©CopyrightJASSS

ScottHeckbert(2013)

MayaSim:AnAgent-BasedModeloftheAncientMayaSocial-EcologicalSystem

JournalofArtificialSocietiesandSocialSimulation 16(4)11<http://jasss.soc.surrey.ac.uk/16/4/11.html>

Received:20-Aug-2012Accepted:02-Jun-2013Published:31-Oct-2013

Abstract

ThispaperpresentsresultsfromtheMayaSimmodel,anintegratedagent-based,cellularautomata,andnetworkmodelrepresentingtheancientMayasocial-ecologicalsystem.Themodelrepresentstherelationshipbetweenpopulationgrowth,agriculturalproduction,soildegradation,climatevariability,primaryproductivity,hydrology,ecosystemservices,forestsuccession,andthestabilityoftradenetworks.Agentsrepresentingsettlementsdevelopandexpandwithinaspatiallandscapethatchangesunderclimatevariationandrespondstoanthropogenicimpacts.ThemodelisabletoreproducespatialpatternsandtimelinessomewhatanalogoustothatoftheancientMaya,althoughthisproof-of-conceptmodelrequiresrefinementandfurtherarchaeologicaldataforcalibration.Thispaperaimstoidentifycandidatefeaturesofaresilientversusvulnerablesocial-ecologicalsystem,andemployscomputersimulationtoexplorethistopic,usingtheancientMayaasanexample.Complexsystemsmodellingidentifieshowinterconnectedvariablesbehave,consideringfast-movingvariablessuchaslandcoverchangeandtradeconnections,meso-speedvariablessuchasdemographicsandclimatevariability,aswellasslow-movingvariablessuchassoildegradation.

Keywords:Social-EcologicalSystem,Archaeology,CellularAutomata,NetworkModel,TradeNetwork,Agent-BasedModel

Introduction

1.1 Fewtopicsgainasmuchcross-disciplinaryinterestastheriseandfallofancientcivilisations.Thestoryofdevelopmentanddemiseincomplexsocietiescontainsnarrativesofthehumanendeavourthreatenedbydevastatingdroughts,greedyrulers,foreignimperialism,andoveruseofnaturalresources,amongothers.Societiesare,however,asetofinteractingelementswhichasawholeexpresscharacteristicfeatures,interpretedasemergentpropertiesofunderlyingprocessesatmultiplescales.Designingaholisticapproachtounderstandingsocial-ecologicalsystemsrequiresmethodswhichsimultaneouslyobservepatternsinmanydimensions,akindofobservationforwhichvanderLeeuw(2012)arguesthattraditionalWesternscienceisnotverywellequipped.AnanalogyistheexampleofsolvingaRubik'sCube,inthatonecannotgetthecube'inorder'bydealingfirstwithoneside,thenthenext,andsoforth.Theonlywaytoarriveatorderisbylookingatthepatternsonallsidessimultaneously,andnotfavouringanyparticularoneatanytime(vanderLeeuw2012).Thispaperpresentsamethodtoidentifycandidatefeaturesofaresilientversusvulnerablesocial-ecologicalsystem,andemployscomplexsystemsscience,usingcomputersimulationtoexplorethistopicusingtheancientMayaasanexample.

1.2 Anumberofresearchquestionsarepresentedforexploration:

WhatdynamicsleadtothedevelopmentofthedenselypopulatedandinterconnectedhumangeographyoftheancientMaya?Isitpossibletousecomputationalsocialscienceto'grow'thethreeMayatemporalperiodsofthePreclassic(1000BC-AD250),Classic(AD250-900),andPostclassic(AD900-1500)?Howdoesthesimulatedsocial-ecologicalsystemdevelopandrespondtochangingconditions,andwhatmodelledindicatorswarnofvulnerability?

Inordertoexploretheseresearchquestions,asimulationmodelwasdesignedandcalibratedforthelandscapeofCentralAmerica.Modelrunsproducetemporalandspatialpatternsthatcanbeunderstoodthroughexaminingtheunderlyingassumptionsofthedifferentintegratedcomponentsofthemodel.MayaSimisacombinedagent-based,cellularautomata,andnetworkmodelthatrepresentstheancientMayasocial-ecologicalsystem.Agents,cells,andnetworksareprogrammedtorepresentelementsofthehistoricalMayacivilisation,includingdemographics,trade,agriculture,soildegradation,provisionofecosystemservices,climatevariability,hydrology,primaryproductivity,andforestsuccession.Simulatingtheseincombinationallowspatternstoemergeatthelandscapelevel,effectivelygrowingthesocial-ecologicalsystemfromthebottomup.Thisapproachconstructsanartificialsocial-ecologicallaboratorywheredifferenttheoriescanbetestedandhypothesesproposedforhowthesystemwillperformunderdifferentconfigurations.

1.3 ThemodelisabletoreproducespatialpatternsandtimelinessomewhatanalogoustothatoftheancientMaya'shistory.Thisproofofconceptmodelrequiresrefinementandfurtherarchaeologicaldataforcalibrationtoimproveresults,althoughitisnotedthatthereislittleempiricalevidencebywhichtovalidatesuchmodels,andsuchevidenceisgenerallysite-specificanddiscontinuousthroughtime.

1.4 Thepurposeofthemodelistobetterunderstandthecomplexdynamicsofsocial-ecologicalsystemsandtotestquantitativeindicatorsofresilienceaspredictorsofsystemsustainability.Anintegratedagent-based,cellularautomata,andnetworkmodelwasconstructedusingthesoftwareNetlogo(Wilensky1999).Thefullmodel,codeanddocumentationisavailableinHeckbert(2012)viathewww.openabm.orgwebsite,andfurtherdescriptionofthemodelinthecontextofMayaarchaeologicalliteratureispresentedinHeckbertetal.(inpress).

