On Modeling Cognition and Culture · ON MODELING COGNITION AND CULTURE 91 (or ‘ cognitive tracks’ or ‘ triggered representations) and to reject the use of discrete-representations

On Modeling Cognition andCulture

Why cultural evolution does not require replication ofrepresentations

JOSEPH HENRICHcurren and ROBERT BOYDcurrencurren

ABSTRACT

Formal models of cultural evolution analyze how cognitive processes combine withsocial interaction to generate the distributions and dynamics of lsquorepresentationsrsquo Recentlycognitive anthropologists have criticized such models They make three points mentalrepresentations are non-discrete cultural transmission is highly inaccurate and mentalrepresentations are not replicated but rather are lsquoreconstructedrsquo through an inferentialprocess that is strongly affected by cognitive lsquoattractorsrsquo They argue that it follows fromthese three claims that 1) models that assume replication or replicators are inappropriate2) selective cultural learning cannot account for stable traditions and 3) selective culturallearning cannot generate cumulative adaptation

Here we use three formal models to show that even if the premises of this critique arecorrect the deductions that have been drawn from them are false In the rst modelwe assume continuously varying representations under the in uence of weak selectivetransmission and strong attractors We show that if the attractors are suf ciently strongrelative to selective forces the continuous representation model reduces to the standarddiscrete-trait replicator model and the weak selective component determines the nalequilibrium of the system In the second model we assume inaccurate replication anddiscrete traits We show that very low delity replication of representations at the individuallevel does not preclude accurate replication at the population level and therefore accurateindividual-level replication of representations is not necessary for either cultural inertiaor cumulative cultural adaptation In the third model we derive plausible conditions forcumulative adaptive evolution assuming continuous cultural representations incompletetransmission and substantial inferential transformations

currenDept of Anthropology Emory University AtlantacurrencurrenDept of Anthropology University of California Los Angeles

cdeg Koninklijke Brill NV Leiden 2002 Journal of Cognition and Culture 22

88 JOSEPH HENRICH AND ROBERT BOYD

Introduction

Formal models of cultural evolution (eg Boyd amp Richerson 1985) providean important tool for understanding cultural phenomena Culture is shapedby both psychological processes that determine how people think andfeel and social processes that determine how people interact whetherthey succeed or fail and if they live or die Formal cultural evolutionarymodels can combine cognitive and affective processes with patterns ofsocial interaction to generate explicit predictions about the distributionsand dynamics of lsquorepresentationsrsquo mdash ideas beliefs schemas or mentalmodels With such predictions empirical data on behavior and beliefs frompopulations can be used to select among alternative models or among thecognitive and social components of these models in a manner that informsour understanding of cognition and connects laboratory experiments withreal life (eg Henrich 2001)

Recently Sperber (1996) Atran (2001 2002) and Boyer (1994 1999)have argued that these ldquoNeo-Darwinianrdquo models1 are inappropriate forstudying cultural evolution because they are ldquobased on a serious distortionof the relevant factsrdquo (Sperber 1996118) They identify three interrelatedproblems with such approaches First cultural transmission processes areusually incomplete and imperfect so unlike genetic systems accuratereplication rarely occurs Replication is the exception rather than therule Second unlike DNA replication inferential processes ldquotransformrdquothese representations during their transmission and reconstruction Thissuggests that mutation-like processes are much more important than selection-like processes in shaping cultural variation Third unlike genes culturalrepresentations are rarely discrete units suggesting that the idea ofa lsquoreplicatorrsquo (or meme) makes little sense for most types of culturalrepresentations2

1These scholars use the term ldquoNeo-Darwinianrdquo for such models even when theyare explicitly derived from disease epidemiology (Cavalli-Sforza amp Feldman 198146-53)learning theory (see Boyd amp Richerson 1985 Chapter 4) or cognitive psychology (Lumsdenamp Wilson 1981)

2While such characterizations apply to the informal theorizing of memeticists (egDawkins 1982 Dennett 1995 or Blackmore 1999) they are wide of the mark for muchformal cultural theory Boyd and Richerson (BR 198575) explain that there is no need toassume particulate ldquounitsrdquo in order to build evolutionary models (BR 198570-75) and 19 of

ON MODELING COGNITION AND CULTURE 89

Building on these three points these authors have claimed Firstbecause representations are non-discrete using replicators and replicatordynamics is entirely inappropriate for culture systems (Sperber 1996101-103 Atran 2002 Chapter 8 2001) Second because of the highlevels of inaccuracy and the incompleteness selective cultural transmissionitself does not lead automatically to lsquocultural inertiarsquo mdash the existenceof social groups in which individuals share a set of relatively stablerepresentations (Sperber 1996 118) From this Sperber (1996 Chapter 5)further asserts that inferential transformations create lsquostrong cognitiveattractorsrsquo that swamp any in uence from the selective components ofcultural evolutionary processes3 Such attractors create powerful forcesthat overwhelm the weaker effects of selective processes and thereforeit is argued selective processes do not usually generate adaptive culturalevolution

Whether social learning is low delity non-discrete and stronglyaffected by cognitive transformations are empirical matters although itis plausible that Atran and Sperber are correct for a wide range of culturaldomains However the deductions they make from these assumptionsare matters of logic and here we use three mathematical models to

the 38 models presented in their book are continuous (non-discrete) trait models that allowfor an arbitrary amount of transmission error Similarly Cavalli-Sforza and Feldman (CSF1981) devote one of their ve chapters entirely to continuous trait models These continuousmodels allow for substantial error and other forms of non-replication BR also explicitlydistinguish public representations from mental representations (though using differentterminology) throughout their book and repeatedly specify the inferential transformationbetween observed behavior and representation formed For example in describing onemodel they write ldquoThe offspring uses each modelrsquos actual behavior [public representation]to estimate [make inferences about] his or her cultural variant [mental representation]rdquo(198575-79) They also make explicit reference to much research in psychology on thenature of social learning After a review of the psychological literature especially Bandurarsquoswork on social learning they specify the following pathway Modeled events AttentionProcesses Retention Processes Motor Reproduction Motivation Processes Matching Of the 396 references 101 were by psychologists or published in psychologyjournals Chapters 4 and 5 discuss how cognitive structures mdash what Sperber (1996) wouldlater call ldquoattractorsrdquo mdash bias cultural change so that some outcomes are more likely thanothers and even use some of the same examples as Boyer (1999)

