017)Ourstudydemonstratesthevalueofusingbothdesign‐andmodel‐basedapproachesforreducingsam‐plingerrorscausedbyimperfectdetectionOtherstudysystemswith thick vegetation cover such as prairies and forested wet‐landsorobstructiveobjectssuchasurbanenvironmentsarealsolikely to underestimate bee abundance even if multiple design‐basedapproachesareusedWhiletraditionalsamplingtechniquesthat do not account for detection have numerous applicationsourstudyhighlightstheimportanceofincorporatingmodel‐basedapproachesforaccountingfordetectionprobabilitywithinnativebeesurveysparticularlywhenattemptingtoestimatebeeabun‐danceordensity
Althoughour results suggest thatHDS representsapromisingtoolformonitoringbumblebeesresearcherswishingtoemploythemethod should recognize its associated limitations For exampledistancemodelsassumethatallanimalsonthetransectlinearede‐tectedperfectlyAlthoughitislikelythisassumptionwasmetwithalargeinsectlikeBombussppthisassumptionmightbeviolatedwithsmallerinsectsMoreoversubjectsareassumedtobeuniformlydis‐tributedinamannerunaffectedbytheobserverWhileitispossiblethatBombussppwerefrightenedbyobserverswetookcaretonotethe locationof first detection forBombus spp apparently flushedandtheirloudflightmadeclosedetectionsalmostcertainWenotethat thismethodwouldnotworkwell for species‐level identifica‐tionbecauseobservationsaremadefromadistanceandsomebeegeneraareexceedinglydifficulttoidentifyevenwithamicroscope(Michener et al 1994)Misidentification of specieswould consti‐tuteafalsepositivewhichwouldviolateanassumptionofdistancesampling
Anotherconsiderationofthisstudydesignandmanymethodsofabundanceestimationisthatanimalsmayviolatetheclosureas‐sumptionInthecaseofBombussppthislikelyoccurredasforagersflew in‐ and out‐ of the effective survey area (~5m from the ob‐serverforHDS)WhilethismayconstituteaproblemforsomestudyobjectivesandmethodswehavenoreasontobelievethatBombus sppmovementwasnonrandomwithrespecttotheobserverandanaccuratedensitycouldthereforestillbemadewhenpassivecountingwasusedClosureviolationmaybeamoreimportantproblemwhenattempting tocalculatedensity fromanettingplotwhereanimals
mayentertheplotandbeunabletoleaveastheyarecapturedandhelduntil thesurveyhasfinished Insuchcasesmovementwouldbebiasedbyindividualsimmigratingintothemonitoredplotbutun‐abletoemigrateandmovementwouldbebiasedtowardstheplotAlthough net‐based sampling is often preferable for investigatingspecies‐specific habitat relationships the potential for movementbias highlights the need for cautious interpretation of net‐baseddensityestimatesforbeesSimilarlyresearchersshouldconsiderthepotentialfordouble‐countingsubjectsAlthoughBombussppinourstudywereapparentlyfewenoughandslowenoughtoavoidmostdouble‐countingthismaybeamoreimportantproblemtoconsiderformoreabundantinsectswithreduceddetectability(egHalictids)
Wealsoadvisecautionwith interpretationofhabitatrelation‐shipsreportedhereasourstudyshouldbe interpretedasasmallldquosnapshotrdquo in time and lacking species‐specific habitat relation‐ships(OlesenBascompteElberlingampJordano2008)Full‐seasonhabitat associations are temporally dynamic forBombus spp andvaryacrossspecies(Goulson1999JhaampKremen2013)Relativefloral resourceavailabilityofdifferentspecieschangesacrosstheseasonandfuturestudiesemployingthesemethodsatregularin‐tervals from early springwhen queens first emerge through lateautumnwould prove valuable In fact examination of queen beedensities would likely prove a better assessment of populationdensityandhabitatqualitythanworkerdensitywhenmonitoringorresearchingcolonialorganismssuchasbumblebeesestimatingthetruenumberofreproducingcoloniesisofmorevaluethanes‐timating the number of foragingworkers aswe have done hereConductingHDSduringthespringandearlysummerwhenqueensare theonly activebumblebee foragersmayprove auseful andnon‐lethalapproachtoestimating theabundanceof reproductiveindividualsandtheexpectednumbersummercoloniesforagivenarea However sampling queens would likely require additionalsamplingsitesorrepeatvisitbecausecountswouldbemuchlowerandHDSmodelsmayhavetroubleconvergingwithrelativelyfewsampling locations Caution should also be exercised with inter‐pretation ofBombus spp density estimates reported here as ourdensitieslikelyconsistofmultiplespeciesofBombus modelled and reportedasoneWealsorecommendfuturestudiesexplorehownon‐Bombusgenera(ormorphospeciesfunctionalgroups)performasthefocusofHDSmodelsAlthoughHDS isnotwithout limita‐tionwebelieveourstudyhighlightstheutilityofHDSmodelsforestimatingdensitiesandelucidatinghabitatassociationsofbumblebeeswhenindividualsaredetectedimperfectly
ACKNOWLEDG EMENTS
Wethank the following individuals andagencies for their supportandlandaccessSproulStateForestandMoshannonStateForestFunding was provided by the Indiana University of PennsylvaniaBUREfundandtheUnitedStatesDepartmentofAgricultureNaturalResources Conservation Service (68‐7482‐12‐502) through theConservationEffectsAssessmentProjectWeareverygrateful toJoanMilamandSamDroegefortheircommentsonearlyversions
234emsp |emsp emspensp McNEIL Et aL
of thismanuscriptWearealsoverygrateful to threeanonymousreviewers spend considerable time strengthening thismanuscriptFundersofourprojectdidnothaveanyinfluenceonthecontentofthesubmittedmanuscriptnordidtheyrequireapprovalofthefinalmanuscripttobepublishedAnyuseoftradefirmorproductnamesisfordescriptivepurposesonlyanddoesnotimplyendorsementbytheUSGovernment
AUTHORSrsquo CONTRIBUTIONS
DJMCRVOELMandJLLconceived researchDJMandELMcol‐lected field data DJM CRVO and ELM conducted statisticalanalysesDJMCRVOELMKRUMDEKADRand JLLwrote themanuscriptJLLsecuredfundingAllauthorsreadandapprovedthemanuscript
ORCID
Darin J McNeil httporcidorg0000‐0003‐4595‐8354
Clint R V Otto httporcidorg0000‐0002‐7582‐3525
Amanda D Rodewald httporcidorg0000‐0002‐6719‐6306
R E FE R E N C E S
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AndersonDR(2007)Model based inference in the life sciences A primer on evidenceBerlinGermanySpringerScienceampBusinessMedia
Arnold T W (2010) Uninformative parameters and model selectionusingAkaikesInformationCriterionJournal of Wildlife Management741175ndash1178httpsdoiorg101111j1937‐28172010tb01236x
Ashman T L Knight TM Steets J A Amarasekare P BurdMCampbellDRhellipMorganMT (2004)Pollen limitationofplantreproductionEcologicalandevolutionarycausesandconsequencesEcology852408ndash2421httpsdoiorg10189003‐8024
BendelCRHovickTJLimbRFampHarmonJP(2018)Variationin grazing management practices supports diverse butterflycommunitiesacrossgrasslandworking landscapesJournal of Insect Conservation221ndash13httpsdoiorg101007s10841‐017‐0041‐9
BuchananALGibbsJKomondyLampSzendreiZ(2017)Beecom‐munityof commercial potato fields inMichigan andBombus impa‐tiensvisitationtoneonicotinoid‐treatedpotatoplantsInsects830httpsdoiorg103390insects8010030
BucklandSTAndersonDRBurnhamKPampLaake JL (2005)Distance samplingHobokenNJJohnWileyampSonsLtd
BurnhamKPampAndersonDR(2002)Model selection and multimodel inference A practical information‐theoretic approachBerlinGermanySpringerScienceampBusinessMedia
BurnhamKPAndersonDRampLaakeJL(1980)Estimationofden‐sity from line transect sampling of biological populationsWildlife Monographs723ndash202
Calderone N W (2012) Insect pollinated crops insect pollinatorsandUSagricultureTrendanalysisofaggregatedatafortheperiod1992ndash2009 PLoS ONE7 e37235 httpsdoiorg101371journalpone0037235
CameronSALozierJDStrangeJPKochJBCordesNSolterL F amp Griswold T L (2011) Patterns of widespread decline in
NorthAmericanbumblebeesProceedings of the National Academy of Sciences108662ndash667httpsdoiorg101073pnas1014743108
RCore Team (2018)R A language and environment for statistical com‐puting Vienna Austria R Foundation for Statistical ComputingRetrievedfromhttpswwwR‐projectorg
Environmental Systems Research Institute (2011) ArcGIS Desktop Release 10RedlandsCaliforniaESRI
Fiske IampChandlerRB (2011)UnmarkedAnRpackage for fittinghierarchicalmodelsofwildlifeoccurrenceandabundanceJournal of Statistical Software431ndash23
Garibaldi L A Steffan‐Dewenter I Winfree R Aizen M ABommarcoRCunninghamSAhellipBartomeusI(2013)Wildpolli‐natorsenhancefruitsetofcropsregardlessofhoneybeeabundanceScience3391608ndash1611httpsdoiorg101126science1230200
Goulson D (1999) Foraging strategies of insects for gathering nec‐tar and pollen and implications for plant ecology and evolutionPerspectives in Plant Ecology Evolution and Systematics2 185ndash209httpsdoiorg1010781433‐8319‐00070
GoulsonDLyeGCampDarvillB(2008)DeclineandconservationofbumblebeesAnnual Review of Entomology53191ndash208httpsdoiorg101146annurevento53103106093454
GoulsonDNicholls E Botiacuteas C amp Rotheray E L (2015) Bee de‐clines driven by combined stress from parasites pesticides andlack of flowers Science 347 1255957 httpsdoiorg101126science1255957
Hammond P S Berggren P Benke H Borchers D L Collet AHeide‐Joslashrgensen M P hellip Oslashien N (2002) Abundance of har‐bour porpoise and other cetaceans in the North Sea and adja‐cent waters Journal of Applied Ecology 39 361ndash376 httpsdoiorg101046j1365‐2664200200713x