Methods

2.1 TheMayaSimmodelrepresentssettlementsasagentslocatedinagriddedlandscape.ThemodelisconstructedusingthesoftwareNetlogo(Wilensky1999).Thesoftwareinterface,showninFigure1,presentsthespatialviewofthemodelwithgraphstrackingmodeldataandauserinterfaceforinteractingwiththe

model.Theviewcanbechangedtoobservedifferentspatialdatalayerswithinthemodel.Themodeloperatesataspatialextentof516,484km2witha20km2

http://jasss.soc.surrey.ac.uk/16/4/11.html 1 15/10/2015

resolution.Temporalextentis650timessteps,eachrepresentingroughly2years.

2.2 Uponmodelinitialisation,baseGISlayersareimportedusingtheNetlogoGISextension.Staticcellvariablesaresettherein,dynamicvariablesareresettodefaultvaluessetontheuserinterface,andsettlementagentsarerandomlyinitialisedinthespatiallandscape.Importedspatialdataincludeelevationandslope(Farretal.2007),soilproductivity(FAO2007),andtemperatureandprecipitation(Hijmansetal.2005).DataforsoilproductivitywasslightlysmoothedusingtheNetlogofunctiondiffusetomakedifferencesalongpolygonboundarieslessstark,butallotherdataisunchangedfromthecitedsources.Dataisresampledata20km2resolutionusingtheNetlogoGISextension(seeWilensky1999).AllGISdataishighresolutionanddeemedtobeofhighqualityexceptpossiblythesoilproductivitydataset.Thelatterdatasetcanbereplacedwithfinerresolutionregionalorcountry-specificdata,butbecausetheregionextendsacrossseveralmoderncountrieswithinconsistentdatasets,thebestgloballyconsistentdatasetavailablewasused.FutureworkwillaimtoreplacetheexistingdatasetwiththeHarmonizedWorldSoilDatabase(FAOetal.2009)forfinerspatialresolutionandconsistencyacrosscountryborders.

Figure1.MayaSimmodelinterfacewithinteractivecontrols,spatialview,andgraphstrackingmodeldata.Agentsoperateonacellularlandscapeandareconnectedbylinkswithinanetwork.

2.3 Thesimulationbeginswithcalculationsofbiophysicalvariablesforwaterflowandnetprimaryproductivity,andthesearefurtherusedtocalculateforestsuccession,agriculturalproduction,andecosystemservices.Settlementagentsinteractwiththespatiallandscapetogenerateagriculturalyieldthroughcropping,derivebenefitfromlocalecosystemservices,andgeneratetradebenefitswithintheirlocaltradenetwork.Thecombinedbenefitsofagriculture,ecosystemservices,andtradedrivesdemographicgrowthincludingmigration.Simulatingtheintegratedsystemrevealshowthesocial-ecologicalsystemfunctionsthroughtime.Additionalagentsincludea'migrant'agentwhosettlenewlocations,a'raindrop'agentwhichrouteshydrologicalsurfaceflow,anda'networksearchagent'whotraverseslinksbetweenconnectedsettlementnodestocalculatenetworkstatistics.Thefollowingsectiondescribesbiophysicalandanthropogenicprocessesthataretrackedinthemodel.

Biophysicalfunctions:climate,hydrology,soil,primaryproductivity,forestsandecosystemservices

2.4 Spatialdataforprecipitationandtemperature(Hijmansetal.2005)representingcurrentconditions(1950topresentday)isadjustedwithinthemodelusingassumptionsthatmimicthepaleoclimaticvariationpresentedinPruferetal.(2011).Variationinprecipitationismorepronouncedtowardsthenorthwestofthecasestudyarea.Thisdiagonalnorth-south/east-westvariationinrainfalliscreatedoverthecurrent-dayGISdataforprecipitation,usingthefunction:

(1)

whereRj,Tisprecipitation[mm]forcelljatinitialtimestepT,andCLnisalocalizedrainfalleffectduetothepresenceofclearedlandonneighbouringcellsn=1…8withweightingparameterδdeterminingthestrengthofthiseffect.DFjisthedistance[km]ofeachcellfromthetopnorthwestcornerofthemapandisthefurthestdistancedcellfromthispoint.RCtcyclesfrom+20%to-10%linearlyovera56timestepcycle,andt=1…650.Thisfunctionservestoreduceandincreaserainfallcyclically,withamorepronouncedeffectfurthertowardsthenorthwest.

2.5 Asurface-flowhydrologicalmodelwasdevisedtorecreatepastconditionsbasedonelevationandrainfall.Thesedataareusedtocalculatesurfaceflowandlocationofpotentialseasonalstandingwater,consistentwithReaney(2008).Eachcellgeneratesamobile'raindrop'agentcontainingprecipitationvolumeRj,T.Theraindropsfollowtheelevationdata,repeatedlymovingtotheadjacentcellwiththelowestelevation(andconsideringthesummedvolume[mm]ofraindropsalreadyatthatlocation).Ifraindropscannotmove(i.e.,alocationisflooded),theraindrops'pool'andformriverandlakepatterns,asshowninFigure2depictingsimulatedwaterflowunderclimatevariationassumptions.ThisflowpatterncanbevalidatedagainsthydrologicalprocessingfunctionsinGISsoftware.Thefunctionservestomovewaterbasedonelevation,andcangeneratethespatialdistributionandsurfacewaterflowasprecipitationvariesacrosstheclimatecycle.SeeequationsinmodelcodereadilyexploredinHeckbert(2012).Theresultoftheseequationsisafinely-resolvedspatialpatternthatisabletorecreatethepotentialriver,lake,andwetlandsystemsunderclimatevariationassumptions.Animportantcaveatofthemodelassumptions,however,isthelackofheterogeneityininfiltrationratesacrosstheregion.Inreality,thesurfacewaterinmanyareasdrainsrapidlytotheaquiferowingtothekarstlimestonebedrock,howeverspatialdatatoinformthisprocesswasnotabletobesourced,andassuchaconstantrateofinfiltrationisassumedacrossthelandscape,andisatopicforfurtherresearcheffort.