3Atran (2001) refers to attractors as ldquocognitive elicitorsrdquo Boyer (1999) speaks ofldquotriggered representationsrdquo arguing that these channel cultural evolution onto ldquocognitivetracksrdquo


show that these deductions do not follow from their assumptions In the rst model we assume continuously varying representations under thein uence of weak selective transmission and strong attractors We showthat if the attractors are suf ciently strong relative to selective forcesthe continuous representation model reduces to the standard discrete-traitreplicator model and the weak selective component determines the nalequilibrium of the system In the second model we assume representationsare discrete but that replication is very inaccurate We show that verylow delity replication of representations at the individual level doesnot preclude accurate replication at the population level and thereforeaccurate individual-level replication of representations is not necessary forselective forces to generate either cultural inertia or cumulative culturaladaptation In the third model we assume continuous (non-discrete)cultural representations incomplete transmission and substantial inferentialtransformations Despite these assumptions the model shows that adaptivecultural evolution is likely in empirically plausible conditions mdash predictionsderived from this model have been tested elsewhere using ethnographicdata (Henrich 2002)

Model 1 Strong attractors give rise to discrete replicators

Formal models of cultural evolution have made use of both continuous anddiscrete representations of cultural variation depending on the situationSperber Atran and Boyer reject the use of discrete-representation modelsAt the same time they emphasize the role of intra-individual cognitivetransformations of representations (lsquostrong attractorsrsquo) and argue thatby comparison selective cultural processes have little or no effect onthe epidemiology of representations (eg Sperber 1996 Chapter 5)In this section we analyze a simple model that assumes continuousrepresentations strong attractors and weak selective forces We show thatthis model reduces to discrete-representation replicator-dynamics in whichthe weak selective forces determine the ultimate outcome The strongerthe cognitive attractors are relative to the selective transmission forcesthe better is the discrete-replicator approximation Therefore assumingthat human cognition gives rise to more than one attractor per domainit is inconsistent to simultaneously advance the idea of strong attractors


(or lsquocognitive tracksrsquo or lsquotriggered representations) and to reject the use ofdiscrete-representations in models

Here we study the evolution of the distribution of mental representa-tions in a population We assume that each individualrsquos mental represen-tation in this domain is a single real number x between zero and 14

Individuals holding different representations (ie different values of x) be-have differently on-average or in Sperberrsquos terminology generate differentldquopublic representationsrdquo During each time period people in the popula-tion observe the behavior of another individual infer the mental represen-tation of the model from his or her behavior and adopt this inference astheir own representation5 Following Sperber cognitive lsquoattractorsrsquo stronglybias the inferential process that underlies social learning mdash an individualwhose model has a representation x on average infers a representationthat is nearer to one of two attractors In particular we assume that the at-tractors are x D 0 and x D 1 and that an individual who observes a modelwith representation x infers a representation x C 1x where 1x lt 0 forx lt m and 1x gt 0 for x gt m We assume that 1x has the form shownin Figure 1

The following example illustrates how domain speci c cognition mightcreate multiple attractors Suppose individuals at Attractor-0 x D 0

perceive the Moon as a self-aware conscious entity with goals emotionsand motivations mdash thus the Moonrsquos behavior can be understood using folkpsychology (Leslie 1994) This means that the quantity (1 iexcl x) tells us thedegree to which an individual attributes the Moonrsquos shape color positionand movements to underlying goals emotions or motivations or to whatdegree the Moonrsquos goal-driven actions in uence events and individualssuch as weather tides personal moods werewolves etc In contrastindividuals with x D 1 (those at Attractor-1) see the Moon as simplya big rock lacking goals consciousness and emotions These individualsattribute the Moonrsquos color shape and movement to the effects of non-agentic interactions with light and other mindless bodies governed byphysical laws that operate throughout the Universe Any effects the Moon

4We restrict the x to [0 1] only for simplicity of exposition Representations that variedover other ranges or multidimensional variable produce the same basic result

5For the moment we do not allow individuals to observe a sample models and makeuse of the pattern of observed behavior in the sample We return to this question below


Figure 1 Graphical representation of the assumptions in Model 1 A learnerwho observes a model with representation x infers a representation x C 1xwhere 1x D iexclmacr0x if x lt m and 1x D macr11 iexcl x if x gt m This creates a strongforce that shifts representations in the population toward attractors at 0 and 1The probability that an individual is chosen as a model is 1 C sx This selectivetransmission process creates a weak force that increases the frequency of larger

values of x in the population

has on things such as tides moods and calendars are merely unintentionalconsequences of the moonrsquos mass and movement Now it is possible toimagine Moon-concepts that mix these poles (1 gt x gt 0) One couldbelieve for example that the moonrsquos movement and shape are out of itscontrol (governed by physical laws) while its color or hue expresses itsmood which in turn in uences the weather Or perhaps the Moonrsquos coloris 23 controlled by its emotions and 77 controlled by the laws of lightrefraction One might also believe that on Tuesdays and Thursdays theMoon is a goal-oriented agent on Mondays Wednesdays and Fridays theMoon is a big rock and on the weekends these two alternate minuteby minute Such beliefs might seem odd to us because they violateintuitive expectations and would consequently be transformed by cognitiveattractors In contrast x D 1 or 0 are ldquoeasier to thinkrdquo To capturethis example in a formal model the underlying mental representationsx would likely need to be a multi-dimensional vector and the analysisrepresented below could be easily adapted to such representations mdash none


of the qualitative ndings would change However to keep the presentationtractable we will limit our analysis to one-dimensional x variables