HanleyMEAwbiAJampFrancoM(2014)GoingnativeFlowerusebybumblebeesinEnglishurbangardensAnnals of Botany113799ndash806httpsdoiorg101093aobmcu006
Hau E amp Von Renouard H (2006) The wind resource London UKElsevier
Hedley S L amp Buckland S T (2004) Spatial models for line tran‐sect sampling Journal of Agricultural Biological and Environmental Statistics9181ndash199httpsdoiorg1011981085711043578
JamesFCampShugartHHJr(1970)AquantitativemethodofhabitatdescriptionAudubon Field Notes24727ndash736
Jepsen S Evans E Thorp R Hatfield R amp Black S H (2003)Petition to list the rusty patched bumble bee Bombus affinis (Cresson) 1863 as an endangered species under the US Endangered Species Act Retrieved from httpwwwxercesorgwp‐ontentuploads 201301Bombus‐petitionpdf
Jha S amp Kremen C (2013) Resource diversity and landscape‐levelhomogeneitydrivenativebee foragingProceedings of the National Academy of Sciences 110 555ndash558 httpsdoiorg101073pnas1208682110
KaranthKUampSunquistME(1995)PreyselectionbytigerleopardanddholeintropicalforestsJournal of Animal Ecology64439ndash450httpsdoiorg1023075647
KeacuteryMampRoyleJA (2015)Applied Hierarchical Modeling in Ecology Analysis of distribution abundance and species richness in R and BUGS Volume 1 Prelude and Static ModelsCambridgeMAAcademicPress
KeacuteryM amp Schmidt B R (2008) Imperfect detection and its conse‐quencesformonitoringforconservationCommunity Ecology9207ndash216httpsdoiorg101556ComEc92008210
Kevan PG (1990)Pollination keystone process in sustainable globalproductivity InVIInternationalSymposiumonPollination288(pp103‐110)
Kremen CWilliams NM amp Thorp RW (2002) Crop pollinationfromnativebeesatriskfromagriculturalintensificationProceedings of the National Academy of Sciences99 16812ndash16816 httpsdoiorg101073pnas262413599
emspensp emsp | emsp235McNEIL Et aL
LofflandH L Polasik J S TingleyMW Elsey E A Loffland CLebuhnGampSiegelRB(2017)Bumblebeeuseofpost‐firechap‐arralinthecentralSierraNevadaThe Journal of Wildlife Management811084ndash1097httpsdoiorg101002jwmg21280
MackenzieD I (2006)Modelingtheprobabilityof resourceuseTheeffectofanddealingwithdetectingaspeciesimperfectlyJournal of Wildlife Management70367ndash374httpsdoiorg1021930022‐541X(2006)70[367MTPORU]20CO2
MacKenzieDINicholsJDLachmanGBDroegeSAndrewRoyleJampLangtimmCA(2002)Estimatingsiteoccupancyrateswhende‐tectionprobabilitiesarelessthanoneEcology832248ndash2255httpsdoiorg1018900012‐9658(2002)083[2248ESORWD]20CO2
MacKenzieDINicholsJDRoyleJAPollockKHBaileyLampHinesJE(2005)Occupancy estimation and modeling Inferring pat‐terns and dynamics of species occurrenceLondonUKElsevier
Mackenzie D I (2003) Assessing site occupancymodelling as a toolfor monitoring Mahoenui giant weta populations Department ofConservation17
Marques T A Thomas L Fancy S G amp Buckland S T (2007)Improvingestimatesofbirddensityusingmultiple‐covariatedistancesamplingThe Auk1241229ndash1243httpsdoiorg1016420004‐8038(2007)124[1229IEOBDU]20CO2
McCaskillGLMcWilliamsWHAlerichCAButlerBJCrockerS JDomkeGMhellipWestfall JA (2009)Pennsylvaniarsquos Forests 2009NewtownSquarePAUSDepartmentofAgricultureForestServiceNorthernResearchStation
MichenerCDMcGinleyRJampDanforthBN(1994)The Bee Genera of North and Central AmericaWashingtonDCSmithsonianInstitutePress
OlesenJMBascompteJElberlingHampJordanoP(2008)TemporaldynamicsinapollinationnetworkEcology891573ndash1582httpsdoiorg10189007‐04511
PerssonA S RundloumlfMCloughYampSmithHG (2015)Bumblebees show trait‐dependent vulnerability to landscape simplifica‐tion Biodiversity and Conservation 24 3469ndash3489 httpsdoiorg101007s10531‐015‐1008‐3
Potts SGVulliamyBDafniANeemanGampWillmer P (2003)Linking bees and flowers How do floral communities structurepollinator communities Ecology 84 2628ndash2642 httpsdoiorg10189002‐0136
PottsSGBiesmeijerJCKremenCNeumannPSchweigerOampKuninWE (2010)Globalpollinatordeclinestrends impactsanddriversTrends in ecology amp evolution25(6)345ndash353
Redhead JW Dreier S Bourke A F HeardM S JordanW CSumner S hellip Carvell C (2016) Effects of habitat compositionandlandscapestructureonworkerforagingdistancesoffivebum‐ble bee species Ecological Applications 26 726ndash739 httpsdoiorg10189015‐0546
Roulston T A H Smith S A amp Brewster A L (2007) A com‐parison of pan trap and intensive net sampling techniques fordocumenting a bee (Hymenoptera Apiformes) fauna Journal of the Kansas Entomological Society 80 179ndash181 httpsdoiorg1023170022‐8567(2007)80[179ACOPTA]20CO2
Royle J A Dawson D K amp Bates S (2004) Modeling abundanceeffects in distance sampling Ecology 85 1591ndash1597 httpsdoiorg10189003‐3127
Scheper J Bommarco R Holzschuh A Potts S G Riedinger VRoberts S P hellipWickens V J (2015) Local and landscape‐level
floral resources explain effects of wildflower strips on wild beesacrossfourEuropeancountriesJournal of Applied Ecology521165ndash1175httpsdoiorg1011111365‐266412479
SeberGA(1986)AreviewofestimatinganimalabundanceBiometrics42267ndash292httpsdoiorg1023072531049
ShultzCH(1999)The Geology of PennsylvaniaPennsylvaniaGeologicalSurveyHarrisburgPAPennsylvaniaGeologicalSurvey
Sillett T S Chandler R B Royle J A KeacuteryM ampMorrison S A(2012) Hierarchical distance‐sampling models to estimate popu‐lation size and habitat‐specific abundance of an island endemicEcological Applications22(7)1997ndash2006
SollmannRGardnerBWilliamsKAGilbertATampVeitRR(2016)AhierarchicaldistancesamplingmodeltoestimateabundanceandcovariateassociationsofspeciesandcommunitiesMethods in Ecology and Evolution7529ndash537httpsdoiorg1011112041‐210X12518
Tepedino V J Durham S Cameron S A amp Goodell K (2015)Documenting bee decline or squandering scarce resourcesConservation Biology 29 280ndash282 httpsdoiorg101111cobi12439
Thomas LBuckland S TBurnhamKPAndersonDR Laake JL Borchers D L amp Strindberg S (2002) Distance samplingEncyclopediaofenvironmetrics
Thomas L Buckland S T Rexstad EA Laake J L Strindberg SHedley S L hellipBurnham K P (2010)Distance softwareDesignand analysis of distance sampling surveys for estimating pop‐ulation size Journal of Applied Ecology 47 5ndash14 httpsdoiorg101111j1365‐2664200901737x
ThompsonWL (2002)TowardsreliablebirdsurveysAccountingforindividualspresentbutnotdetectedThe Auk11918ndash25httpsdoiorg1016420004‐8038(2002)119[0018TRBSAF]20CO2
VanStrienA JTermaatTGroenendijkDMensingVampKeryM(2010) Site‐occupancy models may offer new opportunities fordragonflymonitoringbasedondailyspecies listsBasic and Applied Ecology11495ndash503httpsdoiorg101016jbaae201005003
VilsackTampMcCarthyG(2015)National strategy to promote the health of honey bees and other pollinatorsWashingtonDCReport IssuedbytheWhiteHousethePollinatorHealthTaskForce
WardKCariveauDMayERoswellMVaughanMWilliamsNhellip Gill K (2014) Streamlined Bee Monitoring Protocol for Assessing Pollinator HabitatPortlandORTheXercesSocietyforInvertebrateConservation
WeatherUndergroundInc(2018)WeatherForecastandReports‐LongRangeandLocalWundergroundRetrievedfromhttpswwwwun‐dergroundcom
WherryET Fogg JM JrampWahlHA (1979)Atlas of the flora of Pennsylvania Philadelphia PA The Morris Arboretum of theUniversityofPennsylvania
YoccozNGNichols JDampBoulinierT (2001)Monitoringofbio‐logicaldiversityinspaceandtimeTrends Ecology and Evolution16446ndash453
How to cite this articleMcNeilDJOttoCRVMoserELetalDistancemodelsasatoolformodellingdetectionprobabilityanddensityofnativebumblebeesJ Appl Entomol 2019143225ndash235 httpsdoiorg101111jen12583
232emsp |emsp emspensp McNEIL Et aL
DespitebeingamongthelargestandmostconspicuousofNorthAmerican bees (Michener et al 1994) we found that detectionprobability of Bombus spp was imperfect and declined markedlywithdistancefromthesurveytransectwithalmostnodetectionsbeyond5mDetectionprobabilitiesinourstudywereinfluencedbysurvey‐specific(egtimeofday)andsite‐specific(eggrasscover)variableswithdetectionprobabilityhighestinthemorninginmid‐summerandinhabitatswithabundantgrasscoverWithinregener‐atingtimberharvestsinourstudyarealdquograssrdquocoverwastypicallylow‐growing monocotyledons like Carex pennsylvanica Abundantlow‐growing sedge allowed observers to view Bombus spp fromgreaterdistancesthanwhensitesweredominatedbytallsaplingsshrubs or forbs (egSolidago) Consequently studieswithin habi‐tatsdominatedbylowgrassorothershortvegetationmightfindde‐tectionprobabilityforBombusspptobereliableatdistancesgt5mAlthoughweareuncertainastowhyBombussppwerelessdetect‐ableduringsurveysconductedlaterintheafternoononeplausibleexplanationisthatlongershadowscastbylateafternoonlightmade
Bombussppmoredifficulttodetectwhenforagingin lowvegeta‐tionAdditionalworkexploringthedriversassociatedwithBombus sppdetectionwouldprovevaluabletomonitoringregimesaimedatsurveyingbumblebees