http://jasss.soc.surrey.ac.uk/16/4/11.html 2 15/10/2015

Figure2.Simulatedsurfacewaterflow[m3](blueonwhitebackground,darkerbluebeinggreaterflow)basedonclimatevariationassumptionsofa)-15%,b)0%,andc)+15%changeinannualprecipitationinequation1.

2.6 ThebaseGISlayersforrainfallandtemperatureareusedtocalculatenetprimaryproductivity,whichinturnisusedtocalculateforestsuccession.GISsoildataisusedtocalculateagriculturalproductivity,andallthesecombinetocalculateprovisionofecosystemservices.Whilewerecognizethattheserelationshipsarecomplex,simplifyingassumptionsallowinitialrepresentationsasmethodologiesarefurtherrefined.

2.7 Forestsuccessionoperatesasacellularautomatamodel,wherethestateofacellisdependentoninternalconditionsandisinfluencedbytheconditionofneighbouringcells.Inthisproof-of-conceptstage,cellstakeononeofthreegeneralforeststatesthatrepresentclimaxforest,secondaryregrowth,andcleared/croppedland,referredtoasstate1,2and3respectively.Theforeststateisdecrementedfor3.5%ofrandomlyselectedcells,torepresentnaturaldisturbance.Thedisturbancerateislinearlyamplifiedbypopulationdensityofnearbysettlementstorepresentlocalwoodharvesting,toamaximumof15%.Cellsadvanceintheirforeststatebasedonthetimesincelastdisturbanceandtherelativenetprimaryproductivityofthecell.Oncethetimesincelastdisturbanceisaboveathreshold(40*NPPmaxj,t /NPPj,tyearsforsecondaryregrowthand100*NPPmaxj,t /NPPj,tyearsforclimaxforest,toaccountforspatialvariationinnetprimaryproductivity)theforestconvertstothenewstate.Forconversiontoclimaxforest,acellularautomatafunctionisappliedthatrequiresanumberofneighbouringcellstoalsocontainclimaxforest.Thisrulerepresentstheneedtohavelocalvegetationforseeddispersal.

2.8 NetprimaryproductivityNPPj,t[gCm2-1yr-1]isafunctionofprecipitationandtemperature,calculatedbasedontheMiamimodel(Lieth1972)as:

(2)

whereRj,tisprecipitation[mm]andTjistemperature[degreesC].

2.9 Foreachcell,agriculturalproductivityAGj,tiscalculatedas:

(3)

whereSPjissoilproductivity(FAO2007)[index1-100],Sjisslope[%],WFjiswaterflowcalculatedasthesumvolumeofwateragentstraversinganygivencellj,asdepictedinFigure2,andSDj,tissoildegradation[%lossofproductivity].Soildegradationoccursataconstantrateof1.5%pertimestepforeachcroppedcell.Thisconstantrateofsoildegradationisobviouslyasimplifyingassumption,assoilmanagementandmaintenanceofsoilproductivityisinitselfacomplexsocial-ecologicalsystem.Theβparametersareweightingsforcalibration,andpresentedinHeckbert(2012).

2.10 Ecosystemservicesaremodelledbyquantifyingtheavailabilityprovisioningservices(asdefinedinMA2005;TEEB2010)relatingtowater,food,andrawmaterials.Thisisasubsetofecosystemservicesanddoesnotincludeafullsetofindicatorswhichwouldincorporatesupportingservices(forexampleerosionprevention),habitatservices(suchasmaintenanceofgeneticdiversity)orculturalservices(suchasinspirationforculture,art,anddesign).Thecurrentecosystemservicesequationincorporatesasubsetoffourimportantservicesprovisionbasedonarablesoils,precipitation,accesstoavailablefreshwater,andtimberresources.EcosystemservicesESjarecalculatedas:

(4)

whereAGj,tistakenfromequation3,Rj,tistakenfromequation1,WFj,tisthesimulatedwaterflowvolume,andFj,tistheforeststate[1-3],ESDj,tisacatch-allproxyvariableforallotherecosystemservicesdegradation[%]asafunctionofpopulationdensity.

Anthropogenicfunctions:agriculture,trade,anddemographics

2.11 Eachsettlementagentimaintainsatleastonecelljforgeneratingagriculturalyield.Settlementsperformanagriculturebenefit-costassessmentconsideringthecostsofproduction,travelcostgiventhedistanceofthecellfromthesettlementsite,andwithlargersettlementsachievingeconomiesofscale,modelledas;

(5)

whereBCAj,tisthetotalbenefitprovidedfromagricultureyield,κj,α,andφ,arecropyieldandslopeparameters,AGj,tisagaintakenfromequation3,γistheestablishmentcostofagriculture(annualvariablecosts),Ojistheagriculturetravelcostasafunctionfordistancefromthecityandaperkmcostparameter,andPj,tispopulationofthesettlement.