A second example illustrates how an attractor might be represented bya single quantitative dimension Young and Burke (1998) have shown thatan overwhelming majority of the share cropping contracts in Illinois areone of two types In some communities the farmers and the landownerssplit the crop yield while in other communities the landowners receivetwo shares for every one received by the farmer Interestingly despite widevariation in land quality within communities there is little variation inshare cropping contracts within communities Let us suppose that we werestudying a population of farmers in this region and that xi is individualirsquos mental representation of the fair or appropriate share for the land-owner in a share-cropping contract We scale these representations sothat Attractor-0 x D 0 is a 1 1 share while Attractor 1 x D 1

represents a 2 1 share Cognitively such attractors might arise becauseinteger ratios involving numbers that humans intuitively understand areeasier to represent and remember than other ratios (eg 138 313) Whena person is observed to use other contracts he or she is often thought tobe using (and thinking about) one of the two focal contracts

We also assume that individuals are selective in picking their culturalmodels mdash that is in deciding on whom to focus their inferential processesIn particular we assume individuals focus on people with higher valuesof x Individuals with higher values of x might have more successinteract more or be more salient for other reasons This assumption abouthuman psychology is well founded A substantial amount of evidencefrom both laboratory and eld research demonstrates than humans payparticular attention to preferentially interact with and tend to imitatesuccessfulprestigious individuals (Henrich amp Gil-White 2001 summarizethis evidence and lay an evolutionary foundation) Using our aboveexample it could be that individuals who believe in a 2 1 contracthave more success on average than individuals who have other mentalrepresentations and that their relative success will make them preferredmodels We let wi be the likelihood that individual i is selected as amodel and assume that there is a positive correlation between xi and wi

We analyze this model using the Price Equation (Price 1970) Thisequation (1) says that the mean change in the mean of any property of


a population of things genes mental representations or the hydrogenatoms in the Andromeda galaxy can be decomposed into two parts theextent to which the properties of things covary with the effect of selection6

and the rate at which the things themselves change with time Thereare no assumptions about replication delity discreteness or underlyingdistributions This form is particularly useful here because it partitionsthe change in a population of mental representations into the effect ofselecting particular cultural models (ldquoselective transmissionrdquo) from the effectof inferential processes (ldquoincomplete inferencerdquo)

Nw1 Nx D Covwi xi| z Selective Transmisson

C Ewi1xi| z Incomplete Inference

(1)

1 Nx is the change in the average value of x in the population per time step1xi captures the effect of the cognitive attractors and Nw is the averagereplicability of the xi values carried in the minds of the n individuals inthe group

Another useful property of the Price equation is that it makes it easy todeal with populations that are structured into groups (Price 1972) Here wedivide the population into two groups one for each domain of attractionand express the dynamics for the change in the average value of x in eachdomain of attraction Group 0 is composed of individuals whose mentalrepresentations are less than m and group 1 contains those individualswhose mental representations are greater than m Let Nxj and Nwj be themean value of x and the mean replication rate for group j and let xj i andwj i be the mental representations of the ith individual in group j Thenwe can rewrite (1) as follows

Nw1 Nx D Cov Nwj Nxj C E Nwj 1 Nxj (2)

That is the change in the mean value over the whole population can bedecomposed into the covariance between group means and group meanreplication rates and the average change within each group But noticethat the average change within each group has the same form as the lefthand side of the Price equation Thus we can apply the Price equation

6In the form expressed here we have assumed that the xrsquos proportional representationfrom one time step to the next is a function of its relative replicability (or tness) and itscurrent representation in the population


again this time to the dynamics within each group mdash substituting theexpressions given in (3) into the expectation term in (2)

Nwj 1 Nxj D Covwj i xj i C Ewj i1xj i (3)

The covariance term gives the change within the groups due to thepsychology of model selection and the second term gives the change withineach group due to inferential transformation by attractors

Now we make use of the speci c form of the inferential transformationshown in Figure 1 In group 0 1x0i D iexclmacr0x0i and in group 11x1i D macr11 iexcl x1i Further assume that an individualrsquos likelihood ofbeing selected as a model depends linearly on their value of xj i so thatwj i D 1 C sxj i With these assumptions

Nw01 Nx0 D iexclmacr0 Nx0 C siexclVarx0i iexcl macr0Ex2

0icent

frac14 iexclmacr0 Nx0 (4)

and

Nw11 Nx1 D macr11 iexcl Nx1 C spoundVarx1i iexcl macr1

iexclNx1i iexcl Ex2

1icentcurren

frac14 macr11 iexcl Nx1 (5)

If intra-psychic transformations are strong relative to the selective forces(macr1 macr0 Agrave s) then the rst terms on the right-hand sides of (4) and (5) willdominate the dynamics and determine the equilibrium values of the meanvalues of x in each group

We can now write down the approximate epidemiological dynamicsfor the entire population First let p be the fraction of individuals in group1 and 1 iexcl p the fraction of the population in group 0 Then substituting(4) and (5) into (2) yields

Nw1 Nx frac14poundp Nw1 Nx1 C 1 iexcl p Nw0 Nx0 iexcl Nx Nw

curren| z

Covariance Term from 2

Cpoundpmacr11 iexcl Nx1 iexcl 1 iexcl pmacr0 Nx0

curren| z

Expectation Term from 2

(6)

Because the macrrsquos are so much larger than s the dynamics of the system willbe initially governed by the attractors Nx0 will rapidly evolve toward zeroNx1 toward one and thus Nx frac14 p Substituting these values into (6) gives thefollowing equation for the approximate dynamics after this initial period

1 Nx frac14 1p frac14p Nw1 iexcl Nw

Nw(7)


Equation (7) is the standard formulation for discrete-trait replicatordynamics With this formulation we see that the longer-term dynamicsand the nal equilibrium Nx D 1 are determined by selective culturaltransmission and approximated with standard replicator dynamics Thestronger cognitive attractors are relative to selective cultural transmissionthe better the discrete replicator approximation

These ndings are very general Elsewhere we (in prep) show this nding applies to more than two attractors for a wide range differentintra-psychic transformations and to representations in any number ofdimensions There we also discuss the effect of more complex forms ofselective cultural transmission

Numerical simulations of the model indicate that the approximateanalysis derived above is quite accurate In our simulation we assumed aninitially uniform distribution of xi in a nite population For parametersn D 200 macr0 D macr1 D 050 s D 005 and m D 060 Figure 2 shows thedynamics of the average value of x in group 0 Nx0 the average value of x

in group 1 Nx1 the mean of x (overall Nx ) for one run of the simulationthe mean value of x for 10 simulations and the predictions of replicatordynamics As assumed above Nx0 goes rapidly to 0 and Nx1 goes rapidlyto 1 The trajectory of Nx from one run of the simulation shows the random