ThoughourstudyisnotacomprehensivehabitatassessmentforBombussppwithinregeneratingtimberharvestsofeasternforestsourresultsprovideaglimpseintothehabitatdynamicsofbumble‐beesinregeneratingforestsduringmid‐summerOurfindingsthatBombus sppwerepositivelyassociatedwithshrubsandnegativelyassociatedwithsaplingscanbeexplainedprimarilybyflowerphe‐nology during our survey window Regenerating saplings withinthe timber harvests we monitored were largely oaks hickoriesblackcherry (Prunus serotina)andredmaple (Acer rubrumWherryetal1979)Thesespeciesdonot flowerassmallsaplingsanddosoinearlyspringasmaturetrees(ieoutsidethesamplingperiodWherryetal1979)Incontrastseveralspeciesofshrubwereflow‐eringduringsamplingincludingblackhuckleberry(Gaylussacia bac‐cata)andhillsideblueberryIncontrastmostforbs(eggoldenrod
F I G U R E 4 emspModelledhabitatassociationsbetweenBombussppandstructuralvegetationfeatureswithinregeneratingtimberharvestsaspredictedbyhierarchicaldistancemodels(top)fixed‐width(4m)transectcounts(centre)andnetcounts(bottom)Variablesshownaresaplingcover(left)shrubcover(centre)andgrasscover(right)Solidlinesrepresentmodelpredictionswithdashedlinesas95confidenceintervalsRelationshipsmarkedwithanasteriskwerethosewithmodelsupport(iemoreinformativethananullmodelandβ95CInon‐overlappingzero)
F I G U R E 5 emspLeftBombusspppredictedmeandensityformodelsofnetcounts(ldquoncrdquo)transectcounts(ldquotcrdquo)andhierarchicaldistancesamplingmodels(ldquohdsrdquo)RightPredicteddensity(workersha)generatedfromourtop‐rankedhierarchicaldistancemodel(p [observer+time+grass]λ[sapling])regressedagainstcountdatafromBombus sppnetcounts
emspensp emsp | emsp233McNEIL Et aL
SolidagosppsnakerootAgeratina spp)hadnotbegunfloweringyetFutureworkshouldexplorehowBombussppmaytrackresourcesacrossagrowingseasontopersistwithineasternforestecosystems
Monitoringprograms forBombus spp andothernativepolli‐natorscanbeimprovedbyincorporatingstudydesignandmodel‐based approaches for minimizing detection error Although weincludedseveraldesign‐basedsolutionsforminimizingdetectionerror(egrestrictingsurveytimesonlysurveyinginfairweatherWard et al 2014) detection probability remained imperfectand varied due to time of day observer and vegetation coverConsequentlymethodsthatignoreddetectionprobabilitygener‐ated density estimates 80ndash89 lower than HDS Past studieshaveshowntheimportanceofusingdesign‐basedapproachestominimize false negativeswhen sampling bees (BuchananGibbsKomondyampSzendrei2017)Ourstudydemonstratesthevalueofusingbothdesign‐andmodel‐basedapproachesforreducingsam‐plingerrorscausedbyimperfectdetectionOtherstudysystemswith thick vegetation cover such as prairies and forested wet‐landsorobstructiveobjectssuchasurbanenvironmentsarealsolikely to underestimate bee abundance even if multiple design‐basedapproachesareusedWhiletraditionalsamplingtechniquesthat do not account for detection have numerous applicationsourstudyhighlightstheimportanceofincorporatingmodel‐basedapproachesforaccountingfordetectionprobabilitywithinnativebeesurveysparticularlywhenattemptingtoestimatebeeabun‐danceordensity
Althoughour results suggest thatHDS representsapromisingtoolformonitoringbumblebeesresearcherswishingtoemploythemethod should recognize its associated limitations For exampledistancemodelsassumethatallanimalsonthetransectlinearede‐tectedperfectlyAlthoughitislikelythisassumptionwasmetwithalargeinsectlikeBombussppthisassumptionmightbeviolatedwithsmallerinsectsMoreoversubjectsareassumedtobeuniformlydis‐tributedinamannerunaffectedbytheobserverWhileitispossiblethatBombussppwerefrightenedbyobserverswetookcaretonotethe locationof first detection forBombus spp apparently flushedandtheirloudflightmadeclosedetectionsalmostcertainWenotethat thismethodwouldnotworkwell for species‐level identifica‐tionbecauseobservationsaremadefromadistanceandsomebeegeneraareexceedinglydifficulttoidentifyevenwithamicroscope(Michener et al 1994)Misidentification of specieswould consti‐tuteafalsepositivewhichwouldviolateanassumptionofdistancesampling
Anotherconsiderationofthisstudydesignandmanymethodsofabundanceestimationisthatanimalsmayviolatetheclosureas‐sumptionInthecaseofBombussppthislikelyoccurredasforagersflew in‐ and out‐ of the effective survey area (~5m from the ob‐serverforHDS)WhilethismayconstituteaproblemforsomestudyobjectivesandmethodswehavenoreasontobelievethatBombus sppmovementwasnonrandomwithrespecttotheobserverandanaccuratedensitycouldthereforestillbemadewhenpassivecountingwasusedClosureviolationmaybeamoreimportantproblemwhenattempting tocalculatedensity fromanettingplotwhereanimals
mayentertheplotandbeunabletoleaveastheyarecapturedandhelduntil thesurveyhasfinished Insuchcasesmovementwouldbebiasedbyindividualsimmigratingintothemonitoredplotbutun‐abletoemigrateandmovementwouldbebiasedtowardstheplotAlthough net‐based sampling is often preferable for investigatingspecies‐specific habitat relationships the potential for movementbias highlights the need for cautious interpretation of net‐baseddensityestimatesforbeesSimilarlyresearchersshouldconsiderthepotentialfordouble‐countingsubjectsAlthoughBombussppinourstudywereapparentlyfewenoughandslowenoughtoavoidmostdouble‐countingthismaybeamoreimportantproblemtoconsiderformoreabundantinsectswithreduceddetectability(egHalictids)
Wealsoadvisecautionwith interpretationofhabitatrelation‐shipsreportedhereasourstudyshouldbe interpretedasasmallldquosnapshotrdquo in time and lacking species‐specific habitat relation‐ships(OlesenBascompteElberlingampJordano2008)Full‐seasonhabitat associations are temporally dynamic forBombus spp andvaryacrossspecies(Goulson1999JhaampKremen2013)Relativefloral resourceavailabilityofdifferentspecieschangesacrosstheseasonandfuturestudiesemployingthesemethodsatregularin‐tervals from early springwhen queens first emerge through lateautumnwould prove valuable In fact examination of queen beedensities would likely prove a better assessment of populationdensityandhabitatqualitythanworkerdensitywhenmonitoringorresearchingcolonialorganismssuchasbumblebeesestimatingthetruenumberofreproducingcoloniesisofmorevaluethanes‐timating the number of foragingworkers aswe have done hereConductingHDSduringthespringandearlysummerwhenqueensare theonly activebumblebee foragersmayprove auseful andnon‐lethalapproachtoestimating theabundanceof reproductiveindividualsandtheexpectednumbersummercoloniesforagivenarea However sampling queens would likely require additionalsamplingsitesorrepeatvisitbecausecountswouldbemuchlowerandHDSmodelsmayhavetroubleconvergingwithrelativelyfewsampling locations Caution should also be exercised with inter‐pretation ofBombus spp density estimates reported here as ourdensitieslikelyconsistofmultiplespeciesofBombus modelled and reportedasoneWealsorecommendfuturestudiesexplorehownon‐Bombusgenera(ormorphospeciesfunctionalgroups)performasthefocusofHDSmodelsAlthoughHDS isnotwithout limita‐tionwebelieveourstudyhighlightstheutilityofHDSmodelsforestimatingdensitiesandelucidatinghabitatassociationsofbumblebeeswhenindividualsaredetectedimperfectly
ACKNOWLEDG EMENTS
Wethank the following individuals andagencies for their supportandlandaccessSproulStateForestandMoshannonStateForestFunding was provided by the Indiana University of PennsylvaniaBUREfundandtheUnitedStatesDepartmentofAgricultureNaturalResources Conservation Service (68‐7482‐12‐502) through theConservationEffectsAssessmentProjectWeareverygrateful toJoanMilamandSamDroegefortheircommentsonearlyversions
234emsp |emsp emspensp McNEIL Et aL
of thismanuscriptWearealsoverygrateful to threeanonymousreviewers spend considerable time strengthening thismanuscriptFundersofourprojectdidnothaveanyinfluenceonthecontentofthesubmittedmanuscriptnordidtheyrequireapprovalofthefinalmanuscripttobepublishedAnyuseoftradefirmorproductnamesisfordescriptivepurposesonlyanddoesnotimplyendorsementbytheUSGovernment
AUTHORSrsquo CONTRIBUTIONS
DJMCRVOELMandJLLconceived researchDJMandELMcol‐lected field data DJM CRVO and ELM conducted statisticalanalysesDJMCRVOELMKRUMDEKADRand JLLwrote themanuscriptJLLsecuredfundingAllauthorsreadandapprovedthemanuscript
ORCID
Darin J McNeil httporcidorg0000‐0003‐4595‐8354
Clint R V Otto httporcidorg0000‐0002‐7582‐3525
Amanda D Rodewald httporcidorg0000‐0002‐6719‐6306
R E FE R E N C E S
Allen‐WardellGBernhardtPBitnerRBurquezABuchmannSCaneJhellipInouyeD(1998)Thepotentialconsequencesofpollina‐tordeclinesontheconservationofbiodiversityandstabilityoffoodcropyieldsConservation Biology128ndash17
AndersonDR(2007)Model based inference in the life sciences A primer on evidenceBerlinGermanySpringerScienceampBusinessMedia
Arnold T W (2010) Uninformative parameters and model selectionusingAkaikesInformationCriterionJournal of Wildlife Management741175ndash1178httpsdoiorg101111j1937‐28172010tb01236x
Ashman T L Knight TM Steets J A Amarasekare P BurdMCampbellDRhellipMorganMT (2004)Pollen limitationofplantreproductionEcologicalandevolutionarycausesandconsequencesEcology852408ndash2421httpsdoiorg10189003‐8024
