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REVIEWS Gene- coevolutionarytheory Marc W. Feldman and Kevin N. Laland

tone tools appear in the Gene-culture coevoiutionary theory is a geneticssJ0Jr. And more recently, archaeological record ap branch of theoretical these general methods have been proximately two and a half that models the transmission of genes applied to address specific cases S million years ago. The signifi- and cultural traits from one generation to in which there is an interaction cance of this observation is not the next, exploring how they interact. between a cultural trait and some simply that Homo habifis and later These models have been employed to that influences hominid had the guile to examine the adaptive advantages of its prevalence12-17. manufacture a lithic technology, and culture, to investigate the In a gene-culture model, indi- but also that these skills were forces of cultural change, to partition viduals must be described in terms transmitted from one generation the variance in complex human behavioral of both their genotype and their to the next. These simple artifacts and personality traits, and to address cultural trait, a combination known thus represent the earliest evi- specific cases in human in as a ‘phenogenotype’. Thus, in dence for culture. In fact, compara- which there is an interaction between addition to the rules of mendelian tive evidence for social learning genes and culture. inheritance, transmission rules for in a variety of vertebrate species cultural traits must be described”. suggests that cultural trans- Typically, it is assumed that the mission almost certainly preceded Marc Feldman is at the Dept of Biological Sciences, probability of an individual adopt- Stanford University, Stanford, CA 94305, USA: Homo habilis by a considerable ing a trait depends on whether its Kevin Laland is at the Sub-Dept of Animal Behaviour, length of time. However, social parents have that trait (vertical University of Cambridge, Madingley, learning in animals is rarely stable Cambridge, UK CB3 8AA. transmission), but equivalent mod- enough to support traditions in els have been developed in which which information accumulates learning is from unrelated individ- from one generation to the next. uals (horizontal and oblique trans- The archaeological record documents the fact that for at mission), key individuals in the (indirect least the past two million years hominid species have reli- transmission), or the majority in the group (frequency- ably inherited two kinds of information, one encoded by dependent transmission)sJl. In all cases, in the place of a genes, the other by culture. How does dual inheritance system of recurrence equations that describe how allele or affect the evolutionary process? Gene-culture - genotype frequencies change over time, gene-culture mod- ary theory is designed to answer this question. els use an equivalent system for phenogenotype frequencies. Gene-culture coevolutionary theory is a branch of theo- The methods of gene-culture coevolutionary theory dif- retical , which, in addition to modeling fer from those of , human behavioral , the differential transmission of genes from one generation and evolutionary in two important respects. to the next, incorporates cultural traits into the analysis. First, a population’s culture is not regarded as largely de- The two transmission systems cannot be treated indepen- pendent on either its genetic constitution or the prevailing dently, both because what an individual learns may depend pattern of ecological resources. Instead, consistent with the on its genotype, and also because the selection acting on predominant view in the human sciences, culture is treated the genetic system may be generated or modified by the as shared ideational phenomena (ideas, beliefs, values, spread of a cultural trait. To give a simple example, the fre- knowledge) that are learned and socially transmitted be- quency of the sickle mutant among in West tween individuals. Below, we illustrate through examples Africa depends on their means of subsistencelJ. Populations how this view of culture makes a considerable difference to that chop down trees to cultivate yams create the conditions the evolutionary dynamics of a gene-culture system. Sec- where heavy rainfall will leave pools of standing water in ond, although the framework of gene-culture coevolution- which mosquitoes thrive, leading to more intense selection. ary theory does not preclude an adaptationist perspective, For yam cultivators, there is a correlation between amount and several such models have incorporated the assumption of standing water and sickle cell frequency, but not for other- that an individual’s genotype influences the probability that wise identical populations. In this example, the intensity of a particular cultural trait will be adopted, practitioners are selection on a gene hangs critically on the frequency of a also free to assume that traits may be adopted independent cultural trait (yam farming) in the population. of their consequences. The gene-culture approach is minimalist in that assumptions about the adaptive impor- Gene-culture models tance of traits are not an obligatory step in the modeling The quantitative study of gene-culture coevolution be- exercise. Note that although Lumsden and Wilson’s labeled gan in 1973, when Cavalli-Sforza and Feldman introduced their theoretical work ‘gene-culture coevolution’, their ap- a simple dynamic model of cultural transmission into the proach is in the sociobiological tradition, and should not be -nurture debates. The emerging body of theory has confused with contemporary gene-culture coevolutionary been used in a variety of ways. One class of models is em- theory. ployed to partition the variance in behavioral and personality Mathematical analyses suggest that evolution in popu- traits into a variety of components including a transmitted lations with a dynamic, socially transmitted culture is dif- cultural components-s. Dynamic models address very gen- ferent from evolution in acultural populations for a number eral questions about the adaptive advantages of complex of reasons. First, cultural transmission can modify selection forms of , such as learning and pressures, thereby affecting the course of a population’s culture&g. Other general models explore the forces of cul- evolution. For example, below we describe how the cultural tural change, and the nature of their interaction with tradition of dairy farming may have created the selective

