Ecological and Social Dynamicsof Territoriality and HierarchyFormationPaul L. HooperEric Alden SmithTimothy A. KohlerHenry T. WrightHillard S. Kaplan

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SANTA FE INSTITUTE

EcologicalandSocialDynamicsofTerritorialityandHierarchyFormation

PaulL.Hooper1,EricAldenSmith2,TimothyA.Kohler1,3,HenryT.Wright1,4andHillardS.Kaplan1,5

1SantaFeInstitute,2UniversityofWashington,3WashingtonStateUniversityPullman,

4UniversityofMichigan,and5UniversityofNewMexico

ChapterinavolumetentativelytitledComplexityandSociety:

AnIntroductiontoComplexAdaptiveSystemsandHumanSociety,editedbyJeremySabloffetal.

1

I.Introduction

The origins of complex societies fascinateus: societieswith hierarchically organized politicalsystems, specialized divisions of labor, andrelatively unequal distributions of power andwealth. These societies tend to be politically andsocially integrated at very large scales,encompassing tens of thousands to hundreds ofmillions of individuals. They are the societies inwhichmostofuslive.

It hasn’t always been thisway: for 92-98%of the existence of modernHomo sapiens, itappears thatmostpeople lived in relatively small-scale,egalitariansocieties,withmuteddifferencesinwealth,status,andpoliticalpower(Boehm2001,Smith et al. 2010). What happened? Why did ithappen? These are long-standing questions, onesthat this chapter attempts to address in asystematicandnovelway.

Every state that exists today is a culturalsuccessor to the earliest states that arose duringtheMiddleHolocene.Eachofthesestatesgrewonan economic foundation of intensive agriculturecultivated on well-watered, fertile land (Trigger2003). Agriculturalists, however, are not the onlysocieties to manifest political complexity andinequality.

Despite the fact that most foragers (i.e.hunter-gatherers) known in recent history live inrelatively small-scale, egalitarian groups, foragersare also capable of generating hierarchical andunequal societies. Among foragers of the PacificcoastofNorthAmerica,multi-villagepoliticalunitsencompassing 100-10,000 individuals were led by

chiefsandexhibitedacomplexcontinuumofsocialrank,slavery,andasignificantdegreeofeconomicinequality. These foragers relied on resource-producingsites—salmonruns,fruitandnutgroves,and coastal sites for maritime hunting andforaging—thatwerepredictablyclustered inspaceand time. This spatial and temporal concentrationof resources motivated territorial claims andhierarchically organized, large-scale warfare overaccess to prime sites (Gunter 1972, Ames 1994,Matson&Coupland1994,Ricketal.2005,Kennett2005).

The common denominator of politicalcomplexity among agriculturalists and foragers—the value of claiming and defending durable,defensible resources and resource-producingsites—underlies the central thesis of this chapter:the social dynamics that arise in the context ofeconomically defensible resources are keygenerators of large-scale political integration andpoliticalhierarchy.

Weestablish the theoreticalvalidityof thisthesiswithacomputationalmodelbasedonasetof simple assumptions. The model identifiesfeatures of the natural, social, and technologicalenvironment that favor (or disfavor) the develop-ment of an arms race between larger and morehierarchically organized territorial coalitions. Thefollowingthreesections(II)describethemodel,(III)summarize its results, then (IV) discuss theimplicationsforunderstandinghierarchyandstateformationinhumanhistory.

2

II.ThemodelOverview

This model represents the culturalevolutionofdifferent strategies for gainingaccesstoresourcesites.Thesestrategiesvary inwhetherornottheyattemptto(i)territoriallydefendsites,(ii) form territorial alliances, and (iii) establishterritorial political hierarchies (Figure 1 and Table1). The exogenous parameters of the model areintended to reflect variation in the social andecological circumstances faced by human groupsaccording to time and place (Table 2). Theeconomic defensibility of sites is represented in

termsof thevariance intheexpectedproductivityof resource patches.Whether or not agents formalliancestoclaimanddefendterritorydependsonthis variance in the quality of land (or“patchiness”), as well as the costs of maintainingand cooperating within alliances.Whether or notindividuals are willing to buy into systems ofpolitical hierarchy that monitor and enforce thecooperation of alliancemembers depends on therelativeefficiencyandcostsofhierarchycomparedtonon-hierarchicalalternatives.

Figure1.Anestedtaxonomyofstrategytypes.Theblack(terminal)nodesindicatefullyspecifiedstrategytypes.

Table1.EvolvingstrategiesanddecisionvariablesforindividualiStrategy Symbol Values Associateddecisionvariable Symbol ValuesTerritorial Ti 0,1 Contestthreshold 𝜇!! 0—1

Alliance-forming Ai 0,1 Maximumalliancesize 𝑀!!"# 0—N

Cooperate Ci 0,1 - - -Coordinatedpunisher Pi 0,1 CPcoordinationthreshold τi 0—N

Hierarchical Hi 0,1 - - -Willingleader Li 0,1 Taxofferedasleader ti 0—∞

Allstrategies

Non-territorial(T=0)

Territorial(T=1,μT=?)

Solitary(A=0)

Alliance-forming(A=1,Mmax=?)

Non-hierarchical(H=0)

Opportunist-icallyDefect

(C=0)

Non-punisher(P=0)

Coordinatedpunisher(P=1,τ=?)