2.12 Thebenefit-costofagriculturefunctiongeneratesyieldsthatarespatiallydistributedbasedonindividualconditionsofthecellsandthelocationofsettlements.Costsofproduction,includingdistancefromsettlements,resultsinaddingcroppedcells,generatingyieldandincreasingpopulation,whichinturnaddmore

http://jasss.soc.surrey.ac.uk/16/4/11.html 3 15/10/2015

croppedcells,butcausessoildegradation.Thesystemadjustsovertimeinresponsetothespatially-explicitagriculturalbenefit-cost.

2.13 Aseriesoffunctionsrepresenttradewithinaspatiallyconnectednetworkofagents.Itisassumedthatthroughtheprocessofspecialization,settlementsthatareconnectedtooneanotherwithinanetworkwillgeneratebenefitsfromtrade.Itisassumedalargernetworkproducesgreatertradebenefits,andalsothemorecentralasettlementiswithinthenetwork,thegreaterthetradebenefitsforthatindividualsettlement.Tomodelthesebenefits,settlementsareconnectedviaanetworkoflinksthatrepresenttraderoutes.Asasimplifyingassumptionofhowtheyconnecttogether,itisassumedwhenasettlementreaches(ordropsbelow)acertainsize,theywilladdroutes(orallowroutestodegrade)tonearbysettlementswithina40kmradius.Ateachtimestep,thesizeofthelocalnetworkiscalculatedaswellaseachsettlement'scentralitywithinthatlocalnetwork,furtherdiscussedbelow.

2.14 Combiningthefunctionsforagriculture,ecosystemservices,andtradebenefit,totalrealincomepercapitaRIiiscalculatedas:

(6)

whereNj,tisthenetworksize[#nodes],Cj,tisthecentrality[degree]andTCiisthetravelcost,andϑparametersarepricesforagriculture,ecosystemservices,andtrade,respectively.BenefitsfromagriculturearecalculatedonlyforcellsundercroppingproductionAGJi,t=1…nwhereasecosystemservicesarecalculatedencompassingtheentire'areaofinfluence'ofeachsettlementIJi,t=1…mwhichisbasedonthepopulationsizeofthesettlement,increasinglinearlytoamaximumof40kmindiameterforthemostpopuloussettlements(thosewithpopulationsgreaterthan15000people),astakenfromHeckbertetal.(inpress)andinterpretedfromChaseandChase(1998).Travelcostmeasurestherelative'friction'ofdifferentlandcovertypes,andisrepresentedas:

(7)

whereSjisslopeandWFj,tissimulatedwaterflowvolume,bothdescribedinpreviousequations,resultinginareasofhigherslopebeingrelativelymorecostlytotravelthrough,mitigatedbythepresenceofflowingwaterforcanoetransport.

2.15 ThetermsNJi,tnetworksize,andCi,tcentralityinequation6arecalculatedusinganetworksearchalgorithmcustom-builtforthisapplication.Thenetworksearchalgorithmisthemostdetailedprocedureinthemodel,andusesarecursivesearchfunctionusing'networkwalkingagents'whotraveleverypossiblecombinationofroutesalonganetworkpath.Thesereporttothenetworknodes(settlements)thetotalsizeofthelocalcluster,andthepositionofthenodewithinthatcluster(degree).Thenetworksearchalgorithmisthelengthiestprocedureintermsofamountofcodewritten,isthemostcomputationallyexpensiveprocedureinthemodel(morethandoublesthetotalruntimeofasimulationof650timesteps).TheoutcomeoftheprocedureisdepictedinFigure3fortimestep250,withthenetworklinkscolouredblackandtherangeofvaluesonthevisualscalehalvedcomparedtofollowingfiguresofthesameindicator,forvisualpurposes.

http://jasss.soc.surrey.ac.uk/16/4/11.html 4 15/10/2015

Figure3.Simulated'tradestrength'[lasttermofequation6](redonwhitebackground,darkerredbeinggreatertradestrength)basedoncentrality,sizeoflocalnetworkcluster,andtravelcostofeachsettlement(templeicon),connectedviatraderoutes(blacklinks).Alocalclusterisidentifiedforvisualpurposeswithablue

ovaloverthesamecluster,witha)andb)beingzoomed-inviewsofthewidersystemdepictedinc).

2.16 WeseeinFigure3anareahighlightedbyablueoval,zoomed-inatthreedifferentscales.InFigure3a),weseethatthislocalclusterisnotconnectedtoadjacentclusters,andNi,tnetworksize[#ofnodesinnetwork]issmall.InFigure3b)weseethatthetradestrength(redcolouring)isgreaterforlarger-sizedlocalclustersgiventhelargervalueofNi,t.Lastly,inFigure3c)weobservethatcentralnodesinlargerclusters(thoselocatedinthedarkestredregions),havegreatertradestrengthcomparedtonodesattheperipheryofthesamecluster.

2.17 ThevalueofeachcontributiontoRIi,tisdeterminedbytheweightingϑ,whichisstaticforϑAGandϑES;however,thevalueoftradeϑTRtisdynamic.

Specifically,ϑTRtincreaseseachtimerainfalldecreases,accordingtotheclimatevariationassumptions.Theassumptionhereisthatsettlementsspecialize

productionwithinanoveralltradenetworktoincreasethevalueoftradegoodsrelativetoothercommodities.Theeffectistolinearlyincreasethevalueoftradeeachtimetheclimatecycleisindecline.Thisassumptionisobviouslyrudimentary,andfurtherformulationsareexplored.