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climate in which genes for lactose absorption have been related variability in its incidence. There is a broad range of favored. Second, culture can generate new evolutionary conditions under which the absorption allele does not mechanisms; for instance, Boyd and Richerson8J4JsJ9 have spread despite a significant fitness advantage. Cultural pro- developed a series of models of human cooperation, which cesses complicate the selection process to the extent that demonstrate the feasibility of a culturally preserved process the outcome may differ from that expected under purely gen- of . Third, the interplay between genetic and etic transmission. Here, because of interactions between cultural transmission may produce time lags in the action of genes and culturally influenced behaviors, the response to any selection that may be operating on a traitlo; the equiva- selection is typically slowed down, lent phenomenon has been seen in recent treatments of ma- ternal transmission of quantitative biological traitGO.Fourth, Excess female mortality in the same way that there can be non-linear interactions That the nature of a genetic response to selection may de between genes (linkage disequilibrium), nonrandom asso- pend on the characteristics of cultural transmission is illus- ciations between genes and cultural traits can occur*Q* that trated even more clearly in a gene-culture coevolutionary can significantly affect the genetic response to selection. analysis of the evolutionary and demographic consequences Fifth, because of its strong, homogenizing influence on of excess female mortality. In many regions of the world behavior, and capacity for rapid diffusion, culture may some (China, India, Pakistan), parents exhibit a preference for sons times generate atypically strong selection pressures, leading over daughters and act on this bias to change the natural to very strong selection. Examples of these last two phenom- sex ratio among their offspring27.28.Such behavior includes ena are given in the sex-ratio case discussed below. direct female , the neglect and abandonment of daughters, differential allocation of resources toward sons, lactose absorption and female-biased abortion following sex determination by The evolution of lactose absorption represents a good amniocentesis or ultrasound. The aggregate effect of these example of gene-culture coevolution. Systematic variation activities over vast continents may generate significant dis- exists in the milk digestive of adult humans. In tortion of the adult sex ratio. For instance, in India, the adult fact, most adult humans are lactose malabsorbers: that is, sex ratio has shown a consistent trend toward increasing their level of (lactase) activity is insufficient to break male bias over the past century2’JJ0,while in China, the re- down the -rich sugar lactose, and milk consumption ported sex ratio at birth is 1.14 sons for every daughterzi. typically leads to sickness and diarrhea. Genetic differences Locally, such ratios can be as extreme as five males for are largely responsible for the phenotypic difference be- every female, which represents the killing, abandonment, tween absorbers and malabsorbers, with absorption prob- or premature death of nearly 80% of female children. As ably inherited as an autosomal dominant trait*. A correlation genetic variation distorting the human sex ratio has now exists between incidence of lactose absorption and history been identifieds*J3, Kumm, Laland and FeldmanirJ4 used of dairy farming in populations23,24,with absorbers reaching a gene-culture model to investigate how this culturally frequencies of over 90% in such populations, but typically generated glut of males might influence the selection of less than 20% in populations without dairy traditions. Since distorter genes. milk and milk products have been an important component Kumm et al. found that whether or not parentally medi- of the diets of some human populations for over 6000 years, ated excess female mortality generates selection for a male roughly 300 generations, it is conceivable that dairy farming or female-biased primary sex ratio hangs critically on the may have created the selective regime under which the psychological rules that parents employ when they mani- allele for absorption was favored. fest their preference for sons. If parents act so as to increase Feldman and Cavalli-Sforzai*, following work by Aoki*5,26, the proportion of sons irrespective of the natural sex ratio used gene-culture coevolutionary theory to investigate the among their offspring, and if they compensate for any evolution of lactose absorption. They employed a single- daughters they lose by having further children, the sex ratio locus, diploid model for lactose absorption, with differential will evolve a female bias. This is because any parents who cultural transmission of milk usage. In this model, both dar- express genes that make them more likely to conceive winian selection based on the nutritional properties of milk daughters will end up having proportionally more grand- and cultural transmission of milk use are influenced by the children, since not all sons will mate. At equilibrium, the lactose-absorbing genotype. With three genotypes (AA,Au female bias in the primary sex ratio exactly compensates for and au) and two culturally influenced behavioral states (milk the parental preference for sons, leaving the adult sex ratio users and non-users) there are six combinations, or pheno- unbiased. In contrast, if parents try to achieve a desired sex genotypes. However, because the absorption allele (A) is ratio among their offspring, and if they have fewer children dominant, the dynamics can be explored by monitoring the than impartial parents as a consequence, the primary sex frequency of just four variables, users and non-users in indi- ratio becomes male-biased. This is because under such cir- viduals with or without a copy of the A allele. cumstances parents who express genes that make them The analysis suggested that whether or not the allele for more likely to conceive daughters would have to destroy absorption achieves a high frequency depends critically on more daughters in order to achieve their male-biased de the probability that the children of milk users become users sired sex ratio. In comparison, parents with genes that dis- themselves. If this probability is very high then a significant tort the primary sex ratio toward sons will have to kill fewer viability advantage to absorption will often result in the se- of their offspring to achieve their desired sex ratio, and will lection of A to high frequency within 300 generations. Typi- have more children in total. At equilibrium, the primary sex cally, however, if a significant proportion of the offspring of ratio equals the average parental desired sex ratio, leaving users do not exploit milk products, then very strong selec- the adult sex ratio permanently distorted. Darwin35 may tion favoring absorbers is required for A to spread. As might have been correct when he suggested that the universally be expected, given the dependence of cultural transmission male-biased birth sex ratio may reflect a history of female on genotype, the system is very sensitive to the initial fre- infanticide. quency of allele A: Thus the analysis is able to account for Kumm et d’s study also illustrates the profound effect both the spread of lactose absorption, and the culturally that. cultural processes can have on evolutionary rates.