Cooperate(C=1)

Non-punisher(P=0)

Coordinatedpunisher(P=1,τ=?)

Hierarchical(H=1)

Notwillingtobeleader(L=0)

Willingleader(L=1,t=?)

3

Thecurrentmodelsynthesizesthetheories

of economic defensibility and animal contests(Brown 1964, Maynard Smith and Price 1973,Dyson-Hudson and Smith 1978, Boone 1992)withmodels of the evolution of cooperation,punishment, and political hierarchy fromevolutionary anthropology (Smith & Choi 2007,Hooper et al. 2010, Boyd et al. 2010). Themodelnests the strategies and replicator dynamics ofevolutionarygametheory(McElreath&Boyd2007,Gintis 2009) within a simulation in NetLogo 5.1.0with explicit spatial and demographic dynamics(Wilensky1999).Thismodelbuildson thebaseofprevious evolutionary models by representingexplicit landscapeswithproductivity that varies inspace and time; endogenous returns to scale in

competition for territorial resources; and astatistical analysis of stochastic outcomes as afunction of socioecological parameters. Like allusefulmodels, it aims to establish clear principlesthat sharpen our understanding of real-worldphenomena, rather than re-create the fullcomplexityofrealityitself.Socioecology

Thesocioecologyofthemodelisdefinedbythe spatial variability of resource production andan array of parameters affecting the benefits andcosts of different social behaviors (Table 2). Theexogenous nature of these parameters allows aprincipled statistical analysis of the results andavoidsissuesofinferenceunderendogeneity.

Table2.Exogenoussocioecologicalparameters. Parameter Symbol Values

Focal

Varianceinpatchproductivity var(μk) 0.005,0.030,0.055Decisivenessofalliances α 1,2,4Basecostofalliance* cA 0.05,0.15,0.25Costofcooperation* cC 0.05,0.35,0.65Costofenforcement* cE 0.05,0.35,0.65

Efficiencyofleadershipselectionprocess d 0,0.5,1

Additio

nal

Landscapedimensions(inpatches) w×w 33×33Meanpatchproductivity mean(μk) 0.1

Clusteringofproductivepatches S 0.1,0.2,1.0Spatialreach★ r 0.12,0.36,0.6

Intrinsicrateofincreasecoefficient B 4Roundspergeneration - 25Generationsperrun - 250

Probabilityofmutation - 0.01*Inunitsofμ;★Inunitsofw.

Table3.Othervariablesinthemodel.

Variable Symbol ValuesTotalnumberofagents N 0—∞

Numberofagentsonpatchk Nk 0—NNumberofalliesofi Mi 0—N

Numberofactivedefectorsini’salliance 𝑀!! 0—N

Numberofwillingpunishersini’salliance 𝑀!! 0—N

Thereare≥ 1willingpunishersini’salliance 𝑃(1) 0,1Thereare≥ 𝜏!willingpunishersini’salliance 𝑃(𝜏!) 0,1

Numberoffollowersofi Fi 0—N

4

The spatial landscape of the model is

definedasaw×wtoruscontainingw2patches.Ineach round, each patch k produces one resourceunit (productivity Lk = 1) with probability μk, andproducesnothing(Lk=0)withprobability1-μk.Thespatial distributionofmeanproductivityμk (equalto theprobabilityofproducinga resource ineachround) is taken as an exogenous characteristic ofecology.Thepresentanalysisemploysasetofninelandscapes, specified in terms of the spatialdistributionofμk(Figure2).Theselandscapeshavethe same overallmean productivity of patches𝜇,but different values for both the "patchiness" ofthe landscape (i.e. variance in productivity acrosspatches: var(μk)), and the extent to which

productivepatchesclustertogetherinspace(S).Togenerate these landscapes, the product of twoorthogonal sine waves (both with the samefrequencytunedbytheparameterS)wasraisedtoa power Φ (0 < Φ < 20), then renormalized toachieve the target values of 𝜇 and var(μk).Whilethe theory of economic defensibility emphasizesvariance in resourceproductionacrossbothspaceandtime,forsimplicity,thecurrentmodelfocusesonlyonspatialvariance;itsmainresults,however,can easily be re-interpreted in terms of temporalvariability (or predictability),with some importantdifferences discussed in Dyson-Hudson & Smith(1978).

S=0.1 S=0.2 S=1.0

var(μ k)=

0.005

var(μ k)=

0.030

var(μ k)=

0.055

Figure2.Nineecologiesdifferinginpatchiness,var(μk),andspatialclusteringofproductivepatches,S.Patchinessincreasesfromtoptobottom,whileclusteringincreasesfromlefttoright.Themeanproductivityofeachlandscape,mean(μk),isheldconstantat0.1.

5

StrategiesandinteractionThe landscape is seeded with a small

number of non-territorial agents, interpretable assingle individuals or family units. In each non-overlapping generation, agents interact overmultiple rounds (default = 25). In each round, inrandomorder,eachagentattempts tomoveontoan undefended patch, claim a defended patch, orstay in place, depending on its inherited strategytypesanddecisionvariables(Figure1andTable1).

Eachagentemployseitheranon-territorialstrategy (Ti = 0) or a territorial strategy (Ti = 1).Non-territorialagentsattempttomoveto(orstayon)anundefendedpatchwithintheirspatialreach(r) that yields the highest per capita productivity(Lk/Nk, where Nk is the number of agentsoccupyingpatchk).Non-territorialagentsarethusfacultatively nomadic, moving when productivitycan be improved, and staying when localproductivityremainshigh.