BendelCRHovickTJLimbRFampHarmonJP(2018)Variationin grazing management practices supports diverse butterflycommunitiesacrossgrasslandworking landscapesJournal of Insect Conservation221ndash13httpsdoiorg101007s10841‐017‐0041‐9
BuchananALGibbsJKomondyLampSzendreiZ(2017)Beecom‐munityof commercial potato fields inMichigan andBombus impa‐tiensvisitationtoneonicotinoid‐treatedpotatoplantsInsects830httpsdoiorg103390insects8010030
BucklandSTAndersonDRBurnhamKPampLaake JL (2005)Distance samplingHobokenNJJohnWileyampSonsLtd
BurnhamKPampAndersonDR(2002)Model selection and multimodel inference A practical information‐theoretic approachBerlinGermanySpringerScienceampBusinessMedia
BurnhamKPAndersonDRampLaakeJL(1980)Estimationofden‐sity from line transect sampling of biological populationsWildlife Monographs723ndash202
Calderone N W (2012) Insect pollinated crops insect pollinatorsandUSagricultureTrendanalysisofaggregatedatafortheperiod1992ndash2009 PLoS ONE7 e37235 httpsdoiorg101371journalpone0037235
CameronSALozierJDStrangeJPKochJBCordesNSolterL F amp Griswold T L (2011) Patterns of widespread decline in
NorthAmericanbumblebeesProceedings of the National Academy of Sciences108662ndash667httpsdoiorg101073pnas1014743108
RCore Team (2018)R A language and environment for statistical com‐puting Vienna Austria R Foundation for Statistical ComputingRetrievedfromhttpswwwR‐projectorg
Environmental Systems Research Institute (2011) ArcGIS Desktop Release 10RedlandsCaliforniaESRI
Fiske IampChandlerRB (2011)UnmarkedAnRpackage for fittinghierarchicalmodelsofwildlifeoccurrenceandabundanceJournal of Statistical Software431ndash23
Garibaldi L A Steffan‐Dewenter I Winfree R Aizen M ABommarcoRCunninghamSAhellipBartomeusI(2013)Wildpolli‐natorsenhancefruitsetofcropsregardlessofhoneybeeabundanceScience3391608ndash1611httpsdoiorg101126science1230200
Goulson D (1999) Foraging strategies of insects for gathering nec‐tar and pollen and implications for plant ecology and evolutionPerspectives in Plant Ecology Evolution and Systematics2 185ndash209httpsdoiorg1010781433‐8319‐00070
GoulsonDLyeGCampDarvillB(2008)DeclineandconservationofbumblebeesAnnual Review of Entomology53191ndash208httpsdoiorg101146annurevento53103106093454
GoulsonDNicholls E Botiacuteas C amp Rotheray E L (2015) Bee de‐clines driven by combined stress from parasites pesticides andlack of flowers Science 347 1255957 httpsdoiorg101126science1255957
Hammond P S Berggren P Benke H Borchers D L Collet AHeide‐Joslashrgensen M P hellip Oslashien N (2002) Abundance of har‐bour porpoise and other cetaceans in the North Sea and adja‐cent waters Journal of Applied Ecology 39 361ndash376 httpsdoiorg101046j1365‐2664200200713x
HanleyMEAwbiAJampFrancoM(2014)GoingnativeFlowerusebybumblebeesinEnglishurbangardensAnnals of Botany113799ndash806httpsdoiorg101093aobmcu006
Hau E amp Von Renouard H (2006) The wind resource London UKElsevier
Hedley S L amp Buckland S T (2004) Spatial models for line tran‐sect sampling Journal of Agricultural Biological and Environmental Statistics9181ndash199httpsdoiorg1011981085711043578
JamesFCampShugartHHJr(1970)AquantitativemethodofhabitatdescriptionAudubon Field Notes24727ndash736
Jepsen S Evans E Thorp R Hatfield R amp Black S H (2003)Petition to list the rusty patched bumble bee Bombus affinis (Cresson) 1863 as an endangered species under the US Endangered Species Act Retrieved from httpwwwxercesorgwp‐ontentuploads 201301Bombus‐petitionpdf
Jha S amp Kremen C (2013) Resource diversity and landscape‐levelhomogeneitydrivenativebee foragingProceedings of the National Academy of Sciences 110 555ndash558 httpsdoiorg101073pnas1208682110
KaranthKUampSunquistME(1995)PreyselectionbytigerleopardanddholeintropicalforestsJournal of Animal Ecology64439ndash450httpsdoiorg1023075647
KeacuteryMampRoyleJA (2015)Applied Hierarchical Modeling in Ecology Analysis of distribution abundance and species richness in R and BUGS Volume 1 Prelude and Static ModelsCambridgeMAAcademicPress
KeacuteryM amp Schmidt B R (2008) Imperfect detection and its conse‐quencesformonitoringforconservationCommunity Ecology9207ndash216httpsdoiorg101556ComEc92008210
Kevan PG (1990)Pollination keystone process in sustainable globalproductivity InVIInternationalSymposiumonPollination288(pp103‐110)
Kremen CWilliams NM amp Thorp RW (2002) Crop pollinationfromnativebeesatriskfromagriculturalintensificationProceedings of the National Academy of Sciences99 16812ndash16816 httpsdoiorg101073pnas262413599
emspensp emsp | emsp235McNEIL Et aL
LofflandH L Polasik J S TingleyMW Elsey E A Loffland CLebuhnGampSiegelRB(2017)Bumblebeeuseofpost‐firechap‐arralinthecentralSierraNevadaThe Journal of Wildlife Management811084ndash1097httpsdoiorg101002jwmg21280
MackenzieD I (2006)Modelingtheprobabilityof resourceuseTheeffectofanddealingwithdetectingaspeciesimperfectlyJournal of Wildlife Management70367ndash374httpsdoiorg1021930022‐541X(2006)70[367MTPORU]20CO2
MacKenzieDINicholsJDLachmanGBDroegeSAndrewRoyleJampLangtimmCA(2002)Estimatingsiteoccupancyrateswhende‐tectionprobabilitiesarelessthanoneEcology832248ndash2255httpsdoiorg1018900012‐9658(2002)083[2248ESORWD]20CO2
MacKenzieDINicholsJDRoyleJAPollockKHBaileyLampHinesJE(2005)Occupancy estimation and modeling Inferring pat‐terns and dynamics of species occurrenceLondonUKElsevier
Mackenzie D I (2003) Assessing site occupancymodelling as a toolfor monitoring Mahoenui giant weta populations Department ofConservation17
Marques T A Thomas L Fancy S G amp Buckland S T (2007)Improvingestimatesofbirddensityusingmultiple‐covariatedistancesamplingThe Auk1241229ndash1243httpsdoiorg1016420004‐8038(2007)124[1229IEOBDU]20CO2
McCaskillGLMcWilliamsWHAlerichCAButlerBJCrockerS JDomkeGMhellipWestfall JA (2009)Pennsylvaniarsquos Forests 2009NewtownSquarePAUSDepartmentofAgricultureForestServiceNorthernResearchStation
MichenerCDMcGinleyRJampDanforthBN(1994)The Bee Genera of North and Central AmericaWashingtonDCSmithsonianInstitutePress
OlesenJMBascompteJElberlingHampJordanoP(2008)TemporaldynamicsinapollinationnetworkEcology891573ndash1582httpsdoiorg10189007‐04511
PerssonA S RundloumlfMCloughYampSmithHG (2015)Bumblebees show trait‐dependent vulnerability to landscape simplifica‐tion Biodiversity and Conservation 24 3469ndash3489 httpsdoiorg101007s10531‐015‐1008‐3
Potts SGVulliamyBDafniANeemanGampWillmer P (2003)Linking bees and flowers How do floral communities structurepollinator communities Ecology 84 2628ndash2642 httpsdoiorg10189002‐0136
PottsSGBiesmeijerJCKremenCNeumannPSchweigerOampKuninWE (2010)Globalpollinatordeclinestrends impactsanddriversTrends in ecology amp evolution25(6)345ndash353
Redhead JW Dreier S Bourke A F HeardM S JordanW CSumner S hellip Carvell C (2016) Effects of habitat compositionandlandscapestructureonworkerforagingdistancesoffivebum‐ble bee species Ecological Applications 26 726ndash739 httpsdoiorg10189015‐0546
Roulston T A H Smith S A amp Brewster A L (2007) A com‐parison of pan trap and intensive net sampling techniques fordocumenting a bee (Hymenoptera Apiformes) fauna Journal of the Kansas Entomological Society 80 179ndash181 httpsdoiorg1023170022‐8567(2007)80[179ACOPTA]20CO2
Royle J A Dawson D K amp Bates S (2004) Modeling abundanceeffects in distance sampling Ecology 85 1591ndash1597 httpsdoiorg10189003‐3127
Scheper J Bommarco R Holzschuh A Potts S G Riedinger VRoberts S P hellipWickens V J (2015) Local and landscape‐level
floral resources explain effects of wildflower strips on wild beesacrossfourEuropeancountriesJournal of Applied Ecology521165ndash1175httpsdoiorg1011111365‐266412479
SeberGA(1986)AreviewofestimatinganimalabundanceBiometrics42267ndash292httpsdoiorg1023072531049
ShultzCH(1999)The Geology of PennsylvaniaPennsylvaniaGeologicalSurveyHarrisburgPAPennsylvaniaGeologicalSurvey
Sillett T S Chandler R B Royle J A KeacuteryM ampMorrison S A(2012) Hierarchical distance‐sampling models to estimate popu‐lation size and habitat‐specific abundance of an island endemicEcological Applications22(7)1997ndash2006
SollmannRGardnerBWilliamsKAGilbertATampVeitRR(2016)AhierarchicaldistancesamplingmodeltoestimateabundanceandcovariateassociationsofspeciesandcommunitiesMethods in Ecology and Evolution7529ndash537httpsdoiorg1011112041‐210X12518
Tepedino V J Durham S Cameron S A amp Goodell K (2015)Documenting bee decline or squandering scarce resourcesConservation Biology 29 280ndash282 httpsdoiorg101111cobi12439
Thomas LBuckland S TBurnhamKPAndersonDR Laake JL Borchers D L amp Strindberg S (2002) Distance samplingEncyclopediaofenvironmetrics
Thomas L Buckland S T Rexstad EA Laake J L Strindberg SHedley S L hellipBurnham K P (2010)Distance softwareDesignand analysis of distance sampling surveys for estimating pop‐ulation size Journal of Applied Ecology 47 5ndash14 httpsdoiorg101111j1365‐2664200901737x
ThompsonWL (2002)TowardsreliablebirdsurveysAccountingforindividualspresentbutnotdetectedThe Auk11918ndash25httpsdoiorg1016420004‐8038(2002)119[0018TRBSAF]20CO2
