©CopyrightJASSS

DentonCockburn,StefaniA.Crabtree,ZiadKobti,TimothyA.KohlerandR.KyleBocinsky(2013)

SimulatingSocialandEconomicSpecializationinSmall-ScaleAgriculturalSocieties

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

Received:12-Jan-2012Accepted:25-May-2013Published:31-Oct-2013

Abstract

Weintroduceamodelforagentspecializationinsmall-scalehumansocietiesthatincorporatesplanningbasedonsocialinfluenceandeconomicstate.Agentsallocatetheirtimeamongavailabletasksbasedonexchange,demand,competitionfromotheragents,familyneeds,andpreviousexperiences.Agentsexchangeandrequestgoodsusingbarter,balancedreciprocalexchange,andgeneralizedreciprocalexchange.Weuseaweight-basedreinforcementmodelfortheallocationofresourcesamongtasks.TheVillageEcodynamicsProject(VEP)areaactsasourcasestudy,andtheworkreportedhereextendspreviousversionsoftheVEPagent-basedmodel("Village").ThismodelsimulatessettlementandsubsistencepracticesinPueblosocietiesofthecentralMesaVerderegionbetweenA.D.600and1300.Inthebasemodelonwhichwebuildhere,agentsrepresenthouseholdsseekingtominimizetheircaloriccostsforobtainingenoughcalories,protein,fuel,andwaterfromalandscapewhichisalwayschangingduetobothexogenousfactors(climate)andhumanresourceuse.Comparedtothebaselineconditionofnospecialization,specializationinconjunctionwithbarterincreasespopulationwealth,globalpopulationsize,anddegreeofaggregation.Differencesbetweenscenariosforspecializationinwhichagentsuseonlyaweight-basedmodelfortimeallocationamongtasks,andoneinwhichtheyalsoconsidersocialinfluence,aremoresubtle.Thenetworksgeneratedbybarterinthelatterscenarioexhibithigherclusteringcoefficients,suggestingthatsocialinfluenceallowsafewagentstoassumeparticularlyinfluentialrolesintheglobalexchangenetwork.

Keywords:Specialization,Agent-BasedModeling,Archaeology,SocialNetworks,ModelsofSocialInfluence,Barter

Introduction

1.1 Specializationisonewayinwhichagentscanincreasetheirproductivity(MurcianoandZamora1997)bycooperatingwithotherindividuals(Spencer,CouzinandFranks1998)togenerateincreasingreturnstoscale(populationsizeofsocialgroup).Theoriginsofspecialization,especiallycraftspecialization,havebeenlinkedwithincreasingsociopoliticalcomplexitysinceatleasttheeighteenthcentury.AdamSmith(1776/1937)chosetobeginhisInquiryintotheNatureandCausesoftheWealthofNationsbysuggestingthat"thegreatestimprovementintheproductivepowersoflabour,andthegreaterpartoftheskill,dexterity,andjudgmentwithwhichitisanywheredirected,orapplied,seemtohavebeentheeffectsofthedivisionoflabour."Heconnectedtheoriginofspecializationwithahumanpropensitytoexchange,emphasizingthattheinterdependenceproducedbythejointactionofspecializationandexchangetendstoincreaseoverallproductivity.Suchincreasedproductionquitepossiblyinitiatedapositivefeedback,since,forChilde(1936/1983),surplusproductionfromaneffectiveagricultureunderwrotebothtechnicalandsocialdivisionsoflabour,leadingeventuallyinMesopotamiatotheemergenceofeliteswhowereabletosupportfull-timecraftspecialists.Althoughspecializationandproductionforexchangeareoftenlinkedtotheriseofthestate,itisclearthattheyexistinsmaller-scalesocietiesalongsidesubsistenceproduction(Patterson2005).

1.2 Inthisarticlewedevelopanagent-basedsimulationofspecializationinresourceproduction,andasystemofbarterallowingexchangeofspecializedproducts,inPueblosocietiesexistingbetweenAD600and1300insouthwesternColoradowiththeultimategoalofexaminingtheireffectsinthesemiddle-rangeNeolithicsocieties.Sincebartercanmeanratherdifferentthings,wespecifythatbybarterwemean"moneylessmarketexchange"andnotthesortsofreciprocaltransactionsthatappeartobeuniversallyimportantinsmall-scale,non-marketsocieties(Dalton1982).Ourgoalhereistopresentthecomputationalmachinerymakingspecializationandbarterpossiblewithinourexistingagent-basedmodel.Wearethereforelessconcernedwiththerealismofsomeoftheassumptionsbelow,includingtheamountofstorageweallow,andthegoodsinwhichagentsspecialize.Forexample,specializationinproductionofceramicsisprobablymorelikelyinthesesocieties(Harry2005)thanisspecializationinmakingwateravailabletootherhouseholds;nordowereallybelievethathouseholdsinthesesocietieswereabletostorethelargequantitiesofgoodsweallowbelow.However,usingthesesometimesunrealisticassumptions,wehopeto,asEpstein(2008:3-4)says,"illuminatecoredynamics"ofthesystemsofbarterandexchangeandcapture"behaviorsofoverarchinginterest"withintheAmericanSouthwest.

1.3 Herewedefinespecializationastheagents'choicetoproducequantitiesofsomegoodsinexcessofalevelneededforsubsistence,whilesimultaneouslyunderproducingothergoods.Whenagentsspecialize,iftheydon'tproducealltheirsubsistencerequirements,theymustacquirethesethroughexchangewithotheragents(Evans1978).Specializationaswemodelitcanoccuralongaspectrum.Agentscanbefullyspecialized,performingonetask(here,producingonegood)totheexclusionofallothers,ortheycanbepartiallyspecialized,performingalltaskstovaryingdegrees.Inoursystem,ouragentsareexpectedtobepartiallyspecialized,butitisalsopossibleforsomeagentstobecomefullyspecialized.

1.4 AsSmithrealized,solongasexchangeisrelativelyfrictionless,specializationincreasestheproductivityinamarketsystem( MurcianoandZamora1997).Productiveindividualsincreasethesupplyforgoodsinwhichtheyspecialize,andtheyspecializeinproducinggoodsinwhichtheyhaveacomparativeadvantage;atthesametimetheyincreasedemandforothergoodsthattheyneed,therebyprovidingindirectnetworkeffects(Young1928).Thelevelofspecializationandoutputaredependentonseveralfactors,includingcompetition,thecharacteristicsoftheexchangenetworks,andinitialconditions(Lavezzi2003).Cockburn,KobtiandKohler(2010)createdaneconomicagentspecializationmodelthataddedfeaturesnotfoundinthesimplermodelproducedbyLavezzi(2003),includingconsumption,productionlimits,changingpopulations,andchangingtradingrelationships.Theagentsinthatmodelwerealsosensitivetovaryingsuppliesofresources.Ifmanyagentsarealreadyoutputtingthesameresource,thesupplyforthatresourceislikelytosurpassthedemand,thusdiscouragingadditionalproductionofthatresource.

1.5 Ithasbeenshownthatthelevelofspecializationincomplexsystems,includinghumansocieties(Bonner1993),isaffectedbythesizeofthesystem(Bonner2004).ResearchininsectsocietiesbyJeanson,Fewell,Gorelick,andBertram(2007)indicatesthatwhendemandislowandtherearemanytasks,increaseddivisionoflabourisanemergentproperty,suggestingthatthelevelofspecializationwithininsectsocietiesispositivelyrelatedtothesizeofcolonies.The

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behaviourofcognitiveagentscanbemodeledusingmotivationnetworks(Krink,MayohandMichalewicz1999)inwhichagentschoosebetweenmoving,eatingandbreedingbasedonconditionswithintheenvironment.Ouragentsarenotthissophisticated,andonlyusespecializationtodeterminewhatjobstoperformandhowtodividetheirtimeamongthosetasks.

1.6 CockburnandKobti(2009b)andCockburnetal.(2010)claimthatintroducingsocialinfluenceintoasystemwouldincreasethelevelofspecialization.Buildingontheseassertions,herewecreateamodelthatincorporatesbotheconomicstateandsocialinfluence.Agentsareinfluencedbycompetitionfromotheragentsintheirtopographicallybasedsocialnetwork.Itisexpectedthatthereshouldbemoretaskspecializationinthissociallyinfluencedsystemthaninthemodelswithoutsocialinfluence.Wealsoexpectthatthelevelofwealthwillincreaseinthepopulation(MurcianoandZamora1997).Further,specializationandsocialinfluencemayhaveeffectsonpopulationsofagents,andassocialinfluenceinteractswithexchangenetworks,wemayexpectspecializationtochangethestructureofglobalpopulations.Toassessthepresenceandsizeoftheseeffectswecomparesystemsinwhich(1)agentsonlytrytoprocureenoughresourcestomeettheirneeds;(2)wheretheyplanbasedupontheeconomicstateoftheirfamily,possiblyproducingmoreofsomeresourcesforwhichtheyhaveextractiveadvantageduetotheirlocation;andfinally,(3)wheretheyplanbasedupontheireconomicstatewhilealsoconsideringcompetitionfromagentswithintheirsocialnetwork.