Territorial agents that have not claimed apatch first attempt to find an undefended patchwithin their spatial reach that has expectedproductivitygreaterthanorequaltotheirheritablecontest threshold (i.e 𝜇! ≥ 𝜇!!). If an acceptableundefended patch is available, they occupy andclaim the patch. If no acceptable patch is found,they attempt to find an already defended patchwithin their spatial reach forwhich𝜇! ≥ 𝜇!!. If anacceptablepatchisfound,theycontesttheexistingclaimant forownershipof thepatch.The strengthof an agent in contesting a patch 𝜎! depends onwhether it employs a solitary strategy (Ai = 0) oralliance-forming strategy (Ai = 1). The strength ofsolitaryagentscontestingpatchesisequalto1.Thestrengthofalliance-formingagentsisequaltothe1plus the number of alliance partners thatcooperateincontestingthepatch.

Priortoacontest,analliance-formingagenti that has fewer than 𝑀!

!"# alliance partnersattempts to recruit additional alliance partners.Non-hierarchicalagents(Hi=0)formallianceswithother non-hierarchical agents, while hierarchicalagents (Hi = 1) form alliances with hierarchicalagents. Alliance partnerships (i.e. edges in analliancenetworkorgraph)requirepairwisestabilityas defined in Jackson (2008). Thus, if there isalliance-formingagentjwithini’sspatialreachwho

is not already claiming a patch, has fewer than𝑀!!"#alliancepartners,andisabletofindapatchadjacenttothepatchtargetedbyithatisaboveitscontestthreshold𝜇!!,theniandjbecomelinkedinan offensive alliance. This process repeats until iattains 𝑀!

!"# alliance partners, or no furtherpartnerscanbefound.OnceiandtheirMialliancepartnershavetargetedasetofdefendedpatches,eachdefenderpthatformsalliancesandhasfewerthan𝑀!

!"#partnersattemptstorecruitadditionalpartners. New defensive alliance partners arerequired to occupy patches adjacent to p oranothermemberofp’salliance.

Once alliances have formed, a series of(1+Mi) contests are played out between theoffensive and defensive alliances, one for eachpatchtargetedbythemembersofi’salliance.Thestrength of i’s alliance σi is the sum of i’s owneffort and the effort of those alliance memberswho are cooperative either by heritable strategy(i.e. Ci = 1), or because their cooperation isenforcedbycoordinatedpunishersorahierarchicalleader. If 𝑀!

! is the number of active defectors(opportunistic defectorswhose cooperation is notenforced), then the strength of the alliance is𝜎! = 1+𝑀!−𝑀!

! . Cooperation within non-hierarchicalalliancescanbeenforcedbytheactionof coordinated punishers (forwhomPi= 1). As inBoydetal.(2010),acoordinatedpunisheriswillingtoexpendtheeffort toenforcecooperationwhenthereareat leastτ coordinatedpunisherspresentin the alliance, where τ is a heritable decisionvariableheldbythecoordinatedpunisher.Thecostof enforcing the cooperation of each of 𝑀!opportunistic defectors, cEMD, is divided evenlyamongthe𝑀!willingcoordinatedpunishersinthealliance(i.e.𝑐!𝑀! 𝑀!perpunisher).

Cooperation within hierarchical alliancescanbeenforced through theactionofa leader.Aleader is selected among those members of thehierarchical alliance who are willing to lead (forwhom Li = 1). Each potential leader offers aheritable per capita tax (tj, defined as a fixedamount rather than a fraction or rate), which isobservabletoalliancemembers.

6

Whichpotential leader is selecteddependsontheparameterdreflectingtheefficiencyoftheprocess that selects leaders within groups. Whenthis process is maximally efficient (d = 1), theleader isselectedthatoffersthe lowesttax;whend = 0, the leader is selected offering the highesttax; intermediate values of d select the leaderclosest to that quantile value (e.g.d = 0.5 selectstheleaderofferingthemediantax).Theparameterdcanbeinterpretedastheextenttowhichalliancemembers are able to select the most efficient orgenerous leaders through a low-cost, democraticprocess (or alternatively as the accuracy ofindividual’sperceptionsof the true tax rates).TheleaderreceivesataxtjpaidbyeachoftheFiothergroupmembers (followers), and pays a cost cEMDto enforce the cooperation of MD opportunisticdefectors in the alliance. If no members of ahierarchicalalliancearewillingtolead,theallianceoperates as a non-hierarchical alliance, in whichcooperation either remains unenforced or isenforcedthroughcoordinatedpunishment.

The probability that i is successful in acontestagainstpisdecidedbythecontest-successfunction 𝜎!! (𝜎!! + 𝜎!!) (Hirshleifer, 2001). Theexponent α in this expression represents thedecisiveness of alliances in determining theoutcomeofcontests.Whenα isgreater,theslopeof the S-shape curve around the inflection point(where the two alliances are of equal strength) issteeper, reflecting more of a winner-take-allenvironment. α thus reflects how important therelative size of the alliance is for determining theoutcome of the conflict. If the offensive agent issuccessful, ittakesexclusiveclaimofandoccupiesthepatch,whilethedefensiveagentisejectedtoarandomly chosen undefended patch. If thedefensive agent is successful, neither move.Membersofanoffensivealliancethatsuccessfullyclaims new patches remain linked as allies oncetheyhavesettledontheirnewterritory.Membersofdefensivealliancesthatarenotejectedfromthepatches they claim also remain linked as alliesfollowingthecontest.