2.18 AfterdeterminingRIi,t,settlementdemographicsaccountforbirths,deaths,andmigration.Thebirthrateisassumedtoremainconstantat15%,whiledeathrateandout-migrationdecreaselinearlywithincreasedRIi,tpercapita,withamaximumout-migrationrateof15%andamaximumdeathrateof25%perannum.Settlementswithapopulationbelowaminimumnumberrequiredtomaintainsubsistenceagriculturearedeleted.Settlementsthatregisterout-migrationaboveaminimumthresholdofthenumberofpeoplerequiredtomaintainsubsistenceagriculturecreatea'migrantagent'.Themigrantagentusesautilityfunction(Heckbertetal.2010)toselectlocationstocreateanewsettlement.Themigrationutilityfunctioniscalculatedas:

(8)

whereλparametersareweightingsfortravelcostandecosystemservices,andESj,tistakenfromequation4,andDjisthedistancefromtheoriginsettlementtothepotentialnewsettlementsite.

2.19 Modeloutcomesaredependentonparameterizationofequations1-8.Thisstageofmodeldevelopmentisofferedforproofofconcept,fortransparency,andtoreceivefeedbackonmodelassumptions.Modelcodeandparameterizationisavailablefordownloadviathehttp://www.openabm.orgwebsiteinHeckbert(2012).

Results

3.1 Thissectiondescribesresultsandsensitivityanalysisfromsimulationruns.Thisproof-of-conceptstagemodelrevealsfamiliarpatternsanalogoustotheMayahistoricaltimelineandoffersaquantitativebasisfortheseassessments.Themodelwasinitialisedaccordingtodefaultvalues(Heckbert2012).Simulationruns

wereconductedwithatemporalextentof650timestepswithaspatialresolutionof20km2.Figures5-7describemodelresults,depictingmeanvaluesfor20runs(withconfidenceintervals[a=0.05]whererelevant),andreportingonsocial-ecologicalindicators.

3.2 Figure4presentsspatialoutcomesforfiveindicators,at200timestepintervals.Populationdensity,forestcondition,settlementtradestrength,soildegradation,theconditionofecosystemservicesandforestseachcontainanarrativedescribingthedevelopmentandreorganisationofthesimulatedsocial-ecologicalsystem.Bytimestep200,settlementshaveexpandedintoallregions,firstoccupyingareaswithgreaterecosystemservicesandprogressivelygrowingwithagriculturedevelopment.Populationdensitiesarehigherinareaswheresettlementshaveclusteredandformedlocaltradeconnections.Bytimestep400,asthevalueoftradeincreases,thepopulationdramaticallyincreases,extendinglocaltradeconnectionsto'global'connectivity.Anotablefringeexistsbetweentheconnectednetworkandtheperiphery.ThecentreoftheglobaltradenetworkisapproximatelyinthebroadregionwhereancientMayacaptialsofTikalandCaracolexisted.Theconditionoftheforestismarkedlychanged,withonlysmallpatchesofclimaxforestremaininginagriculturallyunsuitableareas,formingecologicalrefugiawithinthenear-completelysettledlandscape.Dramatically,bytimestep600thetradenetworkhasdisintegrated,thecentreofthemostdenselypopulatedareasisnearlyentirelyabandoned,leavingonlyasmallnumberoflocallyconnectedsettlementsofanynotablesizeinwhatwasoncethefringeofthegloballyconnectednetwork.Abandonedcroplandandsignificantlydecreasedfuelwoodharvestingallowsbroad-levelsecondaryregrowth,andclimaxforesteventualyexpandsoutfromitsrefugiatoanextentsimilartoprepopulationexpantionlevels.However,soilsandecosystemservicesremainseverelyimpactedandlargescaleresettlementofdegradedareasisnotpossible.

http://jasss.soc.surrey.ac.uk/16/4/11.html 5 15/10/2015

Figure4.Populationdensity,forestcondition,settlementtradestrength,soildegradationandtheconditionofecosystemservicesareshownat200timestepintervals.Darkercolouringshowsincreaseda)populationdensity(blue),c)tradestrength(red),d)soildegradation(red),ande)ecosystemservices(green).Forest

conditionb)depictsthreestatesofcleared/croppedcells(yellow),secondaryregrowth(lightgreen)andclimaxforest(darkgreen).

3.3 Themodelreportsquantitiativeindicatorsthroughtimeandcanbeusedtodrilldowninordertoexplorethedynamcisofthedevelopmentandreoganisationobserved.Figure5presentsthetotalpopulationofallsimulatedsettlementsandcontributionstorealincomebyecosystemservices,agricultureandtrade,respectively.Inthefirst_ofthesimulation,ecosystemsservicesprovidethemajorityofvalue.Ecosystemservicesvaluesaresupersededbyagriculturebytimestep150,andbotharesupercededbytradearoundtimestep350.Neitherrecoverastradevaluesdecreaseinthelatterhalfofthesimulationrun,andpopulationadjustsaccordingly.

http://jasss.soc.surrey.ac.uk/16/4/11.html 6 15/10/2015

Figure5.Totalpopulation[#people,primaryaxis]ofallsimulatedsettlementsovertime,andcontributionstorealincomebyecosystemservices,agricultureandtrade[#proxyvalueunits,secondaryaxis].Ecosystemservicesvaluesaresupercededbyagriculturebytimestep150,andbotharesupercededbytradearound

timestep350.Neitherrecoverastradevaluesdecreaseinthelatterhalfofthesimulationrun.