VanStrienA JTermaatTGroenendijkDMensingVampKeryM(2010) Site‐occupancy models may offer new opportunities fordragonflymonitoringbasedondailyspecies listsBasic and Applied Ecology11495ndash503httpsdoiorg101016jbaae201005003
VilsackTampMcCarthyG(2015)National strategy to promote the health of honey bees and other pollinatorsWashingtonDCReport IssuedbytheWhiteHousethePollinatorHealthTaskForce
WardKCariveauDMayERoswellMVaughanMWilliamsNhellip Gill K (2014) Streamlined Bee Monitoring Protocol for Assessing Pollinator HabitatPortlandORTheXercesSocietyforInvertebrateConservation
WeatherUndergroundInc(2018)WeatherForecastandReports‐LongRangeandLocalWundergroundRetrievedfromhttpswwwwun‐dergroundcom
WherryET Fogg JM JrampWahlHA (1979)Atlas of the flora of Pennsylvania Philadelphia PA The Morris Arboretum of theUniversityofPennsylvania
YoccozNGNichols JDampBoulinierT (2001)Monitoringofbio‐logicaldiversityinspaceandtimeTrends Ecology and Evolution16446ndash453
How to cite this articleMcNeilDJOttoCRVMoserELetalDistancemodelsasatoolformodellingdetectionprobabilityanddensityofnativebumblebeesJ Appl Entomol 2019143225ndash235 httpsdoiorg101111jen12583
emspensp emsp | emsp233McNEIL Et aL
SolidagosppsnakerootAgeratina spp)hadnotbegunfloweringyetFutureworkshouldexplorehowBombussppmaytrackresourcesacrossagrowingseasontopersistwithineasternforestecosystems
Monitoringprograms forBombus spp andothernativepolli‐natorscanbeimprovedbyincorporatingstudydesignandmodel‐based approaches for minimizing detection error Although weincludedseveraldesign‐basedsolutionsforminimizingdetectionerror(egrestrictingsurveytimesonlysurveyinginfairweatherWard et al 2014) detection probability remained imperfectand varied due to time of day observer and vegetation coverConsequentlymethodsthatignoreddetectionprobabilitygener‐ated density estimates 80ndash89 lower than HDS Past studieshaveshowntheimportanceofusingdesign‐basedapproachestominimize false negativeswhen sampling bees (BuchananGibbsKomondyampSzendrei2017)Ourstudydemonstratesthevalueofusingbothdesign‐andmodel‐basedapproachesforreducingsam‐plingerrorscausedbyimperfectdetectionOtherstudysystemswith thick vegetation cover such as prairies and forested wet‐landsorobstructiveobjectssuchasurbanenvironmentsarealsolikely to underestimate bee abundance even if multiple design‐basedapproachesareusedWhiletraditionalsamplingtechniquesthat do not account for detection have numerous applicationsourstudyhighlightstheimportanceofincorporatingmodel‐basedapproachesforaccountingfordetectionprobabilitywithinnativebeesurveysparticularlywhenattemptingtoestimatebeeabun‐danceordensity
Althoughour results suggest thatHDS representsapromisingtoolformonitoringbumblebeesresearcherswishingtoemploythemethod should recognize its associated limitations For exampledistancemodelsassumethatallanimalsonthetransectlinearede‐tectedperfectlyAlthoughitislikelythisassumptionwasmetwithalargeinsectlikeBombussppthisassumptionmightbeviolatedwithsmallerinsectsMoreoversubjectsareassumedtobeuniformlydis‐tributedinamannerunaffectedbytheobserverWhileitispossiblethatBombussppwerefrightenedbyobserverswetookcaretonotethe locationof first detection forBombus spp apparently flushedandtheirloudflightmadeclosedetectionsalmostcertainWenotethat thismethodwouldnotworkwell for species‐level identifica‐tionbecauseobservationsaremadefromadistanceandsomebeegeneraareexceedinglydifficulttoidentifyevenwithamicroscope(Michener et al 1994)Misidentification of specieswould consti‐tuteafalsepositivewhichwouldviolateanassumptionofdistancesampling
Anotherconsiderationofthisstudydesignandmanymethodsofabundanceestimationisthatanimalsmayviolatetheclosureas‐sumptionInthecaseofBombussppthislikelyoccurredasforagersflew in‐ and out‐ of the effective survey area (~5m from the ob‐serverforHDS)WhilethismayconstituteaproblemforsomestudyobjectivesandmethodswehavenoreasontobelievethatBombus sppmovementwasnonrandomwithrespecttotheobserverandanaccuratedensitycouldthereforestillbemadewhenpassivecountingwasusedClosureviolationmaybeamoreimportantproblemwhenattempting tocalculatedensity fromanettingplotwhereanimals
mayentertheplotandbeunabletoleaveastheyarecapturedandhelduntil thesurveyhasfinished Insuchcasesmovementwouldbebiasedbyindividualsimmigratingintothemonitoredplotbutun‐abletoemigrateandmovementwouldbebiasedtowardstheplotAlthough net‐based sampling is often preferable for investigatingspecies‐specific habitat relationships the potential for movementbias highlights the need for cautious interpretation of net‐baseddensityestimatesforbeesSimilarlyresearchersshouldconsiderthepotentialfordouble‐countingsubjectsAlthoughBombussppinourstudywereapparentlyfewenoughandslowenoughtoavoidmostdouble‐countingthismaybeamoreimportantproblemtoconsiderformoreabundantinsectswithreduceddetectability(egHalictids)
Wealsoadvisecautionwith interpretationofhabitatrelation‐shipsreportedhereasourstudyshouldbe interpretedasasmallldquosnapshotrdquo in time and lacking species‐specific habitat relation‐ships(OlesenBascompteElberlingampJordano2008)Full‐seasonhabitat associations are temporally dynamic forBombus spp andvaryacrossspecies(Goulson1999JhaampKremen2013)Relativefloral resourceavailabilityofdifferentspecieschangesacrosstheseasonandfuturestudiesemployingthesemethodsatregularin‐tervals from early springwhen queens first emerge through lateautumnwould prove valuable In fact examination of queen beedensities would likely prove a better assessment of populationdensityandhabitatqualitythanworkerdensitywhenmonitoringorresearchingcolonialorganismssuchasbumblebeesestimatingthetruenumberofreproducingcoloniesisofmorevaluethanes‐timating the number of foragingworkers aswe have done hereConductingHDSduringthespringandearlysummerwhenqueensare theonly activebumblebee foragersmayprove auseful andnon‐lethalapproachtoestimating theabundanceof reproductiveindividualsandtheexpectednumbersummercoloniesforagivenarea However sampling queens would likely require additionalsamplingsitesorrepeatvisitbecausecountswouldbemuchlowerandHDSmodelsmayhavetroubleconvergingwithrelativelyfewsampling locations Caution should also be exercised with inter‐pretation ofBombus spp density estimates reported here as ourdensitieslikelyconsistofmultiplespeciesofBombus modelled and reportedasoneWealsorecommendfuturestudiesexplorehownon‐Bombusgenera(ormorphospeciesfunctionalgroups)performasthefocusofHDSmodelsAlthoughHDS isnotwithout limita‐tionwebelieveourstudyhighlightstheutilityofHDSmodelsforestimatingdensitiesandelucidatinghabitatassociationsofbumblebeeswhenindividualsaredetectedimperfectly
ACKNOWLEDG EMENTS
Wethank the following individuals andagencies for their supportandlandaccessSproulStateForestandMoshannonStateForestFunding was provided by the Indiana University of PennsylvaniaBUREfundandtheUnitedStatesDepartmentofAgricultureNaturalResources Conservation Service (68‐7482‐12‐502) through theConservationEffectsAssessmentProjectWeareverygrateful toJoanMilamandSamDroegefortheircommentsonearlyversions
234emsp |emsp emspensp McNEIL Et aL
of thismanuscriptWearealsoverygrateful to threeanonymousreviewers spend considerable time strengthening thismanuscriptFundersofourprojectdidnothaveanyinfluenceonthecontentofthesubmittedmanuscriptnordidtheyrequireapprovalofthefinalmanuscripttobepublishedAnyuseoftradefirmorproductnamesisfordescriptivepurposesonlyanddoesnotimplyendorsementbytheUSGovernment
AUTHORSrsquo CONTRIBUTIONS
DJMCRVOELMandJLLconceived researchDJMandELMcol‐lected field data DJM CRVO and ELM conducted statisticalanalysesDJMCRVOELMKRUMDEKADRand JLLwrote themanuscriptJLLsecuredfundingAllauthorsreadandapprovedthemanuscript
ORCID
Darin J McNeil httporcidorg0000‐0003‐4595‐8354
Clint R V Otto httporcidorg0000‐0002‐7582‐3525
Amanda D Rodewald httporcidorg0000‐0002‐6719‐6306
R E FE R E N C E S
Allen‐WardellGBernhardtPBitnerRBurquezABuchmannSCaneJhellipInouyeD(1998)Thepotentialconsequencesofpollina‐tordeclinesontheconservationofbiodiversityandstabilityoffoodcropyieldsConservation Biology128ndash17
AndersonDR(2007)Model based inference in the life sciences A primer on evidenceBerlinGermanySpringerScienceampBusinessMedia
Arnold T W (2010) Uninformative parameters and model selectionusingAkaikesInformationCriterionJournal of Wildlife Management741175ndash1178httpsdoiorg101111j1937‐28172010tb01236x
Ashman T L Knight TM Steets J A Amarasekare P BurdMCampbellDRhellipMorganMT (2004)Pollen limitationofplantreproductionEcologicalandevolutionarycausesandconsequencesEcology852408ndash2421httpsdoiorg10189003‐8024
BendelCRHovickTJLimbRFampHarmonJP(2018)Variationin grazing management practices supports diverse butterflycommunitiesacrossgrasslandworking landscapesJournal of Insect Conservation221ndash13httpsdoiorg101007s10841‐017‐0041‐9
BuchananALGibbsJKomondyLampSzendreiZ(2017)Beecom‐munityof commercial potato fields inMichigan andBombus impa‐tiensvisitationtoneonicotinoid‐treatedpotatoplantsInsects830httpsdoiorg103390insects8010030
BucklandSTAndersonDRBurnhamKPampLaake JL (2005)Distance samplingHobokenNJJohnWileyampSonsLtd