At the end of each round, the resourcesproducedbyeachpatcharedividedequallyamongand its occupants and added to their cumulativelifetime fitness. The per-round contribution tofitnessof individual i occupyingpatchk (equation1) is thus equal to the per capita productivity ofpatchk (1st term:𝐿!/𝑁!)minus thecostsof theirstrategy- and context-dependent behavior: thecostsofmaintainingalliances(2ndterm:𝑐!𝑀!);thecost of cooperating to defend territory, whetherdictatedbystrategyorstimulatedbyenforcement(3rd term: 𝑐!max 𝐶! ,𝐻! ,𝑃(1) ); the coordinatedpunisher’s cost of enforcing the cooperation ofeach opportunistic defector (4th term:𝑐!𝑃(𝜏!)𝑀!

! 𝑀!!);andthehierarchicalagent’scost

ofbeingtaxed(5th term:𝑡!𝐻!).Hierarchicalagentsthat enforce cooperation as leaders also receivethe benefit of taxation minus the cost ofenforcement for each of Fi followers (6thterm: (𝑡! − 𝑐!𝑀!

! 𝑀!)𝐹!). The individual’s per-round contribution to fitness wi is defined byEquation(1):

ReproductionAfter a generation has interacted through

multiple rounds, each agent’s fitness Wi iscalculated as the mean of their contributions tofitnessacrossroundsmultipliedbyB,acoefficientaffecting the intrinsic rate of increase:𝑊! = 𝐵𝑤!.Eachagentproducesawholenumberofoffspringequal to the integer part ofWi, and produces anadditional offspring with probability equal to thefractional part of Wi. Offspring are distributedrandomlyon the landscape.Offspring inherit theirparent’s strategies anddecision variables,with anindependent probability of mutation (default =0.01) for each variable. Mutations of strategyvariablesswitchbetween0and1;mutationsofthecontest threshold 𝜇!! and tax offered as leader tiincreaseordecreaseby0.01withequalprobability;andmutationsofthemaximumalliancesize𝑀!

!"#

and the coordinated punisher’s coordinationthreshold τi increase or decrease by 1. The oldergenerationdies,territorialclaimsandalliancesarereset,andthenewgenerationbeginsinround1.

𝑤! = 𝐿! 𝑁!⁄ − 𝑐!𝑀! − 𝑐!max !𝐶! ,𝐻!,𝑃!(1)! − 𝑃!(𝜏!)𝑐!𝑀!! 𝑀!

!⁄ − 𝑡!𝐻! + !𝑡! − 𝑐!𝑀!! 𝑀!⁄ !𝐹! (1)

7

SamplingandanalysisThe analyses of the simulation in the

following section characterize the effects ofdifferent socioecological parameters on theprinciple outcomes of the model, as they evolvethrough time (Figure3)andaftera longperiodofevolution(Table4).

To produce the historical trajectoriesplotted in Figure 3, five runs of 250 generationsplaying25roundspergenerationweresimulatedineach of three contrasting socioecologies: (A) anecology with low landscape patchiness, low costsof cooperation and enforcement, and efficientpolitical institutions; (B) an ecology with highlandscape patchiness, high costs of cooperationand enforcement, and inefficient politicalinstitutions;and(C)anecologywithhighlandscapepatchiness, low costs of cooperation andenforcement, and efficient political institutions.Local polynomial regression was used tocharacterize themean frequency of each strategyandgroupsizeasafunctionoftime(usingtheloessfunctioninR;RDevelopmentCoreTeam2008).

For the statistical analysis of long-runoutcomessummarized inTable4,200runsof250generationsplaying25roundspergenerationwereparameterized by randomly sampling theparameter values given in Table 2. For eachparameter (with the exception of landscapepatchiness)oneof threevalueswas sampledwithequal probability. For the landscape patchiness,var(μk),thehigh-varianceconditionwassampledat

twice the rate of the medium- and low-varianceconditions, to better explore subtleties in theconditionsunderlyingtheformationofcompetitivealliances and hierarchies. Long-run strategyfrequencies and mean alliance sizes wereestimated as a function of socioecologicalparameters in a multi-level, mixed-effectsregression using the lmer function in the lme4packageinR(Batesetal.2013).Thesamplefortheregressionincludesoneobservationforeachofthelast 100 generations of each run, with a randomeffect term to capture the non-independence ofoutcomes within each run. Inequality—measuredbytheginicoefficientoffitness,gini(W),inthelastgenerationof each run (using the reldist package;Handcock 2015)—was estimated as a function ofsocioecologicalparametersusingthelmfunction.

The models includes main effects for thelow-, medium-, and high-patchiness conditions,andthe interactionof theseconditionswithotherkeysocioecologicalparameters:thedecisivenessofalliances in determining contests α; the cost ofallies cA; the cost of cooperation cC; the cost ofenforcing cooperation cE; and the efficiency ofpolitical processes selecting leaders d. Thecontinuous predictor and response variables(exceptforthegini)werenormalizedtohavemean0 and standard deviation 1. The reportedstandardized regression coefficients (βs) thusindicate a change of β standard deviations in theresponse variable with an increase of 1 standarddeviationinthepredictorvariable.