Figure 2 Results from simulating model described in text The overall evolutionof the population is very well approximated by a discrete model in which only

weak selective forces are present


effects of drift produced by nite populations but still clearly tracks thereplicator approximation Across 10 simulations the effects of drift areaveraged out and replicator dynamics tracks Nx quite closely A series ofsimulations with a variety of parameter combinations con rms the ndingsderived above In addition it shows how cultural drift is affected by s n

and m As n decreases the force cultural drift increases making it morelikely for x to drift into Domain 0 If s gets too small drift is also morelikely to drive x to zero As m gets large x values are more likely to driftinto Domain 0 and be driven to zero

Model 2 Cultural inertia and cumulative cultural adaptationcan occur even when inference is inaccurate

In this second model we explore the effect of inaccurate replicationWe assume that cognitive processes generate strong attractors but thatinferences based on the available public representations are highlyinaccurate We use discrete-representations to show that even whentransmission delity is very low cultural transmission can still createcultural inertia and adaptive cultural evolution

Much of the confusion about whether selective cultural transmissioncan produce cultural inertia shared traditions and adaptive evolutionarises from a failure to appreciate the differences between cultural andgenetic evolution In genetic evolution both evolutionary inertia and thepossibility of gradual cumulative cultural change have the same causeaccurate unbiased genetic replication In sexual species like humans eachindividual has two parents and this has important consequences for thedistribution of genotypes in populations However except for extremelyrare mutations each gene is a faithful copy of a single gene carriedby a member of the previous generation mdash genetic replication is veryaccurate Moreover each gene that an individual carries again with afew exceptions is equally likely to be included in the individualsrsquo gametesmdash thus genetic reproduction is unbiased These properties of geneticreproduction result in Mendelrsquos laws for the distribution of genotypes

To see how accurate unbiased replication gives rise to genetic inertiaand makes cumulative adaptive change possible consider a simple geneticsystem with only two alleles (or genes) at a single locus segregating in alarge population We label them A and a Let q be the frequency of A


before genetic transmission and q0 the frequency after genetic transmissionFinally suppose that each allele mutates to the other with probability uThis means that

q 0 D 1 iexcl 2uq C u (8)

A plot of q 0 as a function of q is a straight line with a slope slightlysmaller than one as shown in Figure 3 If the slope were exactly one(ie no mutation) then transmission would lead to no change in thepopulation q 0 D q across the generations A population that had 80A alleles before transmission would have 80 after transmission and apopulation that had 20 before transmission would have 20 afterwardHowever any amount of mutation tends to reduce the frequency of themore common allele and thus if no other evolutionary processes affectthe population it will move toward a state in which both alleles have thesame frequency Because mutations are very rare u frac14 10iexcl6 this willoccur very very slowly Thus in the absence of other forces populationswill change very slowly and this explains much genetic inertia Similarlyas long as natural selection is stronger than mutation it can generatecumulative adaptation

By analogy from the process just described Sperber (1996 103-118) and Atran (2001) argue that because cultural replication is highlyinaccurate the social processes of cultural transmission cannot give riseto cultural inertia or cumulative cultural adaptation Unlike genes mentalrepresentations are not replicated during cultural transmission Insteadmental representations give rise to behaviors (or ldquopublic representationsrdquo)that are observed by others who must then infer the underlying mentalrepresentations that gave rise to the behavior Because individuals differand public representations provide incomplete information this inferentialprocess is Sperber Boyer and Atran assert highly inaccurate

If they are correct it does follow that cultural transmission cannotgive rise to cultural inertia for the same reasons as genetic transmissionTo see this suppose there are only two possible mental representations insome domain labeled A and B Each generates different but overlappingdistributions of public representations When cultural learning occursnaiumlve individuals perhaps children observe a sample of individuals fromthese distributions make inferences and then adopt their own mentalrepresentation Following Sperber Atran and Boyer we suppose this


Figure 3 The left hand gure plots the frequency of gene after reproductionq 0 as a function of the frequency before reproduction q As is shown in the righthand part of the gure mutation tends to drive gene frequencies toward 05 but

because the mutation rate u is very low this happens very slowly

process is very inaccurate it is governed by equation (8) but now u D 02(5 orders of magnitude larger than the rate genetic mutation) To get afeeling for the magnitude of u remember that u D 05 means that thereis no transmission at all mdash naiumlve individuals adopt mental representationsat random independent of who they observe Thus we are assumingthat the acquisition of mental representations is 40 error and 60transmission As is shown in Figure 4 very high error rates lead to verydifferent dynamics than accurate replication Under such high error ratespopulations very rapidly converge to a random distribution of mentalrepresentations There is no inertia and extremely strong selective forceswould be required to generate cumulative adaptation

However this logic carries the genetic analogy too far Even if culturaltransmission is inaccurate it does not follow there can be no culturalinertia or cumulative evolution of adaptations Any transmission processthat leads to accurate replication at the level of the population will lead tocultural inertia and allow cumulative adaptation Put another way anytransmission process that produces a plot like that shown in Figure 3 willdo the job The mistake is to assume that the only process that can give rise


Figure 4 The frequency of representations after reproduction q 0 as a functionof the frequency before reproduction q when the error rate u is high As beforeerrors tend to drive representation frequencies toward 05 but now this occurs

very rapidly because the error rate is large

accurate replication at the level of the population is accurate replication atthe level of individuals

Here we show that a tendency to adopt the more common represen-tation can lead to accurate replication at the population level even whenindividual inferences are highly innaccurate Assume that there are twopossible mental representations A and B and that a fraction q of theexperienced population has A Every naiumlve individual observes the publicrepresentations of n models and makes inferences about the mental repre-sentations that gave rise to these public representations In each case thisinferential process is subject to frequent errors The probability of inferringthe correct mental representation is 1 iexcl u and the incorrect representationis u Thus the probability p that a social learner infers that any one ofthe models has mental representation A is

p D q1 iexcl u C 1 iexcl qu (9)