1.7 Thereareseveralapproachestomodelingsociallyinfluencedspecialization,includingsocialinhibition,wherebyagentsdiscourageothersfromcompeting(BeshersandFewell2001).Temporalpolyethismisanother,whereagents'specializationisrelatedtotheirage(Ravaryetal.2007).Agentsmightalsolearnfromexperience(MurcianoandZamora1997;Spenceretal.1998;Theraulaz,BonabeauandDeneubourg1998),forexamplebyrandomlyselectingaspecializationattheoutset,andifsuccessful,selectingthatactioninthenextroundwithhigherprobability.

1.8 Forreinforcement-basedsystemstosucceedindynamicenvironments,agentsmustbeabletoovercomepreviouslylearnedbehaviour,especiallywhenfailuretodosoresultsindeath(Beaudreau2003).Agentsmustbewillingtoengageinbehaviourthatpreviouslyhadpoorresultsandalsomustbeabletorespondtoemergencysituations,wherechangemaybedramaticyetnecessary.Moreover,thelevelofsocialinfluencewithinasocietyalsoaffectsthelevelofspecialization.Themoreagentsareaffectedbytheactionsoftheirneighbours,themorespecializedthesocietybecomes(see,forexample,CockburnandKobti2009a;2009b).

CentralizedMulti-agentsystems

1.9 InMulti-AgentSystems(MAS),thestudyofspecializationisoftenmotivatedbyaninterestinhowspecializationcanincreasetheefficiencyofthesysteminreachingitsgoals.AMarkov-chainmodeltodescribetheevolutionarydynamicsoftheemergenceofspecializationinMASispresentedinChai,Chen,Han,DiandFan(2007).Inthatenvironment,agentssearchforandexploitresourceswithincompleteinformationandagoalofmaximizingtheefficiencyoftheentiresystem.TheMASusesacentralizedmodelfordeterminingtaskspecialization,withtaskallocationsemergingasaresultoflong-termsystemevolution.Thus,agents'specializationisdeterminedbytheoverallneedsofthesystemandnotbyindividualconsiderationsalone.Asaresult,anagentcansometimesbecausedtospecializeintasksthataredangeroustoitspersonalinterestswithoutsufficientreward(i.e.,thejobofcleaningupatoxicspill).Agentspecializationinthesesystemswillresultinhighersystemproductivitythaninnon-specializedsystems(Chaietal.2007).

1.10 Usingacentralizedspecializationsystemalsoaddressesanotherproblem:agentsgenerallydonotpossesscompleteinformation,thusanyspecializationdecisionstheymakearelikelytobesuboptimal.CentralizedMASarebetterabletohandlespecializationincomplexandchangingenvironments(Chaietal.2007),partlybecausetheysuppresscomplicationsarisingfromtheself-adaptivestrivingofindividualagents.Centralizedsystemsalsobenefitfromthefactthatresourcesdiscoveredbyindividualscanbemorequicklyexploitedduetotheglobalknowledgeinthesystemandcentralizeddirection.

1.11 CentralizedMAS,however,puttheburdenon"thesystem"tobefullyawareofallrelevantfactorsinthedecision-makingprocessforallagents.Thereisnocompetitionbetweenagentsinthesesystems.Suchsystemsbegthequestionastohowsocietiesofcooperatingagentscanemergefromsocietiesofautonomousagents,sincetheyassumethatanyconflict-of-interestproblemsinwhichcognitiveagentsmightbetemptedtooverridecentralizeddecisionshavebeensuccessfullysolved.Finally,centralizeddirectionissimplyunrealisticforthecaseofthesocietieswemodelhere,inwhichdecision-makingmusthavebeenmoreconsensualandbottom-upthancentralized(VanVugt&Ahuja2011).

CaseStudy:VillageEcodynamicsProject

2.1 TheVillageEcodynamicsProject(VEP)isamulti-disciplinary,multi-institutionproject(Kohleretal.2007).IthasinvolvedindividualsfromWashingtonStateUniversity,CrowCanyonArchaeologicalCenter,WayneStateUniversity,UniversityofWindsor,SantaFeInstitute,ColoradoSchoolofMines,UniversityofNotreDame,andBBL,Inc.Researchersincludecomputerscientists,archaeologists,ecologists,anthropologists,geologistsandeconomists.TheVEPbeganby

describingandmodeling1800km2ofthecentralMesaVerderegionofSouthwestColorado,occupiedbetweenA.D.600and1300byfarmersancestraltocontemporaryPueblopeoples,whichisthesettingforthismodel.Thousandsofhabitationsitesareknownfromthisarea,whichwecanassigntooneormoreof14periodsbasedeitheronexcavationor,inmostcases,theceramicsontheirsurfaces(Varien,Ortman,Kohler,GlowackiandJohnson2007).TheentirenorthernSouthwestwasdepopulatedtowardstheendofthethirteenthcenturyandoneoftheprimarygoalsoftheVEPresearchistounderstandthereasonsthatledtothisdepopulation(Kohler,Varien,WrightandKuckelman2008).Anothergoalistounderstandwhy,duringcertaintimesinprehistory,mostpeoplelivedinlargeandrelativelycompactvillages,whileatothertimes,theydispersedintosmallerhamlets(Crabtree2012).

2.2 TheoriginalsimulationwasdesignedbyTimKohlerandcolleaguesatWashingtonStateUniversityandtheSantaFeInstitute(Kohler,Kresl,vanWest,CarrandWilshusen2000).Thesimulationcreatesagenthouseholdsthatlive,work,andreproduceinalandscapemodeledonthatofsouthwesternColorado.Muchofthedynamismofthesimulationisprovidedbyannualandspatiallyspecificestimatesofpotentialmaizeproductiononthislandscape,originallydevelopedbyVanWest(1994)andlaterrefinedbyKohler(e.g.,2012).Agentactionsonthislandscapearedesignedtobeasrealisticaspossible,drawingontheconsiderableamountknownaboutthisplaceandtime(Lipe,VarienandWilshusen1999).Agentsareresponsibleforgatheringtheirresources,whilefeedingtheirfamiliesandexchangingwithotheragents.Agentsmustfarmmaize,huntforprotein(cottontailrabbit,jackrabbit,andmuledeer),obtainwaterfromriversandsprings,andgatherfirewoodfromforests.Agentsgetalltheirenergy,asmeasuredincalories,frommaize.Whenproteinisrequired,itcostscaloriestoprocure.Agenthouseholdsmustprovidetheirfamilieswithenoughcaloriestoperformthesetasks,aswellasprovidefortheirbasicmetabolicneeds.Inthecasethatagentscannotobtainalltheresourcestheyneedontheirown,theyareallowedtoexchangewithotheragents.Familiesandfamilymembersaretrackedinthemodel,andweallowdifferentkindsofexchangerelationshipsbetweenkin,andamongnon-kin,drawingonmodelsappropriateforsmall-scalesocieties(Sahlins1972).

2.3 Ifanagentisnotperformingwellatitspresentlocation,itwillmovetoamoresuitablelocationinthestudyarea.Unfortunatelyfortheagents,theyarenotallowedtoexitthestudyarea.Whenconsideringlocationstomoveto,agentsevaluatetheresourceproductivityofprospectiveareas.Thisincludesevaluatingforfarmingproductivity,waterandfuelwoodaccessibility,andhuntingopportunities.Themodelaimstorepresentsoilproductivity,rainfall,animaldensity,forestdensity,andotherfeaturesoftheregionwithafairdegreeofrealism.Eventhevegetationthatfeedstheanimalsinthesimulationisaffectedbyclimaticvariability.

2.4 VEPresearchershaveidentifiedtwopopulationcyclesinthearchaeologicalrecord(Varienetal.2007).Intheearlier,smallercyclethereisrelativelylittleevidenceforspecialization,whereasinthelater,morepopulouscyclethereisevidenceforspecializationinatleastthedomainofpoliticalleadership,andprobablyalsoinprovisionofreligiousservicesandinaspectsofceramicproduction(Bernardini2000).Ortman(2003)providesevidencethathouseholdsrelocatingtothelargestsiteintheVEParea,YellowJacketPueblo,towardstheendofitsoccupationspecializedinceramicproduction.Thisispossiblybecause,aslatearrivals,thenewcomersdidnothaveaccesstohigh-qualityfarmlandandneededtoengageincraftactivitytointegratewiththeeconomy.Theframeworkwecreatehereallowstheemergenceofresource-acquisitionspecialistswithinthesimulation.Ceramicproductionspecificallyisnotmodeledbutcouldlaterbeaddedtothesimulation.

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2.5 KohlerandVarien(2012)presentagreatdealofadditionalinformationaboutthelocalarchaeologicalrecord,thestructureofthesimulation,andourconclusionsderivedfromcomparingthetwo.Theversionofthesimulationreportedinthatvolume—onwhichthispaperbuilds—isavailableathttp://www.openabm.org/model/2518.AlsonotableinthepresentcontextaretheinvestigationsbyKobtietal.ontheroleofexchangeinaggregationanddepopulation,usingculturalalgorithms(Kobti,ReynoldsandKohler2004;Reynolds,KobtiandKohler2004;KobtiandReynolds2005).