III.Results

The effects of social and ecologicalparameters on the population dynamics of non-territorial and territorial agents are illustratedacrosspanelsA,BandCinFigure3.EnvironmentAis characterized by a relatively homogeneousdistribution of productivity across the landscape(the landscape in the 1st row, middle column ofFigure 2). In this environment, non-territorialagents retain the advantage over territorialstrategies,maintaininga long-runmeanofaround2/3rdofthepopulation.

EnvironmentBismarkedbyahighlypatchydistributionofresourcesacrossthelandscape(thelandscape in the3rd row,middlecolumnofFigure2).Despitethe initialnon-territorialstartingpoint,mutant territorial strategies quickly come todominate the population. Because this is anenvironment with relatively high costs ofcooperation and enforcement and inefficientselection of leaders, however, non-hierarchicalterritorial strategies win out over hierarchicalagents.

8

Figure3.Engineofhistory.Meanfrequencies(toprow)andalliancesizes(bottomrow)ofnon-territorial,solitaryterritorial,non-hierarchicalalliance-forming,andhierarchicalstrategiesthroughtime.Panel(A):Anenvironmentwithlowvarianceinlandproductivity(var(μk)=0.005,cC=0.05,cE=0.05,d=1).Panel(B):Anenvironmentwithhighvarianceinlandproductivity,buthighcostsofhierarchy(var(μk)=0.055,cC=0.35,cE=0.35,d=0).Panel(C):Anenvironmentwithhighvarianceinlandproductivityandrelativelylowcostsofhierarchy(var(μk)=0.055,cC=0.05,cE=0.05,d=1).Forallruns,S=0.2,α=4,cA=0.05,andr=0.36.Eachlineshowsalocalpolynomialregressionfitover5runswithloesssmoothingparameter0.3.

Environment C has the same patchylandscape as B, but with relatively lower costs ofcooperation and enforcement, andmore efficientselectionof leaders.Aftertheinitialestablishmentof territorial and alliance-forming strategies,hierarchical territorial agents come to dominatethe landscape.Other territorial andnon-territorialstrategies aremaintained in theminority throughfrequency-dependentselection.

The relationship between alliance size andstrategyfrequenciesacrossecologiesisobservablein the bottom panels of Figure 3. Three mainfeatures of these trajectories are important. First,there is a tendency in all three ecologies for thesize of alliances between territorial agents to firstincrease through time, then level off in dynamicequilibrium. Second, the long-run size of alliances

varies across ecologies, with mean group sizesincreasing from ecology A to B to C. Third, hier-archical strategies consistently maintain largeralliances that non-hierarchical alliance-formingstrategies.Theextentofthisdifference,moreover,increasesunderconditionsfavorableforhierarchy.

The statistical analysis in Table 4 indicatesthat the effects of social parameters (the costs ofalliances, cooperation, and enforcement, and thedecisiveness of alliances) on sociopoliticaloutcomes depend crucially on the underlyingdegree of patchiness. In landscapes with greaterpatchiness, therearenegativeeffectsof the costsofalliance formationandthecostsofcooperationon the frequency of territorial, alliance-forming,and hierarchical strategies. These effects areabsentormutedinlandscapeswithlowpatchiness.

0 50 100 150 200 250

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

(A)

Proportions

Hierarchical

Non-territorial

Non-hierarchicalallied

Solitaryterritorial

0 50 100 150 200 250

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

(B)

Proportions

Hierarchical

Non-territorial

Non-hier.allied

Solitaryterritorial

0 50 100 150 200 250

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

(C)

Proportions

Hierarchical

Non-territorial

Non-hier.allied

Solitaryterritorial

0 50 100 150 200 250

01

23

45

6

Generations

Alli

ance

siz

e

Hierarchical

MeanNon-hier.

allied territorial

Solitary territorial

0 50 100 150 200 250

01

23

45

6

Generations

Alli

ance

siz

e Hierarchical

Mean

Non-hier. allied

Solitary territorial

0 50 100 150 200 250

01

23

45

6

Generations

Alli

ance

siz

e

Hierarchical

Mean

Non-hier. allied

Solitary territorial

9

Table4.Predictedeffectsofsocioecologyonstrategyfrequencies,alliancesize,andinequalitygivenlow,medium,andhighpatchiness. Strategyfrequencies Mean Ineq-Landscapepatchiness Non-terr-

itorialTerr-itorial

Alliance-forming

Coop-erative

Coordin’dpunisher

β

Hier-archical

alliancesize

ualitygini(W)

var(μk) Parameter β β β β β β β

Low

(Intercept) - 1.35*** -1.35*** -0.06 0.43*** 0.97*** -0.22* -0.57*** 0.10***Decisivenessofalliances log(α) -0.02 0.02 0.05 0.03 0.13 0.03 -0.06 0.01

Costofally cA -0.07 . 0.07 . 0.02 -0.01 0.10 0.02 -0.05 0.01 Costofcooperation cC -0.10* 0.10* 0.05 0.10 0.13 0.04 -0.05 0.01 Costofenforcement cE -0.05 0.05 0.04 -0.02 0.06 0.01 -0.03 0.01