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Figure la shows sweeping oscillations in the frequency of the bias against females among parents, coupled with oscil- (a) 1 m/T--. \ _ lations in the genetic variation that distorts the proportion of sons born. This interaction between genetic and cultural processes significantly slows down the response to selec- tion of the allele; several thousand generations are needed to reach equilibrium. In Fig. lb, the entire population is rl I biased toward sons, with the initial sex ratio maintained by OO 500 X00 1500 2000 2500 3000 3500 4000 a genetic . Here, substantial genetic change occurs within just a handful of generations. This strong se- lection results exclusively from the culturally transmitted parental activities. For illustration, consider a population where prejudicial parents act to achieve a sex ratio of three sons for every daughter, and where biased parents have no more children to compensate for those they kill. Under such circumstances, relative to impartial parents, biased parents 2 4 6 8 10 12 14 16 18 20 would have a fitness of 0.667, which represents unusually strong selection. This capacity for culture to generate strong No. of generations selection has been reported in other gene-culture analyses. For instance, Lalandl6 found that cultural influences on Fig. 1. The probabilities that genotypes A,A,, A,A,, A,A, are male are mii, m12, human mating preferences could generate strong sexual m,,, respectively. The frequencies of allele A, (solid line), the fraction 8 (dashed line) of individuals biased against daughters, the primary sex ratio, PSR (dotted line) selection for anatomical and personality traits, such as and the adult sex ratio, ASR (dotted and dashed line) are plotted over time in gen- small feet or macho male behavior. erations using the Variable Adjustment Model of Kumm et a/.1’. (a) m,,=0.5, m,,=0.65, m,,=0.8. Biased individuals seek a sex ratio of 0.7. Allele A, Transmission effects and group selection increases when rare but cannot replace A,. At equilibrium, both alleles are present and the PSR equals the ASR. Here, rapid genetic and cultural responses to each Much gene-culture coevolutionary modeling has ex- other produce oscillations that retard the approach to equilibrium. Figure la is repro- plored the adaptive advantages and disadvantages of differ- duced, with permission, from Ref. 17. (b) m,, = 0.4, m12 = 0.55, m22 = 0.7. Biased ent modes of social transmission under a variety of environ- individuals seek a sex ratio of 0.7. Here, bias remains fixed in the population and mental conditions. In spite of a plurality of approaches, a initially the frequency of A, is 0.6. The conditions used here favor a male-biased consensus is emerging regarding the adaptive advantages of sex ratio, and A, rapidly increases in frequency. The ASR remains male biased. For more details on the rates of cultural transmission and the recursions used see Ref. 17. social learning in changing environments: when environ- Figure lb is reproduced, with permission, from Ref. 53. ments are constant, social learning has no relative to genetic transmission, and cannot invadeaJ6. When environments change very fast relative to the lifetime of an , vertical cultural transmission is of little advan- because it increases the chances of acquiring locally adap- tage, since through social learning, individuals would acquire tive variants in a heterogeneous environment. Boyd and outdated information about previous or distant states of the Richerson found that when there is conformist transmis- environment. Under such circumstances, learning about the sion, interdemic group selection can be a strong force in de- environment just by trial-and-error or Pavlovian condition- termining the eventual equilibrium of the population, even ing is a better strategys,s. However, there are circumstances when sub-populations are arbitrarily large, rates when horizontally or obliquely transmitted culture may be are small, and migration rates are substantial. These authors advantageous in a variable environment, for example, when also suggest that may have driven individuals cannot find or exploit distantly located resources the evolution of an unlearned predisposition for in-group alone37, or when scrounging and scavenging interfere with favoritismig. This analysis demonstrates that when the rules the individual learning of a -producing technique%. It is of cultural transmission are different from those of genetic in slowly changing environments that learning from parents transmission, similar selective regimes may result in very is advantageous; when changes are not so fast that parents different equilibria. and offspring experience different environments, but not so slow that appropriate genetically transmitted behavior could The spread of agriculture evolve8ag. Aoki, Shida and Shigesadass used gene-culture coevolu- The theoretical argument against group selection is based tionary methods to investigate the spread of agriculture into on models that assume genetic inheritance, and the criti- a region previously occupied by hunter-gatherers. Since