Approach

3.1 Amoreformalizeddescriptionofourapproachispresentedintheappendix.Agentsareallowedtodividetheirtimeamongallfourtasksexistingwithinoursimulation(farming,hunting,gatheringwoodandcollectingwater).Thepercentageoftheirtimespentoneachofthesetasksisdependentupontheirneedsfortheresultsofthattask,aswellastheirperceivedabilitytoobtainthoseresourcesmorecheaplyfromcloseneighbours.Ifanagenthas30kglessmaizethanitneeds,itwillseektoincreaseitsmaizeproductionforthefollowingyearby30kg,byadjustingthepercentageofitstimethatshouldpermitthatgoaltobeachieved.Theagentwilltrytodotheoppositeifitisoveritsthresholdforaresource.Itwilloftenhappenthattheagentwillchangemultipleallocations,resultinginatotaloutlaynotequalto100%.Atthispoint,theagentwillnormalizetheseallocations,suchthatitwillspend100%ofitsworkhoursonthesetasks.

3.2 Whenagentshaveexcessstoresofaresource,theywilllettheirneighboursknow.Thoseneighboursthathavehigherproductioncostsfortheseresourceswillpredictthatthisagentwillbeabletohelpthemmeetanyshortfallforthisresourceintheupcomingyear.Theywillbewillingtoreducetheirownproductionaccordingly.Thenetresultofthesefactorsisthatagentswilldynamicallyadjusttheirallocationsbasedonpersonalexperience,aswellascooperationandcompetitionfromothers.

Simulatedenvironment

4.1 TheVEPenvironmentconsistsoffourresources:water,wood,maizeandmeat.Allbutwoodareneededforsurvival.Whileanagentdiesimmediatelyifitdoesnothaveenoughmaizeorifithasbeenshortofmeatproteinforthreeconsecutiveyears,agentsareallowedtosurvivecontinualshortagesofwood(however,theagentsdon'tfactorthisintotheirplanning).Whileagentsareboundbytheseresourcerequirements,theydon'thaveanyunderstandingoftheconsequencesofresourceshortfalls.Thismeansthatanagentdoesnotprioritizewaterormaizeoverwoodorprotein,eventhoughneglectingtheformerincreasesthechancesofdeath.

4.2 Eachresourceisassociatedwithataskthatproducesthatresource.Afarmerproducesmaize,ahunteracquiresprotein,awoodsmangatherswood,andawatercarrierretrieveswater.Eachtaskalsohasconstraintsandrequirementsfortheperformanceofthattask.Farmersrequirelandtoplanttheirmaize.Therearealimitednumberofproductiveplotsonthelandscapeandplotsvaryinproductivity,bothwithinayear(spatially)andfromyeartoyear.Huntingrequiresthepresenceofanimalswithinthepermissiblehuntingrangeof4km.Gatheringwoodrequiresthepresenceofdeadwoodortrees,andcarryingwaterrequiresthattherearewatersourcesthattheagentcantravelto.Forwoodandwater,agentsarenotboundbythedistancetotheseresources;theycantravelasfarasnecessarytoobtainthem.Howeveralltasksrequireenergytoperform,andthusrequiretheagenttohavesufficientcaloriestoperformthetask.Theamountofenergyrequiredforthesetaskswasincorporatedinthesimulationbeforethedevelopmentdescribedherebegan,asexplainedinKohleratal.(2007).

4.3 Agentsmustallocatetheirfamily'stotalcaloriesavailablefortheyearamongthegiventasks.Thenumberofcaloriesrequiredbyeachhouseholdisdeterminedbythenumberofadultsinthehousehold,thenumberofchildreninthehousehold,aswellashowmanyhoursperdayeachisrequired(orwilling)towork.Intheversionofthesimulationreportedhere,thenumberofhourswillingtoworkwassetto6hours/dayforeachindividualinafamilythatisatoraboveworkingage(8yearsold,inoursimulation).Agentsareabletospendanyamountoftheircaloriesonanyspecifictask.Agentsalsohaveasecondarygoal,theaccumulation(storage)ofresourcesthatincreasestheireconomicsecurityfortimeswhentheycannotprocureadditionalresources,suchasduringafamineordrought.Allagentscanonlystoreamaximumof10yearssupplyofanyresource.Ayear'ssupplyistheamountthehousehold(agent)wouldneedforsubsistenceestimatedaccordingtoitscurrentcircumstances.Itshouldbenotedthatwhilethemaximumissetat10,itisrarelythecasethatanagentpossessesthatmuchofaresource.Meat,forexample,israrelyheldinstoragebecauseofthescarcityoftheresourceandthehighrateofdecay.Themaximumstoragewouldtheoreticallyallowahouseholdspecializinginhuntingtostorethemeatfrom10deerwhilewaitingtotradesomeforotherresources.Anyexcessamountabovethemaximumallowedstorage(10years)willbedonatedtonearbyrelatives,ordiscardediftherearenorelativestoacceptthem.Whileagentsmustsustainneedstosurvive,theirfocusisonmaximizingtheirproductivitygiventheirabilities.Allagentshavethesameskilllevel,soabilityisdelineatedbytheproductivityofanagentatperformingatask.Thusanagenthavingmoreproductiveplotswouldgetahigherreturnontheenergyexpendedonthoseplots,andthuscanbeclaimedtobea"better"farmerthananagentwithlessproductiveplots.Topreventagentsfromdyingbeforetheyhavetimetoprocureresources,allhouseholdsaregivenaninitialallocationoftwoyear'ssupplyofmaizeandmeat,astheseresourcescanonlybegatheredinautumnandsummerrespectively.

4.4 Itisnotfeasibletoinitializeanagent'sallocationamongtasksrandomly,sinceanallocationforfarmingthatistoolowwouldlikelyresultinstarvation,withsimilarunfortunateresultsforotherresources.Additionally,theonlywayforanewagenttobeintroducedtothesystemisforahouseholdtosurvivelongenoughtoproduceoffspring.Toaddressthisproblem,wehavehouseholdscalculatehowmuchofeachresourcetheyneedandallocateenoughtimetomeettheseneeds.Thisonlyhappensintheyearinwhichahouseholdiscreated.(Exceptatinitialization,thisisalwaysduetoamarriage.)Weusetheresultingallocationoftimeinthatfirstyeartoseedourweightsforthesecondyear.Ifanagentspends25%ofitsenergyinthefirstyearfarming,thenfarmingwillhavea25%weightinoursystemduringthesecondyear.Afterthis,agentsrelyonaperformanceandfeedbackfunctiontoupdatetheirweightsforsubsequentyears.Ifagentsmaynotbeabletoprovidethemselveswithallthesubsistencegoodstheyneed,theymaytradefororrequestthoseresourcesthroughanexchangenetwork.

4.5 ThesimulationreportedherealsomodifiedtheversionreportedinKohlerandVarien(2012)byallowingagentstopassontheirwealthatdeath.Ifanagenthouseholddies,theresourcesithasstoredwillbedividedequallyamongitschildrenwhoarewithintradingrange,whichissetatthesamedistance(8km)permittedforbalancedreciprocalexchanges(BRN;seebelow).Ifnochildrenarewithinthatrange,thiswealthisdividedequallyamongneighbours,andfinally,ifnootheragentsarewithinrange,theresourcesgotowaste.

4.6 Thegeneraldecision-makingstepsrequiredofeachagentarepresentedinTable1.

Table1:Decision-makingprocessforeachagent(household)

Step Decision/action1 Iffirstyearincurrentlocation,performbasedonfamilyneedsandproceedtostep3.Ifnot,proceedtostep2.2 Ifsecondyearincurrentlocation,useallocationsfrompreviousyeartoinitializeweights.Proceedtostep3.3 Performtasksandexpendenergy.4 Exchangeresourcesifneeded.5 Ifstillalive,updateweights(definedinsection4.4).6 Ifagentlocationnotsustainable,movetonewlocation.7 Returntostep1.

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Agentstates

4.7 Agentshavefourstatesforeachresourcethataffecttheirhealthandwillingnesstotradethatresource.Calculationsforeachstatedependonthesizeandmakeupofeachfamily.Thecalculationsdonotincludeusageoftheresourcesforthepurposesofworkingorperformingothertasks.Thestatesarebasedonhowlongtheagentsestimatetheamountoftheresourcetheypossesswillbeabletomeettheirfamily'sneeds.

TRADING-2yearssupplyormore.SATISFIED-6monthsto2yearssupply.CRITICAL-lessthan6monthssupply(butmorethan0).STARVING-Whenanagentdoesn'thaveanyoftheresource,andneedstoimmediatelyobtainsomeviatradingorbegging.

Exchange

Barter

4.8 Barter—newtothisversionofthesimulation—allowsagentstotradeoneormoreresourcesinexchangeforanotherresource.Previousversionsofthesimulationallowedonlygeneralizedreciprocalexchangeandbalancedreciprocalexchange,andthoseonlyoperatedwithinthedomainsofmeatandmaize,asdiscussedbelowin§4.12and§4.13.Moreover,thebalancedreciprocalexchangesystemonlyallowstime-delayedexchangeswhereasbartersimulatesimmediateexchanges.Wehavedevelopedasimplifiedbartersysteminwhichagentstradegoodsbasedonafairvaluation.Pricesarethereforenotnegotiated.Todeterminevaluesforresources,weusetheagent'scostofproduction.Weacceptthatthisdoesnotresultinthelevelofinequalitythatonewouldexpectinacapitalistbartersystemwherepricesarenegotiated.Forinstance,inasystemwithnegotiation,weexpectthatifanagent(household)hasthesolesupplyofadesiredresource,itcouldinflatethepriceofthatresourcewellbeyonditscostofproduction.Wedidnotincludesuchamechanismasitwouldundulyincreasecomputationalcomplexity.Weusecaloriesasaformofcurrencyinthissimulation.Theinteractionsbetweenthebartersystem,andtheexchangesbasedonreciprocity,areoutlinedbelowin§4.18.Wepostponeforlaterinvestigationwhetherbarterincreasesordecreasesthedegreeofagentinequality(asmeasuredforexamplebytheGinicoefficient)relativetoexchangesbasedonlyongeneralizedandbalancedreciprocity.