3.4 TherapidchangeinthevalueoftradecanbeexplainedbyexaminingFigure6,whichdepitcsthetotalnumberofsettlementnodes,thenumberofnodeswithinthelargestcluster,andtotalnaturalcapital,whichisrepresentedasthetotalsumofecosystemservicestakenfromequation4.Thenetworkgrowsfromlocalclusterstoanear-globallyconnectedsystem.Periodicperturbationsgivetheclustersstructurewhichinevitablyformthe'skeleton'oftheglobalstructure.However,whennaturalcapitalhasreacheditslowestlevel,perturbationsresultincascadingfailureinthenetwork.Althoughnaturalcapitalrecovers,thenumberofsettlementsdoesnotduetothelackoftradenetworkstructure.

http://jasss.soc.surrey.ac.uk/16/4/11.html 7 15/10/2015

Figure6.Totalnumberofsettlementnodesandnumberofnodeswithinthelargestcluster[primaryaxis],andtotalnaturalcapital[totalsumofecosystemservicesvalues,secondaryaxis].Thenetworkgrowsfromlocalclusterstoanear-globallyconnectedsystemthroughgrowthinlinkconnectionsandperiodicperturbations

whichgivetheclustersstructure.However,whennaturalcapitalhasreacheditslowestlevel,perturbationsresultincascadingfailureinthenetwork.

3.5 Figure7depictssoildegradationandforestconditionbythreestatesofcleared/croppedcells(state1),secondaryregrowth(state2)andclimaxforest(state3).Theinitialperiod,correspondingtoroughlythefirstthirdofthesimulationrun,isdescibedbyaccelerateddeclineofclimaxforestandinhibitedregrowthisaresultofcroppingandtimberharvestingforconstructionandfuelwoodasaresultofincreasingpopulationlevels.Thefollowingperiod,correspondingtoroughlythesecondthirdofthesimulationrun,showscontinuedrepressedregrowth,andincreasedareasofcleared/croppedlandaspopulationpressureresultsinmarginallandsbeingputunderagriculturalproduction.Asaresult,soildegradationincreasesatitshighestrateduringthisperiod.Thelastthirdofthesimulationrunshowsarapiddeclineincleared/croppedlandwithcorrespondinglargescalesecondaryregrowth,andeventualsuccessionintoclimaxforestwhichrecoverstonearpre-developmentlevels.

http://jasss.soc.surrey.ac.uk/16/4/11.html 8 15/10/2015

Figure7.Forestcondition[%oftotalarea,primaryaxis]bythreestatesofcleared/croppedcells(state1),secondaryregrowth(state2)andclimaxforest(state3),andsoildegradation[totalproxysoilproductivityunitslost,secondaryaxis].Accelerateddeclineofclimaxforestandinhibitedregrowthisaresultofcroppingandtimberharvesting.Increasedcleared/croppedarearesultsinhighersoildegradationrates,withsoilsbeginningtorecoverafterclimaxforestagainbecomes

dominant.3.6 ThetimelineforeachindicatorpresentedinFigures5-7revealstheunderlyingdynamicsofthemodelledsocial-ecologicalsystem.Table1presentsan

integratednarrativeofmodelindicatorsat100timestepintervals,akintotheanalogyofexaminingaRubik'sCubebylookingatthepatternsonallsidessimultaneously(vanderLeeuw2012).Thiscomplexsystemsperspectivehighlightsthatareductionistmethodofidentifyingfactorscontributingtoresilienceandvulnerabilitycannotbeusedtoidentifyasinglecause(oralinearprogressionofsinglecauses)oftheunravellingofthesocial-ecologicalsystem.

Table1:Narrativedescriptionofmodelledindicatorsforpopulation,forests,soils,andtradein100timestepintervals

TimeStep

100 200 300 400 500 600

Population Numberofsettlementsgrowsbasedonmigrationtounsettledareaswithhighecosystemservices

Populationincreaseswithagriculturedevelopment

Populationincreaseswithtradevalue

Populationreachesheight,significantperturbationswithclimatevariability

Precipitousdeclineinpopulation

Populationdoesnotrecovertopriorlevelsandsettlementsofanysignificantsizearelocatedattheformerfringeofthemostdenselypopulatedareas

Forests Gradualdeclineofclimax-dominatedforestandgradualincreaseofsecondaryregrowthandcleared/croppedareas.

Roughlyevendistributionofthreeforeststates.

Climaxforestreducedto10%oflandscapearea,timberharvestingandcroppingsuppressessecondaryregrowth.

Cleared/croppedlandaccountsfor70%oflandsurface,climaxforestreducedtorefugia.

Broad-scalesecondaryregrowth.

Climaxforestbeginstoemergefromrefugiatonearlyregainpre-developmentlevels.

SoilsandAgriculture

Agriculturalexpansionintoprimesoils.

Increaseofcroppedareasinbroadlysettledlandscape.

Expansionofagricultureintomarginalandmoredistantlocations,soildegradationrateincreases.

Broad-scalecroppingalbeitwithdiminishingreturnsrelativetolandareaunderproduction.Soildegradationreachesheight.

Abandonmentofcropsandlossofeconomiesofscaleinagricultureproduction,legacysoildegradationinhibitsre-sowingcrops.

Soilsremainunproductiveandareassuitableforagriculturearepredominantlyintheformerfringeofdenselycroppedareas.

Tradeandnetworkstructure

Littleconnectivityoftraderoutes,withsmallnetworkclustersizesof<10settlements.

Localconnectivityoftraderoutesintowell-definedclustersof<20settlements.

Regional-scaleconnectivityofpreviouslocalclusters,withkeysettlementsbecomingcriticalnetworklinks.

Near-globalnetworkemergesandexpandstofringes.Tradevaluesupersedescontributionsfromagricultureorecosystemservices.