Effic.ofpoliticalprocess d 0.06 -0.06 -0.07 -0.13 -0.33* -0.03 0.09 0.00

Medium

(Intercept) - -0.27*** 0.27*** -0.15 -0.43*** -0.20 -0.02 0.10 0.23***Decisivenessofalliances log(α) -0.01 0.01 0.16 . 0.03 0.08 0.23* 0.20* 0.01

Costofally cA -0.03 0.03 -0.73*** -0.04 -0.22 . -0.27* -0.54*** -0.02 Costofcooperation cC -0.04 0.04 -0.40*** -0.09 0.03 -0.69*** -0.49*** -0.01 Costofenforcement cE -0.04 0.04 0.06 0.01 -0.04 0.04 0.03 0.01

Effic.ofpoliticalprocess d -0.03 0.03 -0.07 0.02 -0.02 0.05 0.00 0.01

High

(Intercept) - -0.72*** 0.72*** 0.26*** -0.36*** -0.16 . 0.32*** 0.44*** 0.33***Decisivenessofalliances log(α) 0.01 -0.01 0.18** 0.07 0.01 0.28*** 0.13 . 0.06***

Costofally cA -0.10** 0.10** -0.82*** -0.04 -0.24** -0.45*** -0.75*** -0.03*Costofcooperation cC -0.06* 0.06* -0.29*** -0.16** -0.06 -0.69*** -0.21** -0.05***Costofenforcement cE -0.04 0.04 -0.13 . 0.00 -0.01 -0.13 . -0.16* -0.05***

Effic.ofpoliticalprocess d -0.02 0.02 0.00 0.01 0.02 0.13 . 0.02 0.01 Notes:n=20,000generationsin200runsforeachmodel(withrandomeffectsforrun),exceptforinequality,wheren=200runs(withoutrandomeffects).***p<0.001;**p<0.01;*p<0.05;.p<0.1.

In patchier environments, the decisivenessof alliances drives higher frequencies of alliance-formingandhierarchical strategies. Inverypatchylandscapes, therearenegativeeffectsof thecostsof enforcement on alliance-forming andhierarchical strategies, and positive effects of theefficiency of political processes in hierarchicalgroups on the frequency of hierarchicalpreferences.

Table 4 confirms the previous insight thatthe long-run size of alliances increases withlandscape patchiness. Social and ecological para-meters interact to determine alliance size: inpatchierenvironments,alliancesizeincreaseswithgreater decisiveness of alliances, and decreaseswith the costs of alliance formation, cooperation,andenforcement.Theresultsconfirmthatalliancesgrowtolargerscaleswhenthebenefits(intermsofaccess to land) are high, and the social costs ofallianceformationarenotprohibitive.Atverylargescales, hierarchical alliances outcompete non-hierarchical alliances due to their efficiency inorganizing for collective action in territorialcompetition.

Relationships between socioecology andinequality (represented as the gini coefficient offitness)aregiveninthefinalright-handcolumnofTable4.Liketerritorialityandhierarchy, inequalityincreaseswith patchier distributions of resources.In thepatchiestenvironments, inequalitydependson those parameters underlying territoriality,alliance-formation, and hierarchy: highdecisiveness of alliances and low costs ofcooperationandenforcement.

Inequalityisinextricablylinkedtohierarchyacross the worlds simulated in this model. Whilehierarchicalinstitutionsgrowinthecontextofhighpatchiness and inequality, they also amplifyinequalities. In this simulation,hierarchy increasestheginibyroughly50%,ontopofthedirecteffectsof patchiness and territoriality. Thiswould not bethe case if members of hierarchies could alwayschoose the most efficient leaders at zero cost(Hooperetal.2010).

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IV.Conclusions

The ecological and social dynamics thatdrivethismodelmaybefundamentaltothehistoryofsocialhierarchyinourspecies.Themodelshowsthat hierarchy and inequality develop regularly inecologies that favor the formation of coalitions todefendandcontestresources.

Hierarchies for competition over resourcesare particularly likely where egalitarian means ofpromotingcooperationincoalitionsareineffectual,and hierarchies are not unbearably costly.Hierarchies becomemore costly when individualsare restricted in their ability to choose efficientleaders (and othermembers of the hierarchy). Inthe real world as in the model, hierarchicalinstitutions that are inefficient relative to otherfeasiblesocialarrangementsoftenfaceoverthrow,reform,orextinction.Thecostofthesetransitions,however, allows persistence of the kind ofoppressive hierarchies observed countless timesthroughouthistory.

The model illustrates the interaction ofecologicalandsocialdynamicsintwosenses.First,the analysis shows the statistical interactionbetweenecology—intermsofthevarianceoflandproductivity—and other socioecological para-meters, suchas thecostofsocial interactionsandthedecisivenessofcontests(Table4).Second,theendogenous social dynamics are the verymechanismbywhichtheeffectsoftheexogenousecological parameters are manifest through time(Figure 3); conversely, the effects of the socialdynamics necessarily depend on the presence offavorable socioecological conditions. Thus, neithernatural ecology nor social behavior alone issufficienttoexplainthecentralresultofthemodel:the emergence of norms and institutions forcollective action, including hierarchy, in thepresence of concentrated and predictableresources.

We have employed a definition ofsocioecology as the relationship between anorganism and its natural, constructed, and socialenvironments (Steward 1955, Winterhalder &Smith 2000, Odling-Smee et al. 2003, Kappeler etal. 2003). Technologies of production andcompetition therefore play important roles indrivingtransitionsandshapingdynamicequilibria.