Table2:Variablesusedinbarter

Abbreviation MeaningAg AnagentrAG SomeresourceperagenttAG AgentsinthesetofpotentialtradepartnersRWA SetofresourcesanagentiswillingtoacceptREQag AmountofgivenresourcerequiredbyagentAg

4.9 IfforsomeresourcerAG(Table2liststheabbreviationsusedtodescribethebarteralgorithm)anagentisinastateofCRITICALorSTARVING,ittriestoobtainenoughofthatresourcetogetbacktoaSATISFIEDstate.Firstitmustidentifyagentsthatitcanpossiblytradewithfortheresource.Itdoessobythefollowingprocess,whichisrepeatedforeachresource:

1. AskeachagenttAG(withintraderange)ifitiswillingtotradetheneededresourceandwhatitiswillingtoacceptinexchange.2. CallthesetofresourcesthattAGiswillingtoacceptRWA(tAG)3. IftAGhasenoughoftheresourcebeingrequestedbyAG(tAGisinaTRADINGstateforthatresource)and4. IfrAGhasenoughofoneoftheresourcesbeingdemanded(inaSATISFIEDstateorbetter)bytAG,thenaddtAGtoalistoftradepartners,whichwecan

callTList.5. SortTListinorderofpricefortheresourcebeingsought.

4.10 SincethisprocessisrepeatedforeachresourcerAGsought,iftheagentisinneedofmultipleresources,itwillfirstseektoprocureone,thenafterthat(regardlessofsuccess),itwillproceedtothenextresource.Afterfindingoutwhichagentswithinitstraderangearepotentialtradepartners,AGmustthenasktheseagentstotradeinexchangeforwhatitcanofferthem.Thatprocessisasfollows:

4.11 ForeachagenttAGinTList:

a. CalculatehowmuchoftherequiredresourcetAGiswillingtooffer.tAGiswillingtoofferanyamountaslongasitwouldnottakeitbelowitsTRADINGstate.

b. FilterRWA(tAG),removingresourcesrAGnotabovetheCRITICALthresholdforthatresource.TheresultingsetcanbecalledTRADE_SET.c. CalculatehowmuchoftherequiredresourcetAGiswillingtooffer(sothatitdoesn'tfallbelowTRADING);wecancallthissetOFFER.d. LimitOFFERtotheamountrAGdesired.e. CalculateanamountforeachresourceinTRADE_SETthatisequivalentinvaluetoOFFER.rAGisnotallowedtofallbelowSATISFIEDforanyorthese

resources.f. Ifwecanfindacombinationofsuchresources,thentradethatcombinationofresourceswithtAGinexchangefortherequiredresource.g. Ifwecannotfindsuchacombination,thencalculatethemaximumtotalvalueofresourcesthatwearewillingtotradewithtAG.

i. CalculatetheamountoftherequiredresourcethattAGiswillingtogiveforthatvalue.ii. TradetheselectedamountofresourcesinexchangefortheequivalentamountoftherequiredresourcethattAGiswillingtogive.

h. IfrAGisnowinaSATISFIEDstate,thenstop,otherwisemovetothenextagenttAGinTList.

4.12 Asstated,thevalueofaresourceforanofferingagentisdeterminedbythecosttothatagentofacquiringthatresource.Soifitcostsanagent1000caloriestoacquire10kgofprotein,thenthevalueofthatproteinis100calories/kg.Agentsdonotquestionthevalueofresourcesasdeterminedbyotheragents.Agentsarehoweverabletosortthroughthoseprovidingresources.Thereforeanagentknowswhointheirneighbourhoodcanprovidetheresourcemosteconomically.Thisgivestherequestingagentanadvantageintheexchangerelationship,asitcansortsellingagentsbylowestprice,andsellingagentswillacceptthecosttoAGtoproducethegoodsrAGbeinggiveninexchange.

GeneralizedReciprocalExchange

4.13 Evenasweaddbarter,wemaintainreciprocity-basedexchangesinoursystem,sincewecanreadilyobservethatevencontemporarymarketsocietiesretainkinandreputation-basedreciprocalexchangesalongsidemarketexchanges.Werecognizetwodistinctsystemsofreciprocity,whichwemodelseparately.Thefirstisbasedonkinship.Anagenthouseholdknowsthehouseholdsoftheparentsofthehusbandandthewifeaswellasthoseoftheirsiblings(againbilaterally).Thisleadstotheintroductionofthegeneralizedreciprocalnetwork(GRN),whichoperatesoverthisbilateralkinshipnetwork(Kobtietal.2004;Reynoldsetal.2004;KobtiandReynolds2005;Sahlins1972).InGRN,agentsareabletomakerequestsforresourcesfrommembersoftheirclosekin.Thisprovidesasocialsafety

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netwherebyrelatedhouseholdsbandtogethertohelpeachothersurvive.AgentsarenotexpectedtorepaytheresourcesthattheyobtainintheGRN,soifanagentobtainsmaizefromaparent,theyarenotexpectedtorepaythatgift.Thisworksoutinthelongrunforagentsbecauseifthatparentlaterweretoaskthechildforhelp,thechildwouldreciprocate(Crabtree2012;Sahlins1972).DetailsontheinternallogicoftheGRNcanbefoundinthepaperslistedabove.Inadditiontorequests,agentsintheGRNinaTRADINGstatewilldonatesomeoftheirresourcestoamemberoftheirfamily.AlltradinganddonationinGRNinthisinstantiationofthemodelarelimitedtoageographicaldistanceof6km,althoughthisdistanceischangeable.Moreover,kinwillnotputthemselvesbelowtheSATISFIEDstatetohelp,asthismayputtheirownhouseholdatrisk,andimportantly,GRNisonlyimplementedformaizeandmeat.Theorderinwhichthethreetypesofexchangenetworksareactivatedisoutlinedbelow.

BalancedReciprocalExchange

4.14 Thebalancedreciprocalexchangenetwork(BRN)isareputation-basedborrowing/loaningnetworkthatenablesagentstoexchangemaizeormeatwithneighbourswhoarenotkinintheexpectationthattheywillberepaidthesameamountofthesameresourceatalaterdate.Thisisprobabilistic,soagentswillnotautomaticallyloantosomeonerequesting,evenifthathouseholdhasagoodorneutralreputation(inthismodel,weallowa75%chanceofsayingyestotheseindividuals).Ifanagentloansaresourcetoaneighbour(heredefinedasahouseholdwithinBRNtradingdistanceof8km,butlikeGRNthisdistancecanbemodified),itexpectstoreceivethatresourcebackwhenitasksforit.Agentswillasktoberepaidonceperyear,attheendoftheharvest,orimmediatelyiftheagentisindireneed(inaSTARVINGstate;however,agents,asintheGRN,willnotexchangeiftheyarebelowauser-specifiedstateforriskofdeathbystarvation).Iftheneighbourrepayswhenasked,thenitsreputationremainsintact.Iftheneighbourisunabletorepaytheloan,thiswilldamageitsreputation.Reputationsareonlydyadic(betweentwoagents),soanagentcouldhaveanegativereputationwithoneagentwhilebeingheldinhighesteembyanother(Crabtree2012).

4.15 Agentsareabletoimprovetheirreputationsbyloaningresources.Ifaneighbourloansanagentaresource,itsreputationwiththatagentgoesup.Thismeansthatlaterifthisneighbourisinneedofanotherresourcethatitspartnerinapreviousexchangecanprovide,thispartnerismorelikelydoso.ResourcetransactionintheBRNislike-for-like.Thismeansthatifanagentisloanedsomemaize,thedebtisrepaidinmaize.AsforGRN,BRNisonlyimplementedformaizeandmeat.

4.16 Neighbours(thoseagentsinaBRN)aremuchlessgenerousthankin(agentsinaGRN).AnagenthastobeinaTRADINGstatebeforeitwillconsidermakingaBRNexchange.Thenthereputationoftheaskingagentisconsidered.Theaskingagentneedsapositiveorneutralreputationbeforetheneighbourwillproceed.Ifthesetworequirementsaremet,theagentwillconsiderwhetheritisina"loaningmood"(asdeterminedbytheprobabilitynotedabove).AnagentwillnotallowitselftofallbelowaTRADINGstateinloaningaresourcetoaneighbour.

4.17 BRNpromotesastrong"community"bondamongagents,thoughthesebondsareonlyexpresseddyadically.Whileagentsdonotaccountforthis(ineithertheirmovementalgorithm,orbyseekingtoenhancetheirreputationsasagoal)largercommunitieswithmorepositivelinkagesprovidemoreopportunitiesfortradeandassistance.Ofcoursethisisbalancedbycompetitionforresources;iflocalpopulationsbecometoolarge,resourcesmaybecomelimiting.Thiscanresultinagentshavingtoleavetheircommunitytofindamoreproductivelocation,evenatthecostoflosingtheircurrenttradepartners.Notethatwhileweusethewordcommunity,thisisnotaphysicalconstructwithinthesimulation.Hereweregardacommunitysimplyasanetworkofagentswithinacertainradius,tiedtogetherbytheirexchangepractices.