BurnhamKPampAndersonDR(2002)Model selection and multimodel inference A practical information‐theoretic approachBerlinGermanySpringerScienceampBusinessMedia
BurnhamKPAndersonDRampLaakeJL(1980)Estimationofden‐sity from line transect sampling of biological populationsWildlife Monographs723ndash202
Calderone N W (2012) Insect pollinated crops insect pollinatorsandUSagricultureTrendanalysisofaggregatedatafortheperiod1992ndash2009 PLoS ONE7 e37235 httpsdoiorg101371journalpone0037235
CameronSALozierJDStrangeJPKochJBCordesNSolterL F amp Griswold T L (2011) Patterns of widespread decline in
NorthAmericanbumblebeesProceedings of the National Academy of Sciences108662ndash667httpsdoiorg101073pnas1014743108
RCore Team (2018)R A language and environment for statistical com‐puting Vienna Austria R Foundation for Statistical ComputingRetrievedfromhttpswwwR‐projectorg
Environmental Systems Research Institute (2011) ArcGIS Desktop Release 10RedlandsCaliforniaESRI
Fiske IampChandlerRB (2011)UnmarkedAnRpackage for fittinghierarchicalmodelsofwildlifeoccurrenceandabundanceJournal of Statistical Software431ndash23
Garibaldi L A Steffan‐Dewenter I Winfree R Aizen M ABommarcoRCunninghamSAhellipBartomeusI(2013)Wildpolli‐natorsenhancefruitsetofcropsregardlessofhoneybeeabundanceScience3391608ndash1611httpsdoiorg101126science1230200
Goulson D (1999) Foraging strategies of insects for gathering nec‐tar and pollen and implications for plant ecology and evolutionPerspectives in Plant Ecology Evolution and Systematics2 185ndash209httpsdoiorg1010781433‐8319‐00070
GoulsonDLyeGCampDarvillB(2008)DeclineandconservationofbumblebeesAnnual Review of Entomology53191ndash208httpsdoiorg101146annurevento53103106093454
GoulsonDNicholls E Botiacuteas C amp Rotheray E L (2015) Bee de‐clines driven by combined stress from parasites pesticides andlack of flowers Science 347 1255957 httpsdoiorg101126science1255957
Hammond P S Berggren P Benke H Borchers D L Collet AHeide‐Joslashrgensen M P hellip Oslashien N (2002) Abundance of har‐bour porpoise and other cetaceans in the North Sea and adja‐cent waters Journal of Applied Ecology 39 361ndash376 httpsdoiorg101046j1365‐2664200200713x
HanleyMEAwbiAJampFrancoM(2014)GoingnativeFlowerusebybumblebeesinEnglishurbangardensAnnals of Botany113799ndash806httpsdoiorg101093aobmcu006
Hau E amp Von Renouard H (2006) The wind resource London UKElsevier
Hedley S L amp Buckland S T (2004) Spatial models for line tran‐sect sampling Journal of Agricultural Biological and Environmental Statistics9181ndash199httpsdoiorg1011981085711043578
JamesFCampShugartHHJr(1970)AquantitativemethodofhabitatdescriptionAudubon Field Notes24727ndash736
Jepsen S Evans E Thorp R Hatfield R amp Black S H (2003)Petition to list the rusty patched bumble bee Bombus affinis (Cresson) 1863 as an endangered species under the US Endangered Species Act Retrieved from httpwwwxercesorgwp‐ontentuploads 201301Bombus‐petitionpdf
Jha S amp Kremen C (2013) Resource diversity and landscape‐levelhomogeneitydrivenativebee foragingProceedings of the National Academy of Sciences 110 555ndash558 httpsdoiorg101073pnas1208682110
KaranthKUampSunquistME(1995)PreyselectionbytigerleopardanddholeintropicalforestsJournal of Animal Ecology64439ndash450httpsdoiorg1023075647
KeacuteryMampRoyleJA (2015)Applied Hierarchical Modeling in Ecology Analysis of distribution abundance and species richness in R and BUGS Volume 1 Prelude and Static ModelsCambridgeMAAcademicPress
KeacuteryM amp Schmidt B R (2008) Imperfect detection and its conse‐quencesformonitoringforconservationCommunity Ecology9207ndash216httpsdoiorg101556ComEc92008210
Kevan PG (1990)Pollination keystone process in sustainable globalproductivity InVIInternationalSymposiumonPollination288(pp103‐110)
Kremen CWilliams NM amp Thorp RW (2002) Crop pollinationfromnativebeesatriskfromagriculturalintensificationProceedings of the National Academy of Sciences99 16812ndash16816 httpsdoiorg101073pnas262413599
emspensp emsp | emsp235McNEIL Et aL
LofflandH L Polasik J S TingleyMW Elsey E A Loffland CLebuhnGampSiegelRB(2017)Bumblebeeuseofpost‐firechap‐arralinthecentralSierraNevadaThe Journal of Wildlife Management811084ndash1097httpsdoiorg101002jwmg21280
MackenzieD I (2006)Modelingtheprobabilityof resourceuseTheeffectofanddealingwithdetectingaspeciesimperfectlyJournal of Wildlife Management70367ndash374httpsdoiorg1021930022‐541X(2006)70[367MTPORU]20CO2
MacKenzieDINicholsJDLachmanGBDroegeSAndrewRoyleJampLangtimmCA(2002)Estimatingsiteoccupancyrateswhende‐tectionprobabilitiesarelessthanoneEcology832248ndash2255httpsdoiorg1018900012‐9658(2002)083[2248ESORWD]20CO2
MacKenzieDINicholsJDRoyleJAPollockKHBaileyLampHinesJE(2005)Occupancy estimation and modeling Inferring pat‐terns and dynamics of species occurrenceLondonUKElsevier
Mackenzie D I (2003) Assessing site occupancymodelling as a toolfor monitoring Mahoenui giant weta populations Department ofConservation17
Marques T A Thomas L Fancy S G amp Buckland S T (2007)Improvingestimatesofbirddensityusingmultiple‐covariatedistancesamplingThe Auk1241229ndash1243httpsdoiorg1016420004‐8038(2007)124[1229IEOBDU]20CO2
McCaskillGLMcWilliamsWHAlerichCAButlerBJCrockerS JDomkeGMhellipWestfall JA (2009)Pennsylvaniarsquos Forests 2009NewtownSquarePAUSDepartmentofAgricultureForestServiceNorthernResearchStation
MichenerCDMcGinleyRJampDanforthBN(1994)The Bee Genera of North and Central AmericaWashingtonDCSmithsonianInstitutePress
OlesenJMBascompteJElberlingHampJordanoP(2008)TemporaldynamicsinapollinationnetworkEcology891573ndash1582httpsdoiorg10189007‐04511
PerssonA S RundloumlfMCloughYampSmithHG (2015)Bumblebees show trait‐dependent vulnerability to landscape simplifica‐tion Biodiversity and Conservation 24 3469ndash3489 httpsdoiorg101007s10531‐015‐1008‐3
Potts SGVulliamyBDafniANeemanGampWillmer P (2003)Linking bees and flowers How do floral communities structurepollinator communities Ecology 84 2628ndash2642 httpsdoiorg10189002‐0136
PottsSGBiesmeijerJCKremenCNeumannPSchweigerOampKuninWE (2010)Globalpollinatordeclinestrends impactsanddriversTrends in ecology amp evolution25(6)345ndash353
Redhead JW Dreier S Bourke A F HeardM S JordanW CSumner S hellip Carvell C (2016) Effects of habitat compositionandlandscapestructureonworkerforagingdistancesoffivebum‐ble bee species Ecological Applications 26 726ndash739 httpsdoiorg10189015‐0546
Roulston T A H Smith S A amp Brewster A L (2007) A com‐parison of pan trap and intensive net sampling techniques fordocumenting a bee (Hymenoptera Apiformes) fauna Journal of the Kansas Entomological Society 80 179ndash181 httpsdoiorg1023170022‐8567(2007)80[179ACOPTA]20CO2
Royle J A Dawson D K amp Bates S (2004) Modeling abundanceeffects in distance sampling Ecology 85 1591ndash1597 httpsdoiorg10189003‐3127
Scheper J Bommarco R Holzschuh A Potts S G Riedinger VRoberts S P hellipWickens V J (2015) Local and landscape‐level
floral resources explain effects of wildflower strips on wild beesacrossfourEuropeancountriesJournal of Applied Ecology521165ndash1175httpsdoiorg1011111365‐266412479
SeberGA(1986)AreviewofestimatinganimalabundanceBiometrics42267ndash292httpsdoiorg1023072531049
ShultzCH(1999)The Geology of PennsylvaniaPennsylvaniaGeologicalSurveyHarrisburgPAPennsylvaniaGeologicalSurvey
Sillett T S Chandler R B Royle J A KeacuteryM ampMorrison S A(2012) Hierarchical distance‐sampling models to estimate popu‐lation size and habitat‐specific abundance of an island endemicEcological Applications22(7)1997ndash2006
SollmannRGardnerBWilliamsKAGilbertATampVeitRR(2016)AhierarchicaldistancesamplingmodeltoestimateabundanceandcovariateassociationsofspeciesandcommunitiesMethods in Ecology and Evolution7529ndash537httpsdoiorg1011112041‐210X12518
Tepedino V J Durham S Cameron S A amp Goodell K (2015)Documenting bee decline or squandering scarce resourcesConservation Biology 29 280ndash282 httpsdoiorg101111cobi12439
Thomas LBuckland S TBurnhamKPAndersonDR Laake JL Borchers D L amp Strindberg S (2002) Distance samplingEncyclopediaofenvironmetrics
Thomas L Buckland S T Rexstad EA Laake J L Strindberg SHedley S L hellipBurnham K P (2010)Distance softwareDesignand analysis of distance sampling surveys for estimating pop‐ulation size Journal of Applied Ecology 47 5ndash14 httpsdoiorg101111j1365‐2664200901737x
ThompsonWL (2002)TowardsreliablebirdsurveysAccountingforindividualspresentbutnotdetectedThe Auk11918ndash25httpsdoiorg1016420004‐8038(2002)119[0018TRBSAF]20CO2
VanStrienA JTermaatTGroenendijkDMensingVampKeryM(2010) Site‐occupancy models may offer new opportunities fordragonflymonitoringbasedondailyspecies listsBasic and Applied Ecology11495ndash503httpsdoiorg101016jbaae201005003
VilsackTampMcCarthyG(2015)National strategy to promote the health of honey bees and other pollinatorsWashingtonDCReport IssuedbytheWhiteHousethePollinatorHealthTaskForce
WardKCariveauDMayERoswellMVaughanMWilliamsNhellip Gill K (2014) Streamlined Bee Monitoring Protocol for Assessing Pollinator HabitatPortlandORTheXercesSocietyforInvertebrateConservation