Finally suppose that individuals adopt as their own the mentalrepresentation that they believe is most common among their modelsThis means that the probability that a naiumlve individual acquires A andtherefore the frequency of A after transmission q 0 is

q 0 DnX

igtn=2

nin iexcl i

pi1 iexcl pniexcli (10)


Because individuals tend to acquire the more common mental represen-tation this model is one way to represent a ldquoconformistrdquo bias in sociallearning

The conformist bias has well-established theoretical and empiricalfoundations Theoretically evolutionary modeling of the cognitive capacityfor conformist transmission suggests that genes leading to a conformistbias in social learning will be supported in virtually any environmentthat also favors social learning (Henrich amp Boyd 1998) Empiricallypsychological evidence for conformity from pre-1984 studies is summarizedin Boyd and Richerson (1985) Much of recent evidence can be foundin Baron et al (1996) Insko et al (1985) Smith and Bell (1994)Bond and Smith (1996) and Campbell and Fairey (1989) These studiesanalyze everything from economic decisions and strategy choice in strategicgames to perceptual tasks and food choices Moreover by analyzing thedynamics of transmission Henrich (2001) provides evidence of conformisttransmission from eld data on the diffusion of innovations

A conformist bias at the individual level leads to more accuratereplication at the population level Figure 5a plots q 0 as a function ofq for n D 10 and u D 02 This gure shows that social learning processescome much closer to accurately replicating the population frequency ofthe mental representations even though the transmission process is errorprone at the individual level The maximum error rate at the populationlevel (at q D 0 1) is approximately 002 one tenth of the individual rateThe reason for this is simple errors have a bigger effect on populations inwhich one mental representation is common compared to populations inwhich both mental representations have similar frequencies As a result theconformist bias in transmission effectively corrects for the effect of errorsFurthermore even higher error rates can be compensated for by largersamples of cultural parents Figure 5b plots the effect of transmission whenu D 03 and n D 20 Recall that u D 030 means errors occur 60 oftime

This conformist learning mechanism can lead cultural inertia becauseit tends to increases the frequency of common mental representations andreduces the frequency of rare ones (Figure 6a) Observe that the conformistcurves both closely follows the q0 D q line and creates two stable equilibrianear the points 00 and 11 These equilibria occur when the effect of


Figure 5 The post transmission frequency of a cultural representation as afunction of the pre-transmission frequency when the error rate is high but thereis a conformist bias in the cultural transmission rule In the left panel (a) the errorrate is 02 and then number of models is 10 while in the right panel (b) the error

rate is 03 and the number of models is 20

errors and the force of conformist transmission are balanced Two initiallydifferent populations can remain different even in the same environmentCultural inertia is created by conformist transmission even when error ratesare high

Conformist social learning also allows selective forces to generatemore accurate adaptations to the environment Suppose that individualswith mental representation A are twice as successful as individuals withrepresentation B on average and that the probability that individuals arechosen to be models is proportional to the ratio of an individualrsquos successto the average success in the population (lsquoprestige-biased transmissionrsquo)Figure 6b shows that when we combine prestige bias conformist bias andhigh error rates the more successful representation readily spreads

The combination of high error rates and a conformist bias does notresult in the same kind of ldquofrictionlessrdquo adaptation as genetic replicationHighly accurate unbiased genetic replication allows minute selective forcesto generate and preserve adaptations over millions of years Error pronecultural replication even when ldquocorrectedrdquo by a conformist bias imposesmodest but still signi cant forces on the cultural composition of thepopulation This means that only selective forces of similar magnitude willlead to cumulative adaptation We do not think this is a problem becausethe selective forces acting on cultural variation are probably much stronger


Figure 6 (a) The combination of conformist bias and very high error rate u D03 acts to preserve variation between groups because common representationstend to increase in frequency (b) When more successful individuals are more likely

to be imitated the more successful variant spreads

than those that shape genetic variation because they work on shorter timescales and are often driven by psychological not demographic events mdasheg the diffusion of innovations literature shows time scales of decades notmillennia (Rogers 1995)

Model 3 Adaptive evolution in a model without accuratereplication or discrete representations

Evolutionary theory predicts and both eld and laboratory data con rmthat individuals have a psychological propensity to copy particularly skillfulsuccessful and prestigious individuals We call this prestige-biased transmissionHenrich and Gil-White (2001) lay out the theory and summarize theempirical data This tendency creates a selective force that can under theright circumstances generate cumulative adaptation It is easy to see howthis would work if cultural replication were accurate Suppose populationsvary in their ability to perform some important task say prey tracking orarrow manufacturing techniques Further suppose that in choosing modelspeople preferentially imitate the techniques used by the best trackers inthe group If the mental representations that underlie the success of thebest trackers can be accurately copied the mean tracking success of thepopulation will increase through time (Boyd amp Richerson 1985 Ch 8)because good trackers will leave more cultural lsquodescendantsrsquo However


Sperber (1996) and Atran (2001) have argued that because culturalrepresentations are not discrete and cultural replication is inaccurateselective forces such as prestige-biased transmission are unlikely to beimportant (Note Atran et al (in press) now modi es that position)

Here we show that prestige biased transmission can lead to cumulativeadaptation even when cultural transmission is inaccurate and represen-tations are not discrete Consider a population of N individuals who arenumbered i D 1 N Individual i has a z-value (zi ) This value mea-sures the individualrsquos skill in some domain like canoe making arrow manu-facture or medicinal plant selection Later we will show that z may measureeither an individualrsquos mental representation (eg how long they think ar-rows should be) or some phenotypic measure that aggregates many skillsor measures success (like lifetime tapir kills) However for now we assumethat it is a mental representation Each individual is also characterized bya variable f that speci es the relative likelihood that an individual will bechosen as a cultural model If peoplersquos social learning attention is drawnto skilled hunters (and larger values of z lead to hunting skill) then f andz will have a positive partial regression coef cient (other things can affectf as well) The pool of individuals could represent the same group of in-dividuals (same farmers) from one year to the next or it could be differentgenerations or cohorts