Sequenceofexchangesinthemodel

4.18 Agentsfirstseektoobtaintheneededamountofaresourceviathebarternetwork.Iftheagentstillhasnotobtainedenoughoftheresourceitneedsfromitstradingpartnersandit'sinaSTARVINGstate,itattemptstouseoneofthereciprocitynetworks.FirsttheagentusestheGRNtoaskupto4kin(thisnumberisachangeableparameterinthesimulation)togiveittheamountit'sshort.Ifitcannotobtainenoughviathismethod,itthentriestoborrowusingtheBRN.Ifafterallthis,rAGisstilldeficient,thenAGdiesiftheresourceismandatory(water,maize)orsuffersmalnutrition(protein),whichmayalsoleadtodeathafter3years.Sincebalancedandgeneralizedreciprocityexchangesonlypertaintoproteinandmaize,agentscanobtainwaterandwoodonlyviabarterorbydirectprocurement.

SocialInfluence

4.19 Agents'behavioursmaybeinfluencedbythebehavioursofthosearoundthem(Waibel,Floreano,MagnenatandKeller2006).Givenachoicebetweenmultiplespecializations,wefactorinwhatanagent'sneighboursaredoingandallowthattoinfluencetheagent'sdecision.AnagentNisdefinedasaneighbourofanagentAgifNandAgaredirectlyconnectedwithinasocialnetwork(foroursimulationthisnetworkislimitedtothetraderadiusofBRN).Ithasbeenshownthatsocialinfluenceoftencanincreasethelevelofagentspecializationwhencomparedtosystemswithnosocialinfluence(CockburnandKobti2009a).CockburnandKobti(2011)showedthataweight-allocatedsocialpressuresystemwouldbecapableofstimulatingtheemergenceofahighlevelofspecializationwithinapopulation.Webaseourcurrentmodelonthatmethod.

4.20 ForeachagentAg,thereshouldexistacompositefunctionSoc(t)foreachtasktinEC.Soc(t)wouldbeafunctionrepresentingthesocialinfluencetowardsperformingtaskt.Anexampleofsuchafunctionwouldbepeerpressuretowardsperformingatask.Inaneconomicnetwork,thesocialinfluencemaybeareflectionofthedemandforaproduct.Insuchasituation,itisalsopossibletocreatethesocialinfluencefunctionsuchthattherealsoexistsnegativeinfluence.Anexampleofthiswouldbenegativeinfluenceinthecaseofapotentialsalethat'slostbecauseacompetitorcanprovideabetterproduct.ThehandlingoftheresultofSoc(t)isdependentupontheagentandthedomain.Giventhesameexampleofanagentsellingaproductandthesamedemand-influencefunction,anagentmayreduceproductionorreducethepriceofitsproduct.

4.21 Forourcase,wefirstdesignater(t)astheresourceproducedbytaskt.Eachagentrequestingaresourcer(t)exertsproductionpressureonitspossibletradepartnersinthefollowingmanner:

1. Locateallagentswithintraderange,placingtheminalistwecallPOSS2. DetermineaninfluencerateIR=1/thesizeofPOSS3. LetrAmount=amountofresourcer(t)thatAgisseekingtoprocure4. ForagenttAGinPOSS

a. exertupwardproductionpressureontAGfortasktintheamountofrAmount×IR(fortAG:Soc(t)=Soc(t)+rAmount×IR)b. LettAmount=amountofresourcer(t)thattAGhasavailable,ORrAmount,whicheverislowerc. exertdownwardproductionpressureontAGfortasktintheamountof2×tAmount×IR(fortAG:Soc(t)=Soc(t)+amountTraded×IR)d. IftAGandAgcompletedatradeforr(t)

i. ThenamountTraded=theamountofr(t)tradedbetweenAgandtAGii. ExertupwardproductionpressureontAGfortasktintheamountofamountTraded×IR(fortAG:Soc(t)=Soc(t)+amountTraded×IR)

(Interpretationsofquantities:4aindicatestoeachagentthatmayprovidetheresourcethatthisagenthasademandfortheresource;4c:Thispressureaccordswithanagent'sexpectationofcompletingatradefortheamountpossible(tAmount).Iftheagentcompletesthetrade,thepressurewillbereversedbasedontheamountofresourcetraded.Iftheagentisunabletosell,thenthisiseitherbecausethereexistsanotheragentthatwasabettertradepartnerfortherequestingagent,ortherequestingagentdidnothavetheresourcesthatthesellingagentwasdemandinginexchangefortheresource.4dii:Thisrewardstheexpectationofsale.Theneteffectisthatifanagentisaskedforaresourceandisabletoprovideit,thenthatmeanstheircurrentlevelofproductionissufficienttomeetdemand.)

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4.22 AsellingagentAg,havingexcessresourcesavailableattheendofaproductionperiod(inaTRADINGstate)alsoexertspressureonitscompetitorsinthefollowingmanner:

1. Locateallagentswithintraderange,placingtheminalistwecallPOSS2. DetermineaninfluencerateIR=1/thesizeofPOSS3. LetrAmount=amountofresourcer(t)thatAghasthatitisstillwillingtotrade4. ForagenttAGinPOSS

a. Ifproductioncostofr(t)ishigherfortAGthanforAgi. ExertdownwardproductionpressureontAGintheamountofrAmount×IR(stateddifferently:Soc(t)=Soc(t)-rAmount×IRfortAG)

4.23 Thereforeanagentwillattempttoindicatetocompetitorswithhigherproductioncoststhatitisabettersourceoftheresourceandthatitwouldbemorecapableofprovidingthatresourcetothem.Thisdealswithagentswhoarewithinrangeofeachother,butarebothself-sufficientwithregardstoaresource.Exertingcompetitivepressureencouragesthelessefficientagentstolowertheirproductionandrelyonthemoreefficientonesfortheresource.

4.24 Anagentthatispressuredsociallydoesnothavetochangeitsbehaviour.Sometimes,ifanagentisalreadyinaTRADINGstateforaresource,theywillignorepressuretoincreaseproduction.Thereasonbehindthisbehaviouristhattheagentdeterminesthatitalreadyhadsurplus,butnoonewasabletoexchangeforit(possiblybecausenoagenthasanythingtoofferthattheagentiswillingtoaccept).Inthatcase,increasingproductionwillnotleadtoanincreaseintrade.AgentsalsowillnotdecreaseproductioniftheyarebelowaSATISFIEDstate.Thisoccursiftheagentdeterminesitcouldnotprocuremoreoftheresourcebecauseitdidnothaveanythingtotradetothesellingagents.Thereforereducingtheirproductionwillnotresultinthemobtainingmoreneededgoodsandwouldthereforebeantitheticaltotheirsurvival.

Updatefunction

4.25 Weuseauniformupdatefunctionforeachtaskinourweightsystem.Thisupdatefunctionisappliedattheendofeachyear,anddetermineshowtheagentwillallocatetimefortheupcomingyear.Giventasktthatprovidesresourcerandxamountofresourcer:

1. IftheagentisinaTRADINGstate,thenassumey=x-thethresholdforTRADING.Theagentwillthenreducetheweightoftasktproportionallysoitshouldresultintheagentproducingylessofrthanitproducedthisyear.Inotherwords,iftheagenthas200kgtoomuchmaize,thenitwillreducetheweightitappliestofarmingsothattheagentexpectstoproduce200kglessmaizenextyear.Toavoidanagentmakingtoodrasticacut,basedperhapsonanabnormalamountofaresourcebecauseoftrading,werestricttheamountanagentisallowedtoreduceaweightto50%ofthecurrentvalue.

2. IfanagentisinaCRITICALorSTARVINGstate,thentheagentwillattempttoincreasetheweightforthetasktsothatitexpectstoproduceenoughadditionalresourcesinthefollowingyeartogetittoaSATISFIEDstate.Again,toavoidovercompensating,werestrictthemaximumincreaseto300%.

3. Applyanysocialpressureasdeterminedpreviously.

Results

5.1 Toevaluatetheimpactsoftheseadditionstothebasesimulation,weranthesimulationthreetimes,oncewithagentsallocatingeffortbasedonlyonfamilyneeds(Scenario1),whichissimilartotheoriginalsimulationbutwithadditionssuchasthebarternetworkandresourceinheritance.Wedonotexpectthisscenariotoresultinmuchspecialization.Wethenranthesimulationwithagentsallocatingeffortbasedonlyontheircurrenteconomicstate(Scenario2).Inthatcase,agentssettheirweightsfortasksbasedontheamountofaresourcetheyhaveremaining.Iftheyhavemorethantheyneedbasedontheirreservethreshold(TRADINGstate),thentheyreduceproduction.Theyincreaseproductioniftheyarebelowthislevel.Thecalculationforthisupdatewasexplainedpreviously.Finallyweranthesimulationwithbotheconomicstateconsiderationsandsocialinfluenceenabled(Scenario3).Withtheadditionofsocialinfluence,agentswillreducetheirproductionofaresourceiftheyareinaTRADINGstateandthereisanagentavailablethatcanprovidetheresourcemorecheaplythantheagent'scostofproduction.