A shift to reliance on high-qualityagricultural land in the Holocene is likely to haveincreasedtheeffectivevariance(patchiness)intheproductivity of sites, increasing territoriality,alliance formation, and hierarchical territorialalliances. In other words, intensive agriculturetransformed the economic value of territorialresources, and created the crucible that producedthe chiefdoms and states characteristic of themiddle and later Holocene. Sedentism and higherpopulation densities may have also reduced thecosts of alliance formation, enforcement, andcooperation in ways that reinforced theseoutcomes. Mobile foragers relying on widely orunpredictably distributed plant and animalresources,ontheotherhand,havebeenlesslikelyto go down this road to increasing sociopoliticalcomplexity.

The dynamics and outcomes this modelbearanalogywiththedepictionsofLeach’s(1973)Political Systems of Highland Burma and Scott’s(2010) The Art of Not Being Governed. In light ofthe empirical patterns they describe in SoutheastAsia, the threeenvironments in Figure3 couldbestylistically interpreted as: (A) inter-riverine foresttracts utilized by relatively egalitarian andacephalous foragers and farmers; (B) highlandvalleys suitable for shifting cultivation andagriculture inhabited by a mix of anarchic andhierarchical communities; and (C) productivealluvial valleys dominated by intensive agricultureandlarge-scalehierarchicalpolities.

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In the Mississippian southeast, fortified

villages cultivated crops on well-drained, sandyloam soils that were regularly renewed byinundation.Hudson(1976)proposedthatoncethebest riverine soils came under cultivation,communities became environmentally circum-scribedandjoinedtogether“beneaththemantleofachiefpowerfulenoughtoeffectharmony…[and]to stand more strongly against mutual outsidefoes”. The scale of integration and extent ofsociopolitical complexity appears to have waxedandwanedwiththeproductivityandspatialextentofcontiguousarableland(Munozetal.2015).

The development of the Northwest Coasthierarchical complex appears to have requiredmillennia (Ames 1994,Matson&Coupland 1994),suggestingrelativelyslowratesofaccumulationoftheculturaltraitsrequiredforthedevelopmentofcoherent hierarchies. Rapid social transitionsfollowing the introduction of new resources,technologies,or culturalmodels arealso commonin distant and recent history. Small-scalecommunities confronted by colonization and

acculturationinthelasthalfmillenniumhaveoftenmoved toward more hierarchical and unequalsocialstructures(Steward1938,Hämäläinen2009),and subordination to imperial or nationalhierarchies (Lee and Daly 2004; Hooper et al.2014).

Contrary examples of reductions inhierarchy are also well documented (Currie et al.2010, Scott 2010). Contemporary groups such asthe Sungusungu of East Africa and the Kuna ofPanama appear to gain from the complement-arities between hierarchical organization andpracticesthatlimittheabilityofleaderstoadvancepersonalgainovercommunityinterests(Paciotti&Borgerhoff Mulder 2004, Howe 2002, Kim Hill,personalcommunication).Thetheorypredictsthathierarchical institutions provide the greatestbenefitsfortheirconstituentswhentheyco-evolvewith behaviors limiting their power and cost(Bowles 2012). Hierarchical institutions areconstrained and can be replaced when lesshierarchical forms of organization efficientlyprovidethesamefunctions.

ReferencesKennethM.Ames(1994)"TheNorthwestCoast:Complexhunter-gatherers,ecology,andsocialevolution."AnnualReviewofAnthropology,209-229.DouglasBates,MartinMaechler,BenBolker,&StevenWalker(2013)"lme4:Linearmixed-effectsmodelsusingEigenandS4."Rpackageversion1.1-8.ChristopherBoehm(2001).HierarchyintheForest:TheEvolutionofEgalitarianBehavior.Cambridge:HarvardUniversityPress.JamesL.Boone(1992)“Competition,conflict,andthedevelopmentofsocialhierarchies.”InEvolutionaryEcologyandHumanBehavior,E.A.SmithandB.Winterhalder,Eds.Hawthorne,NY:AldinedeGruyter.SamuelBowles(2012)“Pirates,potlatches,andproto-states:Theco-evolutionofleadershipandsolidaritypriortotheemergenceofstates.”WorkingPaper,SantaFeInstitute,SantaFe.

RobertBoyd,HerbertGintis,&SamuelBowles(2010)"Coordinatedpunishmentofdefectorssustainscooperationandcanproliferatewhenrare."Science328.5978:617-620.JerramL.Brown(1964)“Theevolutionofdiversityinavianterritorialsystems.”WilsonBulletin76:160-169.ThomasE.Currie,SimonJ.Greenhill,RussellD.Gray,ToshikazuHasegawa,&RuthMace(2010)"RiseandfallofpoliticalcomplexityinislandSouth-EastAsiaandthePacific."Nature467(7317):801-804.RichardB.Lee&RichardDaly(2004)TheCambridgeEncyclopediaofHuntersandGatherers.Cambridge:CambridgeUniversityPress.RadaDyson-Hudson&EricAldenSmith(1978)“Humanterritoriality:Anecologicalreassessment.”AmericanAnthropologist73:77-95.HerbertGintis(2000)GameTheoryEvolvingPrinceton:PrincetonUniversityPress.