Once again we use the Price Equation to study the combinedeffects of selective transmission and inaccurate inference on continuousrepresentations

1Nz D Covfi zi| z Selective Transmission

C Efi1zi| z Incomplete Inference

(11)

1Nz is the change in the average value of zi per time step If 1Nz is positivethen adaptive evolution is taking place because for example people arebecoming better trackers or arrow makers Covfi zi is the covariationbetween fi and zi and gives the effect of selective cultural forces on 1Nz Inthis case it captures our psychological tendency to copy successfulskillfulpeople mdash here we will assume that all learners attempt to copy the mostskilled individual Efi1Nzi is the replicability-weighted average effect ofall the individual intra-psychic transformations on cultural representations

To capture the idea that inferential processes are incomplete andinaccurate we assume that the inferential processes that underpin social


learning are inaccurate in two senses rst they are noisy so that copiersnever accurately replicate the z-value of their model and second theyare biased so that the behavior acquired by copiers is on average lessskilled than the behavior of their model More formally (as illustrated inFigure 7) individuals who attempt to copy a model with z-value zi endup with a z-value drawn from a Gumbel probability distribution7 withmode zi iexcl reg and dispersion macr Typically copiers construct representationsthat are on average worse than their modelrsquos z-values by an amount regbut occasionally mdash through lucky guesses or errors mdash individuals constructrepresentations that yield z-values higher than their model The probabilityof that occurring for an individual is the area under the distribution to theright of the dashed line (the modelrsquos z-value) Itrsquos also worth noting thatthe probability of an exact copy is zero and the probability of two peoplearriving at exactly the same copy is zero mdash no replicas in this model

With these assumptions equation (11) becomes

1Nz D iexclreg C macr C LnN (12)

The rst term represents the effect of systematic errors and is alwaysnegative mdash it operates against adaptive evolution In the second termLnN is the natural logarithm of N the number of social learners in thepopulation The parameter is the Euler-gamma constant which equals0577 The parameters macr LnN and are all always positive so thesecond term is always positive mdash and favors adaptive evolution Thismeans that adaptive cultural evolution depends on the relative sizes of thetwo terms Interestingly the two components of inference systematic bias(measured by reg) and random noise (measured by macr ) have opposite effectson adaptive evolution Systematic bias operates against adaptive evolutionwhile noise mdash the tendency of individuals to make different inferences fromobserving the operation of the same underlying representation mdash favorsadaptive evolution The more individuals tend to make different inferencesthe faster cultural evolution goes (or the more likely it is to be adaptive)Similarly the larger the population of social learners N the faster adaptiveevolution proceeds (or the more likely selective forces will favor adaptiveprocesses)

7The speci c form of this distribution does not qualitatively impact our results (seeHenrich 2002 for more information)


Figure 7 A graphical representation of the assumptions of Model 3 Learnersobserve a model with a behavior zi given by the dotted line They infer a valuedrawn from the probability density function Their most likely value is reg less thanthe models value and since larger values of z are better this represents systematicerror However there is some probability that individuals acquire larger values

(this is the area under the curves to the right of the dotted vertical line)

Setting 1Nz gt 0 and solving (12) yields the conditions under whichselective cultural transmission will drive adaptive cultural evolution

N curren gt eregmacr

iexcl (13)

N curren is the critical number of social learners necessary to produce cumulativeadaptive cultural evolution for a speci ed set of inferential processes (reg macr )Figure 8 plots this inequality and graphically shows the conditions underwhich selective transmission will drive adaptive evolution

This result provides several insights about cultural adaptation in a noisyenvironment First cumulative adaptive evolution is facilitated by both alarge pool of social learners and an inferential tendency to make differentldquomistakesrdquo (large macr a tendency for individuals to form quite differentrepresentations) This nding contradicts Sperber (1996) and Atran (2001)who have argued that because cultural transmission leads to differentrepresentations in each individualrsquos mind cumulative cultural evolutionis not possible Second no matter how poor individuals are at imitating


there are some values of macr and N that generate cumulative evolution mdashelsewhere Henrich (2002) has shown how a sudden drop in populationsize (N ) initiated a process of technological devolution in Tasmania overthe last 8000 years So both the social environment and the nature ofcognition in uence the conditions for cumulative adaptation Looking onlyat the inferential processes and the conditions for adaptation what mattersis not reg but reg=macr So if the typical inaccuracy of copies doubles (reg) whilethe variation in different representations triples cumulative adaptation willstill occur However the model also illustrates that in particular culturaldomains mdash those with large reg and small macr (eg some religious beliefs)mdash we may not expect to observe cumulative adaptation Finally havingincorporated Sperber Atran and Boyerrsquos claims about the nature of cultureinto this simple model that bears no resemblance to genetic models (otherthan both being about evolutionary processes) we derived insights that arenot obvious from verbal reasoning alone

Sperber Atran and Boyer have argued that evolutionary modelscannot be applied to phenotypes (or public representations) alone theyare applicable only if there are identi ed lsquounitsrsquo of transmission Thisis not the case and suggests a failure to apprehend the more generalnature of evolutionary processes (Boyd and Richerson 2000) Neithergenetic nor cultural evolutionary models require lsquounits of transmissionrsquo

Figure 8


mdash genetic evolutionary models were providing insights into the nature ofevolution long before anyone knew anything about DNA discreteness orreplication and genetic models of quantitative characters like height stillignore these ldquounitsrdquo The most general form of the Price Equation forexample is exact for anything one can measure about the constituentparts of any evolutionary system This feature allows us to study theevolution of and interrelation between phenotypically expressed behavior(ldquopublic representationsrdquo) and the epidemiology of the underlying mentalrepresentations Suppose now instead of a mental representation of a skillz measures success in some domain such as hunting (perhaps quanti ed inlifetime tapir kills) combat (in lsquoheads-takenrsquo) canoe making or farming(in sacks harvested per hectare of wheat sown) Equation (11) wouldstill govern the evolution of z However if we wanted to get at theunderlying mental representations that produce particular values of zwe would have to specify how each mental representation contributesto individualsrsquo behavioral expressions (to their success) For illustrativepurposes suppose z is hunting returns (a phenotypic measure) and y andAacute are mental representations related to prey pursuit time and arrow lengthmdash presumably there are many more relevant representations for huntingUsing a linear regression equation we can express the causal relationshipof between mental representations y and Aacute on success z as follows8

zi D sup1 C cedil1yi C cedil2Aacutei C i (14)