5.2 Wecomparethedifferentmethodsusingseveralmeasures.Onesuchmeasureistheleveloftaskspecialization(asexplainedbelow),whichisapplicableonlytothesecondandthirdscenarios.Wealsocomparetheproportionofthepopulationineachofthree"settlementtypes"differentiatedbythenumberofhouseholdscohabitingspecificcellsinthemodel.Wealsonotethechangeinthevolumeofexchangewhenagentsallocatebasedonlyonneeds,andwhentheyattempttospecialize.Additionally,wemeasuretheaccumulatedwealth(measuredasdefinedbelow)ofthepopulationunderthesethreescenarios.

5.3 Finally,wecomparethestructureoftheexchangenetworksthatforminScenario2,andinScenario3,usinganapproachdesignedtorevealthedegreeofcompartmentalizationinthenetworks.Theexchangenetworkprovidesanothermeansofcharacterizingtheoverallstructureofthesystem;forexample,howdoesthedegreeofspecializationaffectthestructureoftheseexchangenetworks?Innetworkanalysisoneanalyzesthefrequencyofnodes(theagents)andthefrequencyofedges(here,theexchangesbetweenagents)(Newman2010).Byunderstandinghowtheconnectance(theproportionofpossiblelinksbetweenagentsthatarerealized)ofeachagentchanges,andvariabilityinthenumberofedges,wecanbetterunderstandphenomenaofinterestinthereferencesystemsuchastheresilienceofthenetworktoperturbationortheefficiencyofthenetworkindistributinggoodsorinformation.Wepresumethatdifferentnetworkstructureshavedifferentoutcomesfortransmissionofinfluence,innovations,andsociallyinfluencedbehavioursingeneral.Belowwecontrastyearsofhighandlowpopulationwithinandbetweenscenarios.

5.4 Tomeasurethedegreeoftaskspecialization,weuseamethoddevelopedinGorelick,Bertram,KilleenandFewell(2004)tocalculatetheleveloftaskspecializationwithinthesystem.Weusetheweightgiventoeachtasktocalculatetheleveloftaskspecializationattheendofeachstepinthesimulation.Theweightsofallagentsarethenstoredinann-x-mmatrix,wherenisthenumberofagentsandmisthenumberoftasks.Thereforeeachrowinthematrixrepresentsanagent'stimeallocationamongalltasks.Thematrixisthennormalizedsuchthatthetotalofallvaluesinthematrixis1.ThemutualinformationandShannonentropyindex(Shannon1948)arethencalculatedforthedistributionofagentsacrosstasks.TheShannonentropyisthendividedbythemutualinformationscore,resultinginavaluebetween0and1.Avalueof1indicatesthatallagentsspendalltheirtimeononetask(notofcourseinthesametask),whileascoreof0meansthatthereisnotaskspecialization,aswouldbethecasewheneachagentdividesitstimeequallyamongtasks.SeeGorelicketal.(2004)forafullexplanationofthismethod.

EffectsonPopulationSizeandDegreeofSpecialization

5.5 AscanbeseeninFigure1,andasexpected,thereisamarkedincreaseinpopulationsizewhenspecializationisadded(Scenario2vs.1).Somewhatsurprisingisthatpopulationlevelsareslightlylowerwhensocialinfluenceisaddedtoeconomicspecialization,thoughpopulationsconvergelateinthesimulation(Scenario3vs.2).Perhapstheadditionofsocialinfluencecanmakeagentstooreliantonthesuccessofothersfortheirownsuccess,somewhatanalogoustoHegmon'sdemonstrationthatsharingtoobroadlycanbedetrimentaltocommunitysurvival(Hegmon1989).Anotherpotentialexplanationmaybethatsinceagentsheredonotconsidersocialnetworkswhenmoving,theymaybeabletomoveoutsideoftheirsocialnetwork,populatinganareawheretheyhavenoexchangepartners.Thisincreasesthelikelihoodthatagentswillnotbeabletoexchangeuntiltheyareabletorebuildanexchangenetwork(Crabtree2012).

5.6 Wealsofoundthatthedegreeofproductionspecializationincreasedsignificantlyasweaddedsocialinfluencetothefactorsthatagentsconsider(Figure2,Scenario3vs.2).ThisfurtherconfirmsthefindingsofCockburnandKobti(2009a;2009b).Inallfigures,AD600correspondswiththeinitialcolonizationoftheVEPareabyfarmers.However,thisareawasinfactdepopulatedaroundAD1280,afactnotreplicatedinthesesimulations.Instead,weseeaspikeinthelevelsofspecializationaroundthistimeinoursimulation.

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5.7 Therearefactorstobenotedintheperformanceoftheunderlyingspecializationmechanismthatwewerenotabletofullyexplorehere.Namely,thenumberofyearsofstoragewealloweachagentisveryimportant.Aswehavenomonetarycurrency(outsideofcaloriccosts)anddonotallowexchangesofgoodsforlabour,storedresourcesaretheonlysourceofwealthandassetsforexchange.Investigationsnotpresentedhereshowthatthelevelofspecializationincreasesasweincreasethenumberofyearsofstorageallowed.Wecanconcludethataddingsocialinfluencetoourreferencesystemwitheconomicspecializationleadstoapopulationthatisnotnecessarilylargerinsize,butonethatismorespecialized.

Figure1.Populationlevelsforeachofthethreescenarios;Scenario1needsonly;Scenario2economicstate;Scenario3basedonbotheconomicstateandsocialinfluence.Tonoteishowmuchhigherpopulationsarewhentheyarenotbasedonneedsonly.

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Figure2.ThedegreeofproductionspecializationbetweenScenario2foreconomicstateandScenario3foreconomicstateandsocialinfluence.

EffectsonDegreeofAggregation

5.8 Asnoted,agentswillmoveiftheyarenotthrivingattheircurrentlocation.Whenchoosingadestination,agentsdonotfactorinthepresenceofpotentialexchangepartners,oranyexchangenetworksthatmayexistamongthosehouseholds,unlikeinCrabtree(2012).Ourresultsshowthatagentsaremorelikelytocohabitthesamecellwhentheyspecialize,asseeninFigure3.Withoutspecialization,agentsprimarilyliveinsmallhamletsof1-2households,andfewincommunitycenters(of9ormorehouseholds).Wefoundthatwithjusteconomicstateinfluencingplanning(Scenario2vs.1),agentsaremorelikelytoliveinbighamlets(3-8households),surpassingtheproportionlivinginsmallerhamletsafteraboutAD750intherunspresentedhere.Theproportionofagentslivingincommunitycentersisalsogreaterineitherscenario2or3thanin1.Thismaysuggestthatagentsmovelessasaresultofspecialization,oritmaysuggestthattheyarebetterabletotoleratetheeffectsofscramblecompetitionforresourceswhentheirresourceneedsarecomplementaryratherthanredundant.Moregenerallytheseresultssuggestthatanincreaseinspecializationmightoftenleadtoincreasesinsizesofthelargestsites,andinthedegreeofaggregation,inthearchaeologicalrecord.

5.9 Interestingly,whencomparingScenario3vs.2,weseethatagentstakingintoaccountonlyeconomicstate(Scenario2)aremorelikelytoliveincommunitycenters(>8households)formostofthesimulation.AgentsinScenario3aremorelikelytoliveinbighamlets(of3-8households)thanaretheScenario2agents.Thesedifferencesarerelativelyslight,however,andmightdisappearifweweretorepeatthisexerciseusingmultiplerealizationsofeachoftheseeconomicscenariosusingdifferentrandomnumberseedsanddifferentparametersettingsforbasicagentoperation.ThestrongersignalisthecleardifferencebetweenthegreateraggregationexpectedunderScenarios2or3relativetoScenario1.

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Figure3.Proportionofhouseholdsineachtypeofsettlement,hamlets,bighamletsandcommunitycentersforScenario1needs,Scenario2economicstateandScenario3economicstateandsocialinfluence.

EffectsonVolumeofExchange

5.10 Alongwithanincreaseintheproportionofhouseholdslivinginlargercommunities,weobservedasignificantincreaseinbarterundereitherofthescenariospromotingspecialization,comparedtotheconditionwhereagentsallocateeffortsbasedontheirprivatesubsistencerequirements(Scenario1).Thisisdueinparttoworkersworkingmorehoursonaverage,andthustryingtoproducemorethantheyneedtomeettheirfamily'sneeds.Theexcesssupplyofresourcesresultsinmoreagentsinshortagebeingabletofindsomeonewillingtomeetthatdemand.WeseeinFigure4thatthereisverylittletradinginsomeresourcessuchaswoodinthe"needsonly"scenario(whereasmuchisrequested,butalmostnoneisexchanged).Withagentsjusttryingtoproduceenoughfortheirownfamily,it'sunlikelythattheywilloverproduce,andsotheyaccumulatenoexchangeablesurplus.Thereforethereisnobarter,despitethefactthattherestillisahighlevelofdemandforwood.Withthechangeinallocationstrategymoreofthedemandforsuchresourcescanbemetbecausethereismoreoverproductionofresources.Althoughthelevelofdemandisnotfullymetunderspecialization,theunmetdemandismuchlessthaninthe"needsonly"scenario.

Figure4.Volumeofexchangeofwoodperscenario;solidlinedepictsrequestedwood,whiledottedlinerequestsexchangedwood.NotehowinScenario1theneedsonlyscenariowoodisrequestedfrequentlybutseldomexchanged.