Globalnetworkfullyconnectedthroughkeylocations,overallnetworkstructurevulnerabletoperturbance.

Cascadingnetworkfailureresultsinexistenceofonlysmalllocalnetworksattheformerfringe.

Discussionandconclusions

4.1 TheMayaSimmodelpresentsaproof-of-conceptagent-basedmodelrepresentingkeyelementsoftheancientMayasocial-ecologicalsystem.Agents,cells,andnetworksareprogrammedtorepresentdemographics,trade,agriculture,soildegradation,ecosystemservices,climatevariability,hydrology,primaryproductivity,andforestsuccession.Simulatingeachoftheseincombinationallowspatternstoemergeatthelandscapelevel,effectivelygrowingthesocial-ecologicalsystemfromthebottomup.ThisallowsinvestigationofwhatconditionsleadtothedevelopmentofdenselypopulatedandhighlyinterconnectedhumangeographyoftheancientMaya,andrevealsdynamicsofhowpastsocietiesimpactedtheirenvironmentandviceversa.

4.2 Themodelverificationprocessinvolveddebuggingandindividuallytestingmoduleswithintheoverallmodel.Throughthisprocess,itwasobservedthatmodeloutcomeswereparticularlysensitivetotherelationshipbetweensoildegradationandtherateofincreaseintradevalue,againwithintherangeofnon-extremeclimatevariation.Therelationshipliesinthefactthatsettlementswithhigherpercapitarealincome,duetotradeflows,increaseinpopulationandlocalmarginallandsareputunderproduction.Areaswithbettersoilsareabletomaintainpopulationsandtradeconnectionsovermultiplecyclesofdisturbanceandintheendbecomecriticalnodesinthetradenetwork.Thisinturnincreaseslocalsoildegradation.Whensoildegradationbecomessevere,acriticalnodeintheoverallglobaltradenetworkmaynotbeablesustainsufficientlocalpopulationtomaintaintradeconnections.Thedemiseofagloballysignificantnodecanthenresultincascadingfailureinthenetwork,witheffectsnotnecessarilylocatednearby,buteverywhereonthenetwork.

4.3 Theverificationprocessandmanualdebuggingoverthousandsofrunsproducedaninformalsensitivityanalysis,whichrevealedthatthatthemodelledMayasocial-ecologicalsystem,undergivenassumptions,doesnotalwaysreachalargepopulation'peak'.Itisonlyunderanarrowsetofconditionsthatthepopulationisabletogrowlargeenough,andwiththeproperspatialdistribution,toresultinthegloballyconnectedtradenetworkwhichinturnallowsforfurther

http://jasss.soc.surrey.ac.uk/16/4/11.html 9 15/10/2015

populationgrowth.Inordertogetthepeakwhichisanalogoustotheobservedprehistoricalrecord,arelativebalanceinthesetofparametersrelatingtotrade,ecosystemservices,andagriculturalrealincomemustoccur.Inotherwords,theequationsrelatingtodemographics,soildegradation,andtradevaluemustallbewithinaspecificrangeforthepopulationtorisesubstantiallyenoughtocreatepatternsthatarerecognisableasPreclassic,ClassicandPostClassictemporalperiods.Thetwoprimaryparametersthatseemtorequirebalancearetheincreaseintradevalueandtherateofsoildegradation.

4.4 Furtherresearchwillfocusoncalibratingmodelinputsfromagronomicmodels,inputtingfinerresolutionsoilandvegetationdata,andrunningthemodeloverageneratedpaleoclimatereconstruction.Rudimentaryassumtionsonhowtradevaluechangescanbereplacedwithothercandiateassumtions.FuturevalidationispossibleusingGIS-basedarcheologicalsitedataforsettlementlocationsovertime,comparisonofsimulatedbuiltareastoLIDARdata,comparingpollencorecontenttosimulatedcatchmentlandcover,aswellasnetworkconnectivityofsettlementsasevidencedthroughceramicinteractionsovertime.

4.5 Revisitingresearchquestionsinlightofthemodelresults,wecanidentifycriticaldynamicsofhowtheMayacametodevelopintoahighlyinterconnectedanddenselypopulatedsocial-ecologicalsystem.Theseprocessescanbeinterpretedintoatemporalpatternofdevelopmentandreorganisation,thatinthesimulatedmodelproducesoutcomesroughlyanalogoustothearchaeologicaldescriptionoftheMayaPreclassic(<modeltimestep200),Classic(roughlytimestep200-450),andPostclassicperiods(>modeltimestep450).Fromacomplexsystemsscienceperspective,thereisnoonecauseofthedramaticre-organisationwhichoccurstomarktheendoftheClassicperiod,andnotablyinthismodelthereisno'drought',merelycyclicalclimatevariabilitywhoseeffectcompletelydependsontheentiretyoftherestofthestatevariablesinthesocial-ecologicalsystem.Climatevariability,soildegradation,deforestation,demographicpressure,andthephysicalconfigurationoftradenetworksareallfactorswhichconcurrentlycontributetoresilienceorvulnerability,andcannotbe'ordered'or'prioritised'intoanygivensequenceofeventswhichcausesthere-organisationintothePostclassicperiod.Complexsystemsmodellingcanhoweveridentifyhowthesevariablesinteract,andprovidesapictureofhowaninterconnectedsystemrespondsgivenitsembeddedfast-movingvariablessuchaslandcoverchangeandtradeconnections,meso-speedvariablessuchasdemographicsandclimatevariability,aswellasslow-movingvariablessuchassoildegradation.