The cedilrsquos give the relative contribution of an individualrsquos y and Aacute mentalrepresentations to the observed success zi i gives uncorrelated randomerror and sup1 speci es the constant term With this we can express thechange in the average value of representation y as

1 Ny D Covfi yi| z Selective Transmisson

C Efi1yi| z Incomplete Inference

(15)

But because an individualrsquos likelihood of being selected as a cultural modeldepends on f and f depends on individuals observing z (eg hunting

8In general we can do this for any number of mental representations and study theinteraction of different mental representations


returns) then this can be rewritten as

1 Ny D cedil1frac12Varyi| z Selective Transmisson


(16)

where frac12 is the partial regression coef cient on f on z The introductionof cedil1 shows us that effective transmission of y depends on how much itaffects z The 1yi term would have the same form as above it dependson how dif cult it was to infer the underlying yi by observing the modelsrsquobehavior The reminder of the derivation proceeds as above

Conclusion

Formal models help us develop a more complete of understanding of cog-nition and culture Our minds are not well equipped to understand thepopulation-level outcomes that arise from numerous minor interactionsweak cognitive biases random errors migration rates and micro-level de-cisions The history of population ecology epidemiology and evolutionarybiology over the last 40 years provides strong evidence that simple mathe-matical models provide powerful tools for understanding such problems

The simple models described in this paper yield several ndings thatchallenge the untutored intuitions of many

1 Strong attractors generate replicator dynamics such that weakselective forces determine the nal state of the system The strongerthe attractors the better the assumption of discrete-trait replicatordynamics

2 Conformist transmission can compensate for even very high errorrates in social inference in a manner that violates the intuitionsimported from genetics Prestige-biased transmission combines withconformist transmission to spread adaptive representations togetherthey predict the conditions for inertia and change

3 Adaptive cultural evolution can occur even when representationsare continuous and inferences are biased against adaptation Poorinferences can be compensated for by larger pools of social learnersor greater amount of random error (ie by the fact that peopledonrsquot all make the same inferential mistakes)

4 Discrete units of transmission are not necessary for adaptiveevolution Dawkins (1976 1982) claims notwithstanding


The crux of Sperber Atran and Boyerrsquos position is that the transmis-sion of culture requires domain speci c cognitive mechanisms and thattherefore that population dynamic models of culture proceed from unten-able assumptions We accept that social learning like all other forms oflearning requires innate expectations about objects in the environmentand the nature of relationships among them How these innate structuresshape the human mind is obviously of great importance for understand-ing human culture The mistake is to see these ideas as incompatible withmaking population dynamic models of cultural change It will never beenough to focus on the mind and ignore the interactions between differ-ent minds To keep track of such interactions some kind of populationdynamic models will be necessary What is needed is both more effort bycoevolutionary theorists to incorporate rich cognition into formal modelsof social learning and more effort by cognitive scientists to consider howinnate cognitive structure interacts with social processes and the cognitionof social learning to in uence the epidemiology of representations and itsassociated behavioral products

REFERENCES

ATRAN S2001 The trouble with memes Inference versus imitation in cultural creation Human

Nature 12(4)351-3812002 In gods we trust The evolutionary landscape of religion New York Oxford University

PressATRAN S MEDIN D ROSS N LYNCH E VAPNARSKY V UCAN EKrsquo ECOLEY J TIMURA C amp BARAN M

(in press) Folkecology cultural epidemiology and the spirit of the commons A gardenexperiment in the Maya lowlands 1991-2001 Current Anthropology 43(3)

BARON R VANDELLO J amp BRUNSMAN B

1996 The forgotten variable in conformity research impact of task importance onsocial in uence Journal of Personality amp Social Psychology 71(5)915-927

BLACKMORE S1999 The Meme Machine Oxford Oxford University Press

BOND R amp SMITH PB1996 Culture and conformity a meta-analysis of studies using Aschrsquos (1952b 1956)

line judgment task Psychological Bulletin 119(1)111-137BOYD R amp RICHERSON PJ

1985 Culture and the Evolutionary Process Chicago IL University of Chicago Press


2000 Memes Universal Acid or a Better Mouse Trap R Aunger (editor) DarwinizingCulture The Status of Memetics as a Science (pp 143-162) Oxford Oxford UniversityPress

BOYER P1994 The Naturalness of Religious Ideas Berkeley University of California1999 Cognitive tracks of cultural inheritance how evolved intuitive ontology governs

cultural transmission American Anthropologist 100(4)876-889CAMPBELL JD amp FAIREY PJ

1989 Informational and normative routes to conformity the effect of faction size as afunction of norm extremity and attention to the stimulus Journal of Personality ampSocial Psychology 57(3)457-468

CAVAILLI-SFORZA LL amp FELDMAN M1981 Cultural Transmission and Evolution Princeton Princeton University Press

DAWKINS R1976 The Selsh Gene Oxford Oxford University Press1982 The Extended Phenotype Oxford Oxford University Press

DENNETT D1995 Darwinrsquos Dangerous Idea London Penguin Press

HENRICH J amp BOYD R

1998 The evolution of conformist transmission and the emergence of between-groupdifferences Evolution and Human Behavior 19215-242

HENRICH J amp GIL-WHITE F

2001 The Evolution of Prestige freely conferred deference as a mechanism forenhancing the bene ts of cultural transmission Evolution and Human Behavior22(3)165-196

HENRICH J

2001 Cultural transmission and the diffusion of innovations American Anthropologist103(4)1-23

2002 Demography and Cultural Evolution How adaptive cultural processes producedmaladaptive losses in Tasmania httpwebuserbusumicheduhenrich

INSKO CA SMITH RH ALICKE MD WADE J amp TAYLO R S

1985 Conformity and group size the concern with being right and the concern withbeing liked Personality amp Social Psychology Bulletin 11(1)41-50