EffectsonVolumeofStorage

5.11 Figure5revealsthatwhenagentsallocatetheirlabourbasedonlyonneeds(Scenario1),wefoundthattheystorelessthaninthespecializationscenarios(2and3),despitethefactthattheirstoragerestrictionsareidentical.Thisisasexpectedsinceagentsprocuringonlywhattheyneedrarelyoverproduce.Overproductioninthatcaseisdueeithertotheinabilityofanagenttoaccuratelyestimatetheneedsofitsfamily,orinabilitytoprocureexactlytheamountrequired(forexampleit'snotpossibletoonlykillhalfadeer).Ontheotherhand,whenallocatinglabourbasedoneconomicandsocialfactors,agentsaremuchmoreproductive.Theresourcestheyoverproducearemaintainedinthesystem(thesociety),resultinginhigheraverageagentwealth.Wecanseethatthereisstillalowstorageamountformeat.Thisisduebothtothehighdecayrateforthisresourceinstorage,aswellasthelandscape-widedepressionofthemostimportantmeatsource,deer(bothinourmodels,andintheworldtheyreference).Averagestoragelevelsdonotchangenoticeablywhensocialinfluenceisaddedtoeconomicspecialization,eventhoughthatadditionresultsinasmallincreaseofspecialization,aswesawinsection5.1.

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Figure5.Storagebasedoneachscenario.Notethatintheneedsbasedscenario,Scenario1,agentsstoremuchlessthanintheothertwoscenarios.

EffectsonSocialNetworks

5.12 Asseenabove,exchangeincreaseswheneconomicstateandsocialinfluencearetakenintoaccount,asshowninFigure4forwood.Additionally,storageofmostresourcesisgreaterwhenagentsspecializethanwhentheyonlytakeintoaccounttheirneeds,asseeninFigure5.Finally,whenagentsspecialize,populationsincrease(seeFigure4forexample).Thesethreeresultsleadustoexpectthatthesocialnetworksthatformfrombarteringofeachoftheseresourceswillbemarkedlydifferentamongthethreescenarios:whenagentstakeintoaccountonlytheirneeds(Scenario1)andwhentheyspecialize(Scenarios2and3).Performinganetworkanalysisonthedyadicexchangesbetweenagentsprovidesameansforcomparingthestructureofthesystememergingfromtheseinteractions.

5.13 Forthisanalysisweidentifiedfourpointsintime(asreportedinTable3)fromScenarios2and3.Table4reportsthenumberofexchangesthroughtimeinthebarternetworkforScenario2.Table5reportsthecorrespondingfigureswhenallocationofeffortisbasedoneconomicstateandsocialinfluence(Scenario3).

5.14 Notsurprisingly,whenthesimulationbeginsexchangeishigh.Whentheagentsareinitiallyseeded,randomly,onthelandscape,manyareplacedinareaswithpoorproduction.Consequentlytheagentstrytomakeupfordeficienciesofresourcesbybarteringwithoneanother.Withrespecttothenumberofedgespernode,bothScenario2and3arerathersimilar,anddeclineslightlythroughtime.However,exceptinthefirstyearofthesimulation,Scenario3alwaysgeneratesmoreexchangingagents—nodes—andmoreexchanges—edges—thandoesScenario2.

5.15 Anotherinterestingcontrastbetweenthetwoscenariosliesisinthedifferingdegreeoftheclusteringcoefficientthateachnetworkgenerates.Thenetwork'sclusteringcoefficientisthemeasurementofthenumberofedgesbetweentheneighboursofanodendividedbythemaximumnumberofedgesthatcouldexistbetweentheneighboursofnoden,asdescribedinAssenov,Ramirez,Schelhorn,LengauerandAlbrecht(2008).Theclusteringcoefficientofanodenis:

Cn=en/(kn(kn-1))

"whereknisthenumberofneighborsn,andenisthenumberofconnectedpairsbetweenallneighborsofn"(Assenovetal.2008NetworkAnalyzerSupplementalMaterials).Theclusteringcoefficientofanodeisalwaysscaledbetween0and1,whichallowsforcomparability(Assenovetal.2008;Donchevaetal.2012).Inthiscontext,ahigherclusteringcoefficientmeansthattheentiresystemofexchangesexhibitsmoreclusteringintocondensedcomponents.Alowerclusteringcoefficientmeansthatthesystemofexchangesismoredispersedoverall.Notethatthisis"aspatial"inthattheclusteringofexchangesisnotnecessarilyrelatedtothelocationofagentsonthelandscape.Here,wecalculatetheclusteringcoefficientasaveragedacrossallofthenodestogiveaclusteringcoefficientfortheentirenetwork.Clusteringcoefficientsarecalculateddifferentlydependinguponwhetherthenetworkisdirectedorundirected.Networksofexchangearedirected,sinceonehouseholdisprovidingresourcesforanother,soanalysesarebasedondirectionality;eventhoughexchangeisreciprocal,eachexchangeitselfis

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directional.Forthisanalysistheclusteringcoefficientiscomputedfordirectednetworks.TheseresultsarereportedbelowinFigure6.

5.16 ComparingScenarios2and3,weseeinFigure6andTable5thatthesociallyinfluencednetworkgenerallyexhibitsahigherclusteringcoefficientevenastheoverallconnectivityoftheagentsisdeclining.Thissuggeststhatthesociallyinfluencednetwork(Scenario3)ismorereliantonafewnodestosupplytherestofthenetwork.Bascompte(2010)characterizestherelianceonfewnodestosupplythenetworkasa"compartmentalization"or"thetendencyofacomplexnetworktobecomeorganizedin'compartments'characterizedbyagroupofspeciesinteractingmorestronglyamongthemselves"(Bascompte2010:765).

5.17 ThoughBascomptereferstobiologicalnetworks,compartmentalizationissimilarlyusefulhere.Insteadofdifferentspeciesinteracting,thecompartmentsareformedofgroupsofagentswhotogethercanbeconceptualizedascommunities.Forexample,inyear1100ofScenario3(Figure7c)theoverallnetworkhasbeendividedintomultiplegroups;someofthesegroupsareconnectedthroughjustafewindividuals.Therearealsooutlyinggroupsthatarecompletelycutofffromtheflowofgoodsinthemainnetworkandothersubnetworks.Thesenetworksappeartobemorecompartmentalized,asalsoindicatedbytheslightlyhigherclusteringcoefficientinTable5,thanthenetworksgeneratedunderScenario2.

5.18 IfonewantedtodisrupttheflowoftheScenario3networkstherearecertainnodesthatwouldbeinstrumentaltodestroy.InScenario2year1100(Figure6c),ontheotherhand,thereisamoreequaldistributionofnodeinteractions;ifonerandomnodeweretoberemoved,itwouldbelessdisruptivetotheoverallflowofthenetworksincenode-to-edgedistributionisfairlyequal.InScenario3ifoneweretoremovearandomnodetherewouldbeahighprobabilityofremovinganon-essentialnode.However,if,perchance,oneofthe"hub"nodes(thenodewiththemostconnections)wereremoved,itsentirenetworkwouldcollapse.Thehubnodesprovidethebulkoftheinteractions,andonceremovedmorecompartmentalizationwouldoccur—portionsofthenetworkwouldnolongerbeconnectedtoeachother(seeReynolds,Kobti,KohlerandYap2005).

Table3:Characteristicsofpopulationatyearswhennetworksareassessed

Year Characteristicofpopulation600 Startofsimulation1000 Populationpeak1100 Populationtrough1200 Populationpeak1300 Populationtrough

5.19 Wehavenotyetinvestigatedwhetherthe"hubnodes"ofScenario3arealsorelativelywealthy,thoughitislikelythattheyhavebothlargefamilies,andmorestoragethanaverage;wedoknowtheyarerelatively"rich"inthenumberofconnectionstheyhave.Wealsohypothesizethattheyareadvantageouslyplacedonthelandscapebothwithrespecttolandscapeproductivityandwithrespecttotheirabilitytoactasintermediariesbetweentwonetworksegmentsbecauseoftheirlocation.Clearlytheyareinstrumentaltothedistributionofthegoods.

5.20 Uponvisualinspectionofthefigureswecanseethatexchangeslookverysimilarinyear600forbothstrategies(Figures7aand8a).Foryear1100,inthenetworkcreatedbyScenario2agentstherearefewexchanges,anditappearsthateachexchangingagentisequallyconnected.However,inyear1100underScenario3weseethatexchangeismorefrequent.Possiblythesocialinfluencethathelpstocreate"hub"nodesalsofacilitateexchangeamonglargernumbersofagentsthanispossiblethrougheconomicstatealone.

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Figure6.NetworkclusteringcoefficientforeachofScenario2economicstateandScenario3economicstateplussocialinfluenceforyear600,1000,1100,1200and1300.CoefficientsarereportedinTable4andTable5.