WeatherUndergroundInc(2018)WeatherForecastandReports‐LongRangeandLocalWundergroundRetrievedfromhttpswwwwun‐dergroundcom
WherryET Fogg JM JrampWahlHA (1979)Atlas of the flora of Pennsylvania Philadelphia PA The Morris Arboretum of theUniversityofPennsylvania
YoccozNGNichols JDampBoulinierT (2001)Monitoringofbio‐logicaldiversityinspaceandtimeTrends Ecology and Evolution16446ndash453
How to cite this articleMcNeilDJOttoCRVMoserELetalDistancemodelsasatoolformodellingdetectionprobabilityanddensityofnativebumblebeesJ Appl Entomol 2019143225ndash235 httpsdoiorg101111jen12583
234emsp |emsp emspensp McNEIL Et aL
of thismanuscriptWearealsoverygrateful to threeanonymousreviewers spend considerable time strengthening thismanuscriptFundersofourprojectdidnothaveanyinfluenceonthecontentofthesubmittedmanuscriptnordidtheyrequireapprovalofthefinalmanuscripttobepublishedAnyuseoftradefirmorproductnamesisfordescriptivepurposesonlyanddoesnotimplyendorsementbytheUSGovernment
AUTHORSrsquo CONTRIBUTIONS
DJMCRVOELMandJLLconceived researchDJMandELMcol‐lected field data DJM CRVO and ELM conducted statisticalanalysesDJMCRVOELMKRUMDEKADRand JLLwrote themanuscriptJLLsecuredfundingAllauthorsreadandapprovedthemanuscript
ORCID
Darin J McNeil httporcidorg0000‐0003‐4595‐8354
Clint R V Otto httporcidorg0000‐0002‐7582‐3525
Amanda D Rodewald httporcidorg0000‐0002‐6719‐6306
R E FE R E N C E S
Allen‐WardellGBernhardtPBitnerRBurquezABuchmannSCaneJhellipInouyeD(1998)Thepotentialconsequencesofpollina‐tordeclinesontheconservationofbiodiversityandstabilityoffoodcropyieldsConservation Biology128ndash17
AndersonDR(2007)Model based inference in the life sciences A primer on evidenceBerlinGermanySpringerScienceampBusinessMedia
Arnold T W (2010) Uninformative parameters and model selectionusingAkaikesInformationCriterionJournal of Wildlife Management741175ndash1178httpsdoiorg101111j1937‐28172010tb01236x
Ashman T L Knight TM Steets J A Amarasekare P BurdMCampbellDRhellipMorganMT (2004)Pollen limitationofplantreproductionEcologicalandevolutionarycausesandconsequencesEcology852408ndash2421httpsdoiorg10189003‐8024
BendelCRHovickTJLimbRFampHarmonJP(2018)Variationin grazing management practices supports diverse butterflycommunitiesacrossgrasslandworking landscapesJournal of Insect Conservation221ndash13httpsdoiorg101007s10841‐017‐0041‐9
BuchananALGibbsJKomondyLampSzendreiZ(2017)Beecom‐munityof commercial potato fields inMichigan andBombus impa‐tiensvisitationtoneonicotinoid‐treatedpotatoplantsInsects830httpsdoiorg103390insects8010030
BucklandSTAndersonDRBurnhamKPampLaake JL (2005)Distance samplingHobokenNJJohnWileyampSonsLtd
BurnhamKPampAndersonDR(2002)Model selection and multimodel inference A practical information‐theoretic approachBerlinGermanySpringerScienceampBusinessMedia
BurnhamKPAndersonDRampLaakeJL(1980)Estimationofden‐sity from line transect sampling of biological populationsWildlife Monographs723ndash202
Calderone N W (2012) Insect pollinated crops insect pollinatorsandUSagricultureTrendanalysisofaggregatedatafortheperiod1992ndash2009 PLoS ONE7 e37235 httpsdoiorg101371journalpone0037235
CameronSALozierJDStrangeJPKochJBCordesNSolterL F amp Griswold T L (2011) Patterns of widespread decline in
NorthAmericanbumblebeesProceedings of the National Academy of Sciences108662ndash667httpsdoiorg101073pnas1014743108
RCore Team (2018)R A language and environment for statistical com‐puting Vienna Austria R Foundation for Statistical ComputingRetrievedfromhttpswwwR‐projectorg
Environmental Systems Research Institute (2011) ArcGIS Desktop Release 10RedlandsCaliforniaESRI
Fiske IampChandlerRB (2011)UnmarkedAnRpackage for fittinghierarchicalmodelsofwildlifeoccurrenceandabundanceJournal of Statistical Software431ndash23
Garibaldi L A Steffan‐Dewenter I Winfree R Aizen M ABommarcoRCunninghamSAhellipBartomeusI(2013)Wildpolli‐natorsenhancefruitsetofcropsregardlessofhoneybeeabundanceScience3391608ndash1611httpsdoiorg101126science1230200
Goulson D (1999) Foraging strategies of insects for gathering nec‐tar and pollen and implications for plant ecology and evolutionPerspectives in Plant Ecology Evolution and Systematics2 185ndash209httpsdoiorg1010781433‐8319‐00070
GoulsonDLyeGCampDarvillB(2008)DeclineandconservationofbumblebeesAnnual Review of Entomology53191ndash208httpsdoiorg101146annurevento53103106093454
GoulsonDNicholls E Botiacuteas C amp Rotheray E L (2015) Bee de‐clines driven by combined stress from parasites pesticides andlack of flowers Science 347 1255957 httpsdoiorg101126science1255957
Hammond P S Berggren P Benke H Borchers D L Collet AHeide‐Joslashrgensen M P hellip Oslashien N (2002) Abundance of har‐bour porpoise and other cetaceans in the North Sea and adja‐cent waters Journal of Applied Ecology 39 361ndash376 httpsdoiorg101046j1365‐2664200200713x
HanleyMEAwbiAJampFrancoM(2014)GoingnativeFlowerusebybumblebeesinEnglishurbangardensAnnals of Botany113799ndash806httpsdoiorg101093aobmcu006
Hau E amp Von Renouard H (2006) The wind resource London UKElsevier
Hedley S L amp Buckland S T (2004) Spatial models for line tran‐sect sampling Journal of Agricultural Biological and Environmental Statistics9181ndash199httpsdoiorg1011981085711043578
JamesFCampShugartHHJr(1970)AquantitativemethodofhabitatdescriptionAudubon Field Notes24727ndash736
Jepsen S Evans E Thorp R Hatfield R amp Black S H (2003)Petition to list the rusty patched bumble bee Bombus affinis (Cresson) 1863 as an endangered species under the US Endangered Species Act Retrieved from httpwwwxercesorgwp‐ontentuploads 201301Bombus‐petitionpdf
Jha S amp Kremen C (2013) Resource diversity and landscape‐levelhomogeneitydrivenativebee foragingProceedings of the National Academy of Sciences 110 555ndash558 httpsdoiorg101073pnas1208682110
KaranthKUampSunquistME(1995)PreyselectionbytigerleopardanddholeintropicalforestsJournal of Animal Ecology64439ndash450httpsdoiorg1023075647
KeacuteryMampRoyleJA (2015)Applied Hierarchical Modeling in Ecology Analysis of distribution abundance and species richness in R and BUGS Volume 1 Prelude and Static ModelsCambridgeMAAcademicPress
KeacuteryM amp Schmidt B R (2008) Imperfect detection and its conse‐quencesformonitoringforconservationCommunity Ecology9207ndash216httpsdoiorg101556ComEc92008210
Kevan PG (1990)Pollination keystone process in sustainable globalproductivity InVIInternationalSymposiumonPollination288(pp103‐110)
Kremen CWilliams NM amp Thorp RW (2002) Crop pollinationfromnativebeesatriskfromagriculturalintensificationProceedings of the National Academy of Sciences99 16812ndash16816 httpsdoiorg101073pnas262413599
emspensp emsp | emsp235McNEIL Et aL
LofflandH L Polasik J S TingleyMW Elsey E A Loffland CLebuhnGampSiegelRB(2017)Bumblebeeuseofpost‐firechap‐arralinthecentralSierraNevadaThe Journal of Wildlife Management811084ndash1097httpsdoiorg101002jwmg21280
MackenzieD I (2006)Modelingtheprobabilityof resourceuseTheeffectofanddealingwithdetectingaspeciesimperfectlyJournal of Wildlife Management70367ndash374httpsdoiorg1021930022‐541X(2006)70[367MTPORU]20CO2
MacKenzieDINicholsJDLachmanGBDroegeSAndrewRoyleJampLangtimmCA(2002)Estimatingsiteoccupancyrateswhende‐tectionprobabilitiesarelessthanoneEcology832248ndash2255httpsdoiorg1018900012‐9658(2002)083[2248ESORWD]20CO2
MacKenzieDINicholsJDRoyleJAPollockKHBaileyLampHinesJE(2005)Occupancy estimation and modeling Inferring pat‐terns and dynamics of species occurrenceLondonUKElsevier
Mackenzie D I (2003) Assessing site occupancymodelling as a toolfor monitoring Mahoenui giant weta populations Department ofConservation17
Marques T A Thomas L Fancy S G amp Buckland S T (2007)Improvingestimatesofbirddensityusingmultiple‐covariatedistancesamplingThe Auk1241229ndash1243httpsdoiorg1016420004‐8038(2007)124[1229IEOBDU]20CO2
McCaskillGLMcWilliamsWHAlerichCAButlerBJCrockerS JDomkeGMhellipWestfall JA (2009)Pennsylvaniarsquos Forests 2009NewtownSquarePAUSDepartmentofAgricultureForestServiceNorthernResearchStation
MichenerCDMcGinleyRJampDanforthBN(1994)The Bee Genera of North and Central AmericaWashingtonDCSmithsonianInstitutePress
OlesenJMBascompteJElberlingHampJordanoP(2008)TemporaldynamicsinapollinationnetworkEcology891573ndash1582httpsdoiorg10189007‐04511
PerssonA S RundloumlfMCloughYampSmithHG (2015)Bumblebees show trait‐dependent vulnerability to landscape simplifica‐tion Biodiversity and Conservation 24 3469ndash3489 httpsdoiorg101007s10531‐015‐1008‐3
Potts SGVulliamyBDafniANeemanGampWillmer P (2003)Linking bees and flowers How do floral communities structurepollinator communities Ecology 84 2628ndash2642 httpsdoiorg10189002‐0136
PottsSGBiesmeijerJCKremenCNeumannPSchweigerOampKuninWE (2010)Globalpollinatordeclinestrends impactsanddriversTrends in ecology amp evolution25(6)345ndash353
Redhead JW Dreier S Bourke A F HeardM S JordanW CSumner S hellip Carvell C (2016) Effects of habitat compositionandlandscapestructureonworkerforagingdistancesoffivebum‐ble bee species Ecological Applications 26 726ndash739 httpsdoiorg10189015‐0546