LESLIE AM1994 ToMM ToBY and Agency Core architecture and domain speci city In

LA Hirschfeld amp SA Gelman (eds) Mapping the Mind Domain specicity incognition and culture (pp 119-148) Cambridge Cambridge University Press

LUMSDEN C amp WILSON EO1981 Genes Mind and Culture Cambridge Harvard University Press

PRICE GR1970 Selection and Covariance Nature 520-5211972 Extensions of Covariance Selection Mathematics Annals of Human Genetics 35485-

490


ROGERS EM1995 Diffusion of Innovations New York Free Press

SMITH JM amp BELL PA

1994 Conformity as a determinant of behavior in a resource dilemma Journal of SocialPsychology 134(2)191-200

SPERBER D1996 Explaining Culture a Naturalistic Aapproach Oxford UK Cambridge Mass

BlackwellYOUNG HP amp BURKE MA

1998 Competition and custom in economic contracts A case study of illinoisagriculture American Economic Review 93(3)559-573


Introduction

Formal models of cultural evolution (eg Boyd amp Richerson 1985) providean important tool for understanding cultural phenomena Culture is shapedby both psychological processes that determine how people think andfeel and social processes that determine how people interact whetherthey succeed or fail and if they live or die Formal cultural evolutionarymodels can combine cognitive and affective processes with patterns ofsocial interaction to generate explicit predictions about the distributionsand dynamics of lsquorepresentationsrsquo mdash ideas beliefs schemas or mentalmodels With such predictions empirical data on behavior and beliefs frompopulations can be used to select among alternative models or among thecognitive and social components of these models in a manner that informsour understanding of cognition and connects laboratory experiments withreal life (eg Henrich 2001)

Recently Sperber (1996) Atran (2001 2002) and Boyer (1994 1999)have argued that these ldquoNeo-Darwinianrdquo models1 are inappropriate forstudying cultural evolution because they are ldquobased on a serious distortionof the relevant factsrdquo (Sperber 1996118) They identify three interrelatedproblems with such approaches First cultural transmission processes areusually incomplete and imperfect so unlike genetic systems accuratereplication rarely occurs Replication is the exception rather than therule Second unlike DNA replication inferential processes ldquotransformrdquothese representations during their transmission and reconstruction Thissuggests that mutation-like processes are much more important than selection-like processes in shaping cultural variation Third unlike genes culturalrepresentations are rarely discrete units suggesting that the idea ofa lsquoreplicatorrsquo (or meme) makes little sense for most types of culturalrepresentations2

1These scholars use the term ldquoNeo-Darwinianrdquo for such models even when theyare explicitly derived from disease epidemiology (Cavalli-Sforza amp Feldman 198146-53)learning theory (see Boyd amp Richerson 1985 Chapter 4) or cognitive psychology (Lumsdenamp Wilson 1981)

2While such characterizations apply to the informal theorizing of memeticists (egDawkins 1982 Dennett 1995 or Blackmore 1999) they are wide of the mark for muchformal cultural theory Boyd and Richerson (BR 198575) explain that there is no need toassume particulate ldquounitsrdquo in order to build evolutionary models (BR 198570-75) and 19 of

































(1)












0icent


and


iexclNx1i iexcl Ex2

1icentcurren





curren| z



curren| z


(6)



Nw(7)

































q 0 DnX

igtn=2

nin iexcl i

























(11)














iexcl (13)






Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490








































(1)












0icent


and


iexclNx1i iexcl Ex2

1icentcurren





curren| z



curren| z


(6)



Nw(7)

































q 0 DnX

igtn=2

nin iexcl i

























(11)














iexcl (13)






Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490



































(1)












0icent


and


iexclNx1i iexcl Ex2

1icentcurren





curren| z



curren| z


(6)



Nw(7)

































q 0 DnX

igtn=2

nin iexcl i

























(11)














iexcl (13)






Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490































(1)












0icent


and


iexclNx1i iexcl Ex2

1icentcurren





curren| z



curren| z


(6)



Nw(7)

































q 0 DnX

igtn=2

nin iexcl i

























(11)














iexcl (13)






Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490























(1)












0icent


and


iexclNx1i iexcl Ex2

1icentcurren





curren| z



curren| z


(6)



Nw(7)

































q 0 DnX

igtn=2

nin iexcl i

























(11)














iexcl (13)






Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490



















(1)












0icent


and


iexclNx1i iexcl Ex2

1icentcurren





curren| z



curren| z


(6)



Nw(7)

































q 0 DnX

igtn=2

nin iexcl i

























(11)














iexcl (13)






Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490













(1)












0icent


and


iexclNx1i iexcl Ex2

1icentcurren





curren| z



curren| z


(6)



Nw(7)

































q 0 DnX

igtn=2

nin iexcl i

























(11)














iexcl (13)






Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490














0icent


and


iexclNx1i iexcl Ex2

1icentcurren





curren| z



curren| z


(6)



Nw(7)

































q 0 DnX

igtn=2

nin iexcl i

























(11)














iexcl (13)






Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490








































q 0 DnX

igtn=2

nin iexcl i

























(11)














iexcl (13)






Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490

































q 0 DnX

igtn=2

nin iexcl i

























(11)














iexcl (13)






Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490


























q 0 DnX

igtn=2

nin iexcl i

























(11)














iexcl (13)






Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490




















q 0 DnX

igtn=2

nin iexcl i

























(11)














iexcl (13)






Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490















q 0 DnX

igtn=2

nin iexcl i

























(11)














iexcl (13)






Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490































(11)














iexcl (13)






Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490


























(11)














iexcl (13)






Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490




















(11)














iexcl (13)






Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490














(11)














iexcl (13)






Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490



















iexcl (13)






Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490













iexcl (13)






Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490











Figure 8







(15)







(16)


Conclusion









REFERENCES























HENRICH J









490














(15)







(16)


Conclusion









REFERENCES























HENRICH J









490












(16)


Conclusion









REFERENCES























HENRICH J









490










REFERENCES























HENRICH J









490




















HENRICH J









490















Documents

On Modeling Cognition and Culture · ON MODELING COGNITION AND CULTURE 91 (or ‘ cognitive tracks’ or ‘ triggered representations) and to reject the use of discrete-representations