Table4:Connectivitywhenallocatingonlybasedoneconomicstate(Scenario2)

Year Nodes Edges NetworkClusteringCoefficient Numberedges/node600 181 478 0.130 2.641000 595 1592 0.013 2.681100 443 1194 0.014 2.701200 271 678 0.011 2.501300 317 749 0.016 2.36

Table5:Connectivitywhenallocatingbasedoneconomicstateandsocialinfluence(Scenario3)

Year Nodes Edges NetworkClusteringCoefficient Numberedges/node600 180 468 0.091 2.601000 625 1746 0.026 2.791100 495 1320 0.020 2.671200 455 1160 0.023 2.551300 470 1185 0.016 2.52

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Figure7.Exampleexchangenetworks,scenario2.Pinkdotsrepresenthouseholdsandbluelinesrepresentexchanges.Multiplelinesrepresentmultipleexchangesforthosehouseholds.a.year600,b.year1000,c.year1100,d.year1200,e.year1300.Graphsareformedbasedonconnectance,notonphysicalspace.Nodes

towardtheedgesaretheleastconnected,whilenodestowardthecenterarethemostconnected.

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Figure8.Exampleexchangenetworks,scenario3.Pinkdotsrepresenthouseholdsandbluelinesrepresentanexchange.Multiplelinesrepresentmultipleexchangesforthosehouseholds.a.year600,b.year1000,c.year1100,d.year1200,e.year1300

Conclusions

6.1 Inthispaperwecreatedaweight-basedsystemforagenttimeallocation,resultinginspecializationofproduction.Thisinturnrequiredustodevelopasystemofbartersothatagentscouldexchangethegoodstheyvariablyproduced.Weexploredtwoscenariosforsuchspecialization.Inone,agentsareallowedtodeterminethedegreeofspecializationbasedonlyontheireconomicstate.Inthesecond,theytakeintoaccountboththeireconomicstateandasocialinfluencefromtheirneighbours.Asexpected,householdsbecamemorespecializedwhentheywere"allowed"todoso.Agentsalsobecameincreasinglyco-resident(thatis,morehouseholdsco-residewithinspecific200m×200mcellsinthesimulation),exchangedmoregoodswitheachother,andachievedhigherglobalpopulationlevelsineitherofthespecializationscenariosthaninScenario1.

6.2 Thesocialnetworksformedfromthetwotypesofspecializationdisplayedsomewhatdifferentcharacteristics.Whilebothdisplayedincreasingcompartmentalizationthroughtime,Scenario3displayedagenerallyhigherclusteringcoefficient.Thesocialinfluenceofagentsinthissimulationisimportanttofacilitatetheflowofgoodsthroughoutthesystem.Futureresearchintothe"wealth"ofthehubnodeswillhelpelucidatehowthesenodessupplythenetwork.

6.3 Aswebegintoexplorethisnewmodelusingparameterizationsmorereasonableforourreferencecase—theBasketmakerIIIthroughPuebloIIIperiodsinthecentralMesaVerderegion—wewillinvestigateseveralquestionsraisedbytheanalysishere.Whatarethespatialcharacteristicsofthenetworksformedbythecombinationofspecializationandbarter?Howdothesizesandlocationsofthecommunitiesdiscoverableinthemodelcomparewiththoseknownfromourstudyarea?Doesthecombinationofbarterandspecializationincreasethesizesofthecommunitiesinthemodel,relativetocommunitiesdiscoverablefromthenetworksgeneratedbyreciprocityamongagentswithlargelyredundantproduction?

6.4 Kohler,HerrandRoot(2004)suggestedthatmanyofthedifferencesbetweenpre-AD1280inSouthwestColoradoandthepost-AD1375PueblosocietiesinthenorthernRioGrandecanbeattributedtotheadditionofproto-marketforcestoeconomiespreviouslystructuredbyeconomiesbasedmostlyonreciprocity.Abbottetal.(2007)suggestedthatintheHohokamareainthedesertsofsouthernArizona,periodicmarketplacesandbarteringoodssuchasearthenwarecontainersmaybeimportantstructuringforcesevenearlier,byaroundAD1000.Furtherworkwiththismodelwillhelpusunderstandtheextenttowhichdifferencesinsiteandcommunitysizesandlocationscanbelegitimatelyattributedtotheadditionofbarterandspecializationtoeconomiespreviouslybasedonreciprocity.

6.5 Inthemodelspresentedhereweareengagingincounter-factualexplorations,sinceitappearsunlikelytousthatthehighdegreesofspecializationandlargeamountsofbarterthattypifyourScenarios2and3infactcharacterizedtheeconomiesofsocietiesinsouthwesternColoradobetweenAD600and1300,whentheareawemodelwasdepopulatedinacollapsethataffectedtheentirenorthernSouthwest.Assumingthatthisdepopulationwasnotjustduetoalargeexternalshock(whichmayinfacthavebeenthecase)wecanusethesemodelstoguideourintuitionsastowhetherthepre-1300societiesinsouthwesternColoradowouldhavebeenmore(orless)resistanttothiscollapseiftheyhadinfactdevelopedmorespecializationandbarter.

6.6 Intheirrecentreviewofthestructuralcharacteristicsofsystemsapproachingandundergoingcriticaltransitions,Schefferetal.(2012)proposethat,ingeneral,modularityandheterogeneitycreatemorerobust(lessfragile)systemsthandoconnectivityandhomogeneity.Inourmodelsystems,itistruethatspecializationandbarterleadtomoreconnectivityamonghouseholds,aspointedoutinsection5.5,butontheotherhand,thosehouseholdsaremoreheterogeneousthanintheScenario1case,whereallhouseholdsengageinthesamesuiteofactivitiestoapproximatelythesameextent.So,whiletheirhighconnectivitymaymakeScenario2-and3-typesystemsmorepronetoundergoingacriticaltransitionsuchascollapse,theirheterogeneitymayprovidesomeprotectionagainstthatpossibility.Thatthepost-1300PueblosocietiesinthenorthernRioGrandeseemtohavebeenhighlystableinspiteoftheir(presumed)highdegreeofconnectivitymaysignalthatheterogenetityismorefundamentaltostabilitythanisdegreeofconnectivity.ItisalsopossiblethattheagriculturalsystemsdevelopedinthenorthernRioGrande—basedonwatermanagementratherthanrainfall—weresomuchmorestablethatanydeleteriousconsequencesforhighconnectivitywereneverexpressed.

6.7 ThenextphaseinthisstrandofVEPresearchwillinvolveenlargingourstudyareatoincludebothsouthwesternColoradoandthenorthernRioGrande.ThiswillprovideuswithanopportunitytoseetheextenttowhichthestructureoftheenvironmentinthenorthernRioGrandeitselfencouragestheformationofspecializationandbarter,orwhetherthepossibilityofengaginginasinglespecialization(suchasgrowingcotton,whichwasnotpossiblethroughoutthatarea,orinsouthwesternColorado)canprovokeacascadeofotherspecializationsinthemodelhouseholds.

Acknowledgements

ThisresearchwasmadepossiblebygrantDEB-0816400toKohler,CraigAllen,ZiadKobti,andMarkVarien.CrabtreealsoacknowledgessupportfromgrantDGE-080667.CrabtreeandKohlerthanktheLaboratoireChrono-Environnement(UMR-6249)oftheMaisondesSciencesdel'Hommeetdel'EnvironnementC.N.LedouxandtheUniversitéofFranche-ComtéofBesançonforsupportwhilecompletingfinaleditstothismanuscript.

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Appendix-FormalProblemDescriptionandApproach

ProblemDescription

GivenagentAg,thesettAGandaresourcerAG,howdoesanagentallocateitsrAGamongeachtasktintAG?

So:Σxi=S(RAg)whereiiseachtaskintAG,S(rAG)referstotheamountoftheresourcerAGavailable,andxireferstoafractionofS(rAG).

Theproblemalsoinvolvesthefollowingconditions:TheproblemiscontinuousoveraperiodofiterationsS(rAG)changesbetweeniterationsxiisallowedtochangeoveriterationsEachagentAgalsohasasetREQ(Ag),suchthataresourcerinREQ(Ag)needssomeamountofrforsubsistencebetweeniterations.

Weight-basedmodelfortimeallocationamongtasks

Weusedaweight-basedapproachforagents'timeallocationbasedonCockburnandKobti'sstudy(2011).Aquicksummaryofthatapproach(namedWASPS)ispresentedhere.

ForeachagentAg,weproposeasetEC,whereeiinEC.ThereisataskiintAGandeirepresentstheweightoftaski.

TaskweightsinECarerelative,thereforeforthegivenataskiandaresourcetobeallocatedrAG,theamountofrAGtobeallocatedtotaskiis:ei/S(EC)×S(rAG)whereS(EC)isthesumofallelementsinEC.WemakenoassumptionsabouttheinitializationoftheweightsinEC.Theycanberandomlyassigned,orinitializedbysomeothermethod.Ataskhavingaweightof0willresultinthetaskbeingallocatednoneofrAG.AgmustpossesssomeevaluationfunctionP(t)foreachtasktinEC.P(t)isassumedtobeacompositefunction,assumedtobeaneconomicperformancefunction.P(t)isappliedtoeachtaskinECaftertheperformanceofthattask,thereforerepresentingtheresultofperformingthetask.IfP(t)>0,thetaskisassumedtohavehadapositiveresult,inwhichcaseetisincreasedbysomefactor,whichisdomaindependent.InthecaseofP(t)<0,etissimilarlydecreasedbysomefactor.TheresultofthisprocessistheupdatingoftheweightsinEC,whichinturndeterminehoweachagentallocatestheresourceinquestion.MoredetailsonthemethodologycanbefoundinCockburnandKobti(2011)

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