Roulston T A H Smith S A amp Brewster A L (2007) A com‐parison of pan trap and intensive net sampling techniques fordocumenting a bee (Hymenoptera Apiformes) fauna Journal of the Kansas Entomological Society 80 179ndash181 httpsdoiorg1023170022‐8567(2007)80[179ACOPTA]20CO2
Royle J A Dawson D K amp Bates S (2004) Modeling abundanceeffects in distance sampling Ecology 85 1591ndash1597 httpsdoiorg10189003‐3127
Scheper J Bommarco R Holzschuh A Potts S G Riedinger VRoberts S P hellipWickens V J (2015) Local and landscape‐level
floral resources explain effects of wildflower strips on wild beesacrossfourEuropeancountriesJournal of Applied Ecology521165ndash1175httpsdoiorg1011111365‐266412479
SeberGA(1986)AreviewofestimatinganimalabundanceBiometrics42267ndash292httpsdoiorg1023072531049
ShultzCH(1999)The Geology of PennsylvaniaPennsylvaniaGeologicalSurveyHarrisburgPAPennsylvaniaGeologicalSurvey
Sillett T S Chandler R B Royle J A KeacuteryM ampMorrison S A(2012) Hierarchical distance‐sampling models to estimate popu‐lation size and habitat‐specific abundance of an island endemicEcological Applications22(7)1997ndash2006
SollmannRGardnerBWilliamsKAGilbertATampVeitRR(2016)AhierarchicaldistancesamplingmodeltoestimateabundanceandcovariateassociationsofspeciesandcommunitiesMethods in Ecology and Evolution7529ndash537httpsdoiorg1011112041‐210X12518
Tepedino V J Durham S Cameron S A amp Goodell K (2015)Documenting bee decline or squandering scarce resourcesConservation Biology 29 280ndash282 httpsdoiorg101111cobi12439
Thomas LBuckland S TBurnhamKPAndersonDR Laake JL Borchers D L amp Strindberg S (2002) Distance samplingEncyclopediaofenvironmetrics
Thomas L Buckland S T Rexstad EA Laake J L Strindberg SHedley S L hellipBurnham K P (2010)Distance softwareDesignand analysis of distance sampling surveys for estimating pop‐ulation size Journal of Applied Ecology 47 5ndash14 httpsdoiorg101111j1365‐2664200901737x
ThompsonWL (2002)TowardsreliablebirdsurveysAccountingforindividualspresentbutnotdetectedThe Auk11918ndash25httpsdoiorg1016420004‐8038(2002)119[0018TRBSAF]20CO2
VanStrienA JTermaatTGroenendijkDMensingVampKeryM(2010) Site‐occupancy models may offer new opportunities fordragonflymonitoringbasedondailyspecies listsBasic and Applied Ecology11495ndash503httpsdoiorg101016jbaae201005003
VilsackTampMcCarthyG(2015)National strategy to promote the health of honey bees and other pollinatorsWashingtonDCReport IssuedbytheWhiteHousethePollinatorHealthTaskForce
WardKCariveauDMayERoswellMVaughanMWilliamsNhellip Gill K (2014) Streamlined Bee Monitoring Protocol for Assessing Pollinator HabitatPortlandORTheXercesSocietyforInvertebrateConservation
WeatherUndergroundInc(2018)WeatherForecastandReports‐LongRangeandLocalWundergroundRetrievedfromhttpswwwwun‐dergroundcom
WherryET Fogg JM JrampWahlHA (1979)Atlas of the flora of Pennsylvania Philadelphia PA The Morris Arboretum of theUniversityofPennsylvania
YoccozNGNichols JDampBoulinierT (2001)Monitoringofbio‐logicaldiversityinspaceandtimeTrends Ecology and Evolution16446ndash453
How to cite this articleMcNeilDJOttoCRVMoserELetalDistancemodelsasatoolformodellingdetectionprobabilityanddensityofnativebumblebeesJ Appl Entomol 2019143225ndash235 httpsdoiorg101111jen12583
emspensp emsp | emsp235McNEIL Et aL
LofflandH L Polasik J S TingleyMW Elsey E A Loffland CLebuhnGampSiegelRB(2017)Bumblebeeuseofpost‐firechap‐arralinthecentralSierraNevadaThe Journal of Wildlife Management811084ndash1097httpsdoiorg101002jwmg21280
MackenzieD I (2006)Modelingtheprobabilityof resourceuseTheeffectofanddealingwithdetectingaspeciesimperfectlyJournal of Wildlife Management70367ndash374httpsdoiorg1021930022‐541X(2006)70[367MTPORU]20CO2
MacKenzieDINicholsJDLachmanGBDroegeSAndrewRoyleJampLangtimmCA(2002)Estimatingsiteoccupancyrateswhende‐tectionprobabilitiesarelessthanoneEcology832248ndash2255httpsdoiorg1018900012‐9658(2002)083[2248ESORWD]20CO2
MacKenzieDINicholsJDRoyleJAPollockKHBaileyLampHinesJE(2005)Occupancy estimation and modeling Inferring pat‐terns and dynamics of species occurrenceLondonUKElsevier
Mackenzie D I (2003) Assessing site occupancymodelling as a toolfor monitoring Mahoenui giant weta populations Department ofConservation17
Marques T A Thomas L Fancy S G amp Buckland S T (2007)Improvingestimatesofbirddensityusingmultiple‐covariatedistancesamplingThe Auk1241229ndash1243httpsdoiorg1016420004‐8038(2007)124[1229IEOBDU]20CO2
McCaskillGLMcWilliamsWHAlerichCAButlerBJCrockerS JDomkeGMhellipWestfall JA (2009)Pennsylvaniarsquos Forests 2009NewtownSquarePAUSDepartmentofAgricultureForestServiceNorthernResearchStation
MichenerCDMcGinleyRJampDanforthBN(1994)The Bee Genera of North and Central AmericaWashingtonDCSmithsonianInstitutePress
OlesenJMBascompteJElberlingHampJordanoP(2008)TemporaldynamicsinapollinationnetworkEcology891573ndash1582httpsdoiorg10189007‐04511
PerssonA S RundloumlfMCloughYampSmithHG (2015)Bumblebees show trait‐dependent vulnerability to landscape simplifica‐tion Biodiversity and Conservation 24 3469ndash3489 httpsdoiorg101007s10531‐015‐1008‐3
Potts SGVulliamyBDafniANeemanGampWillmer P (2003)Linking bees and flowers How do floral communities structurepollinator communities Ecology 84 2628ndash2642 httpsdoiorg10189002‐0136
PottsSGBiesmeijerJCKremenCNeumannPSchweigerOampKuninWE (2010)Globalpollinatordeclinestrends impactsanddriversTrends in ecology amp evolution25(6)345ndash353
Redhead JW Dreier S Bourke A F HeardM S JordanW CSumner S hellip Carvell C (2016) Effects of habitat compositionandlandscapestructureonworkerforagingdistancesoffivebum‐ble bee species Ecological Applications 26 726ndash739 httpsdoiorg10189015‐0546
Roulston T A H Smith S A amp Brewster A L (2007) A com‐parison of pan trap and intensive net sampling techniques fordocumenting a bee (Hymenoptera Apiformes) fauna Journal of the Kansas Entomological Society 80 179ndash181 httpsdoiorg1023170022‐8567(2007)80[179ACOPTA]20CO2
Royle J A Dawson D K amp Bates S (2004) Modeling abundanceeffects in distance sampling Ecology 85 1591ndash1597 httpsdoiorg10189003‐3127
Scheper J Bommarco R Holzschuh A Potts S G Riedinger VRoberts S P hellipWickens V J (2015) Local and landscape‐level
floral resources explain effects of wildflower strips on wild beesacrossfourEuropeancountriesJournal of Applied Ecology521165ndash1175httpsdoiorg1011111365‐266412479
SeberGA(1986)AreviewofestimatinganimalabundanceBiometrics42267ndash292httpsdoiorg1023072531049
ShultzCH(1999)The Geology of PennsylvaniaPennsylvaniaGeologicalSurveyHarrisburgPAPennsylvaniaGeologicalSurvey
Sillett T S Chandler R B Royle J A KeacuteryM ampMorrison S A(2012) Hierarchical distance‐sampling models to estimate popu‐lation size and habitat‐specific abundance of an island endemicEcological Applications22(7)1997ndash2006
SollmannRGardnerBWilliamsKAGilbertATampVeitRR(2016)AhierarchicaldistancesamplingmodeltoestimateabundanceandcovariateassociationsofspeciesandcommunitiesMethods in Ecology and Evolution7529ndash537httpsdoiorg1011112041‐210X12518
Tepedino V J Durham S Cameron S A amp Goodell K (2015)Documenting bee decline or squandering scarce resourcesConservation Biology 29 280ndash282 httpsdoiorg101111cobi12439
Thomas LBuckland S TBurnhamKPAndersonDR Laake JL Borchers D L amp Strindberg S (2002) Distance samplingEncyclopediaofenvironmetrics
Thomas L Buckland S T Rexstad EA Laake J L Strindberg SHedley S L hellipBurnham K P (2010)Distance softwareDesignand analysis of distance sampling surveys for estimating pop‐ulation size Journal of Applied Ecology 47 5ndash14 httpsdoiorg101111j1365‐2664200901737x
ThompsonWL (2002)TowardsreliablebirdsurveysAccountingforindividualspresentbutnotdetectedThe Auk11918ndash25httpsdoiorg1016420004‐8038(2002)119[0018TRBSAF]20CO2
VanStrienA JTermaatTGroenendijkDMensingVampKeryM(2010) Site‐occupancy models may offer new opportunities fordragonflymonitoringbasedondailyspecies listsBasic and Applied Ecology11495ndash503httpsdoiorg101016jbaae201005003
VilsackTampMcCarthyG(2015)National strategy to promote the health of honey bees and other pollinatorsWashingtonDCReport IssuedbytheWhiteHousethePollinatorHealthTaskForce
WardKCariveauDMayERoswellMVaughanMWilliamsNhellip Gill K (2014) Streamlined Bee Monitoring Protocol for Assessing Pollinator HabitatPortlandORTheXercesSocietyforInvertebrateConservation
WeatherUndergroundInc(2018)WeatherForecastandReports‐LongRangeandLocalWundergroundRetrievedfromhttpswwwwun‐dergroundcom
WherryET Fogg JM JrampWahlHA (1979)Atlas of the flora of Pennsylvania Philadelphia PA The Morris Arboretum of theUniversityofPennsylvania
YoccozNGNichols JDampBoulinierT (2001)Monitoringofbio‐logicaldiversityinspaceandtimeTrends Ecology and Evolution16446ndash453
How to cite this articleMcNeilDJOttoCRVMoserELetalDistancemodelsasatoolformodellingdetectionprobabilityanddensityofnativebumblebeesJ Appl Entomol 2019143225ndash235 httpsdoiorg101111jen12583