Acknowledgements

TheauthorwouldliketoacknowledgethecontributionsofChristianIsendahl,JoelGunn,AndrewReeson,SimonBrewer,TimBaynes,VernonScarborough,ArlenChase,DianeChase,RobertCostanza,JohnMurphy,DerekRobinson,NicholasDunning,CarstenLemmen,LaelParrot,TimothyBeach,SherylLuzzadder-Beach,DavidLentz,PaulSinclair,CaroleCrumleyandSandervanderLeeuw.ThisprojectwassupportedbyAlbertaInnovatesTechnologyFutures,PortlandStateUniversity,ArizonaStateUniversity,UppsalaUniversity,andUniversityofCincinnati.

References

CHASE,A.F.andChase,D.Z.(1998).ScaleandIntensityinClassicPeriodMayaAgriculture:TerracingandSettlementatthe'GardenCity'ofCaracol,Belize,CultureandAgriculture20(2):60-77.[doi:10.1525/cag.1998.20.2-3.60]

FAO(2007).SoilProductionIndex.http://www.fao.org:80/geonetwork?uuid=f7a2b3c0-bdbf-11db-a0f6-000d939bc5d8

FAO/IIASA/ISRIC/ISSCAS/JRC,(2009).HarmonizedWorldSoilDatabase(version1.1).FAO,Rome,ItalyandIIASA,Laxenburg,Austria.

FARR,T.G.,Rosen,P.A.,Caro,E.,Crippen,R.,Duren,R.,Hensley,S.,Kobrick,M.,Paller,M.,Rodriguez,E.,Roth,L.,Seal,D.,Shaffer,S.,Shimada,J.,Umland,J.,Werner,M.,Oskin,M.,Burbank,D.,andAlsdorf,D.(2007),TheShuttleRadarTopographyMission,Rev.Geophys.,45,RG2004.[doi:10.1029/2005RG000183]

HECKBERT,S.,Adamowicz,W.,Boxall,P.,&Hanneman,D.(2010).CumulativeEffectsandEmergentPropertiesofMultiple-UseNaturalResources.LectureNotesinComputerScience,5683,1-13.[doi:10.1007/978-3-642-13553-8_1]

HECKBERT,S.(2012).MayaSim:Anagent-basedmodeloftheancientMayasocial-ecologicalsystem.http://www.openabm.org/model/3063/version/3

HECKBERT,S.,Isendahl,C.,Gunn,J.,Brewer,S.,Scarborough,V.,Chase,A.F.,Chase,D.Z.,Costanza,R.,Dunning,N.,Beach,T.,Luzzadder-Beach,S.,Lentz,D.,Sinclair,P.(2014,inpress).GrowingtheancientMayasocial-ecologicalsystemfromthebottomup.In:Isendahl,C.,andStump,D.(eds.),AppliedArchaeology,HistoricalEcologyandtheUseablePast.OxfordUniversityPress.

HIJMANS,R.J.,S.E.Cameron,J.L.Parra,P.G.JonesandA.Jarvis,(2005).Veryhighresolutioninterpolatedclimatesurfacesforgloballandareas.InternationalJournalofClimatology25:1965-1978.Availableat:http://www.worldclim.org/[doi:10.1002/joc.1276]

LIETH,H.,1975.Modelingtheprimaryproductivityoftheworld.In:Lieth,H.,Whittaker,R.H.(Eds.),PrimaryProductivityoftheBiosphere.Springer-Verlag,NewYork,pp.237-263.[doi:10.1007/978-3-642-80913-2_12]

MA(2005).MillenniumEcosystemAssessment.EcosystemsandHumanWell-being:Synthesis.IslandPress.Washington,DC.

PRUFER,K.,Scarborough,V.L.Chase,A.F.,Chase,DZ.,Cobos,R.,Dunning,N.,Gunn,J.,Fedick,S.,Fialko,V.,Iannone,G.,Lentz,D.,Liendo,R.,Lucero,L.,Sabloff,J.,Tainter,J.,Valdez,F.,andvanderLeeuw,S.(2011).IHOPEMaya:ResilienceandRigidityintheDevelopmentandDisintegrationofComplexSocietiesintheTropicalLowlandsofMesoamerica,paperpresentedatResilience2011,ArizonaStateUniversity,Tempe,Arizona.

REANEY,S.M.(2008).Theuseofagentbasedmodellingtechniquesinhydrology:determiningthespatialandtemporaloriginofchannelflowinsemi-aridcatchments.EarthSurfaceProcessesandLandforms.33,pp.317-327.[doi:10.1002/esp.1540]

TEEB(2010).TheEconomicsofEcosystemsandBiodiversity.MainstreamingtheEconomicsofNature:Asynthesisoftheapproach,conclusionsandrecommendationsofTEEB.ProgressPress,Malta.

VANDERLEEUW,S.,Costanza,R.,Aulenbach,S.,Brewer,S.,Burek,M.,Cornell,S.,Crumley,C.,Dearing,J.,Downy,C.,Graumlich,L,Hegmon,M.,Heckbert,S.,Hibbard,K.,Jackson,ST.,Kubiszewski,I.,Sinclair,P.,Sörlin,S,andSteffen,W.(2011).TowardanIntegratedHistorytoGuidetheFuture.EcologyandSociety.(16)4.[doi:10.5751/es-04341-160402]

WILENSKY,U.(1999).NetLogo.CenterforConnectedLearningandComputer-BasedModeling,NorthwesternUniversity.Evanston,IL.http://ccl.northwestern.edu/netlogo/.

http://jasss.soc.surrey.ac.uk/16/4/11.html 10 15/10/2015