12

ErnaGunther(1972)IndianlifeontheNorthwestcoastofNorthAmericaasseenbytheearlyexplorersandfurtradersduringthelastdecadesoftheeighteenthcentury.Chicago:UniversityofChicagoPress.PekkaHämäläinen(2009)TheComancheEmpire.NewHaven:YaleUniversityPress.MarkS.Handcock(2015)“reldist:Relativedistributionmethods”RPackageVersion1.6-4.PaulL.Hooper,HillardS.Kaplan&JamesL.Boone(2010)"Atheoryofleadershipinhumancooperativegroups."JournalofTheoreticalBiology265(4):633-646.PaulL.Hooper,MichaelGurven&HillardS.Kaplan(2014)“Socialandeconomicunderpinningsofhumanbiodemography.”InSociality,Hierarchy,Health:ComparativeBiodemography.M.WeinsteinandM.A.Lane,Eds.Washington,D.C.:NationalAcademies.169-196.JamesHowe(2002)TheKunaGathering:ContemporaryVillagePoliticsinPanama,2ndEd.Tucson:FenestraBooks.CharlesHudson(1976)TheSoutheasternIndians.Knoxville:UniversityofTennesseePress.MatthewO.Jackson(2008)SocialandEconomicNetworks.Princeton:PrincetonUniversityPress.PeterM.Kappeler,MichaelE.Pereira&CarelP.vanSchaik(2003)“Primatelifehistoriesandsocioecology”InPrimateLifeHistoriesandSocioecology,P.M.KappelerandM.E.Pereira,Eds.Chicago:UniversityofChicagoPress.1-20.DouglasJ.Kennett(2005).TheIslandChumashBerkeley:UniversityofCaliforniaPress.EdmundR.Leach(1973)PoliticalSystemsofHighlandBurma.London:AthlonePress.RichardGhiaMatson&GaryCoupland(1994)ThePrehistoryoftheNorthwestCoast.WalnutCreek:LeftCoastPress.JohnMaynardSmith&GeorgeR.Price(1973)"Thelogicofanimalconflict."Nature246.RichardMcElreath&RobertBoyd(2008)MathematicalModelsofSocialEvolution.Chicago:UniversityofChicagoPress.SamuelE.Munoz,KristineE.Gruley,AshtinMassie,DavidA.Fike,SisselSchroeder&JohnW.Williams(2015)“Cahokia’semergenceanddeclinecoincidedwithshiftsoffloodfrequencyontheMississippiRiver.”ProceedingsoftheNationalAcademyofSciences112(20):6319-6324.

JohnF.Odling-Smee,KevinN.Laland,&MarcusW.Feldman.NicheConstruction:TheNeglectedProcessinEvolution.Princeton:PrincetonUniversityPress,2003.BrianPaciotti&MoniqueBorgerhoffMulder(2004)"Sungusungu:TheroleofpreexistingandevolvingsocialinstitutionsamongTanzanianvigilanteorganizations."HumanOrganization63(1):112-124.RDevelopmentCoreTeam(2008)“R:Alanguageandenvironmentforstatisticalcomputing.”Vienna:RFoundationforStatisticalComputing.TorbenC.Rick,JonM.Erlandson,RenéL.Vellanoweth&ToddJ.Braje(2005)"FromPleistocenemarinerstocomplexhunter-gatherers:ThearchaeologyoftheCaliforniaChannelIslands."JournalofWorldPrehistory19(3):169-228.JamesC.Scott(2010)TheArtofNotBeingGoverned:AnAnarchistHistoryofUplandSoutheastAsia.NewHaven:YaleUniversityPress.EricAldenSmith&Jung-KyooChoi(2007)“Theemergenceofinequalityinsmall-scalesocieties:Simplescenariosandagent-basedsimulations”InTheModel-BasedArchaeologyofSocio-NaturalSystems.S.vanderLeeuwandT.Kohler,Eds.SantaFe:SARPress.EricAldenSmith,KimHill,FrankMarlowe,DavidNolin,PollyWiessner,MichaelGurven,SamuelBowles,MoniqueBorgerhoffMulder,TomHertz&AdrianBell(2010)"Wealthtransmissionandinequalityamonghunter-gatherers."CurrentAnthropology51,19-33.JulianH.Steward(1938)Basin-PlateauAboriginalSociopoliticalGroups.Washington,D.C.:BureauofAmericanEthnologyBulletin120.JulianH.Steward(1955)“Theconceptandmethodofculturalecology”InTheTheoryofCultureChange:TheMethodologyofMultilinearEvolution.J.H.Steward,Ed.Urbana:UniversityofIllinoisPress.30-42.BruceG.Trigger(2003).UnderstandingEarlyCivilizations:AComparativeStudy.Cambridge:CambridgeUniversityPress.UriWilensky(1999).“NetLogo.”Evanston:CenterforConnectedLearningandComputer-BasedModeling,NorthwesternUniversity.BruceWinterhalder&EricAldenSmith(2000)“Analyzingadaptivestrategies:HumanBehavioralEcologyattwenty-five.”EvolutionaryAnthropology9(2):51-72.

Acknowledgements:Thisworkwasmadepossiblebygrantno.15705,“ThePrinciplesofComplexity:RevealingtheHiddenSourcesofOrderamongtheProdigiesofNatureandCulture”,totheSantaFeInstitutefromtheJohnTempletonFoundation.