cisms may not hold for culturally transmitted traits. When farming allows human populations to attain a higher density individuals adopt the behavior of the majority, a conform- than hunter-gathering@, a population that adopts farming ist transmission is generated. As a result of its frequency- may increase in number and expand geographically. But dependence, conformist transmission can act to amplify farming may also spread through the conversion of hunter- differences in the frequency of cultural traits in different gatherers by social learning. In Aoki et al.3 model, there are subpopulations. Boyd and Richerson8J4J5J9have shown that no genes influencing which behavior (farming or hunting and one of the by-products of a conformist frequency-dependent gathering) is adopted. However, there are two kinds of se- bias is an increase in the strength of the group selection of lection operating, darwinian selection and cultural selection, cultural variation so that it may be a strong force relative to the latter representing the conversion of hunter-gatherers forces acting within groups, such as . Since to farmers. The model monitors the dynamics of initial farm- selection between groups may favor beliefs and attitudes ers, converted farmers and hunter-gatherers, and yields the that benefit the group at the expense of the individual, this conditions under which wave fronts of initial or converted provides a new explanation for human cooperation. Con- farmers advance. Aoki et al. found that the composition of formist transmission may be favored by natural selection the expanding wave of farmers depends on the relative mag even though it has this deleterious effect for individuals, nitude of r, versus r, t eL, where rr and rc represent intrinsic

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growth rates of initial and converted farmers, L is the carry- the neuroticism data, the narrow was close to ing capacity of environments containing hunter-gatherers, zero. Otto et d’s findings strongly repudiate the claim that and e is the rate at which hunter-gatherers are converted personality variables are not influenced by social learning46. to farmers. If rf< r, t eL, an advancing wave of converted One of the important findings to emerge from gene- farmers may be generated, provided the conversion rate is culture coevolutionary theory is that there are a variety of not too small. However, if r,> r, t eL, an advancing wave of mechanisms by which culture can lead to the transmission of initial farmers is generated. In the former case, in the wake behavior, which confers a fitness cost relative to behavioral of the advancing wave, initial farmers and converted farm- alternatives. Cavalli-Sforza and Feldman11 provided theo- ers may mix through diffusion or interbreeding. If there are retical confirmation of the intuitive notion that a maladap- genetic differences between initial and converted farmers, tive behavior may increase in frequency in a population if it this process should generate gene frequency clines in the is adopted with sufficient regularity through social learning. region occupied by the farmers. Aoki et al. also compute Boyd and Richerson’s model of indirect biass, where indi- expressions that give the rate of spread of farming. This viduals adopt the behavior of influential or successful mem- analysis provides a theoretical framework that can aid the bers of their , also found that maladaptive cultural reconstruction of major demographic changes associated variants can spread, even if associated with a substantial with the dispersal of human populations. viability disadvantage. Other gene-culture models reach the same conclusion9,‘0,‘6,47.Moreover, if social transmission Behavioral traits may result in the spread of maladaptive behavior in human An additional application of gene-culture methods is to populations, the same processes may operate among those aid understanding of the inheritance of complex behavioral animals capable of social learning. This has incited some and personality traits. Following the early work by Cavalli- controversy48, since most instances of animal social learning Sforza and Feldmans, Otto, Christiansen and Feldman5 have appear to enhance fitness. The criticism is misguided, since combined gene-culture models and path analysis methods the findings of the models are consistent with the obser- to specify how the phenotype of an individual is determined vation that most social learning will be adaptive; indeed the and how genetic and cultural effects are transmitted analyses conclude that social learning would not be favored between generations. They consider the effects of a variety if it were not generally adaptive. What the theoretical work of different mechanisms of cultural inheritance, deviations implies is that, in a spatially or temporally variable environ- from random mating, and non-transmitted environmental ment, individuals that adopt the behavior of others may components, and develop models applicable to data for acquire information that is inappropriate or sub-optimal. different patterns of relatedness between individuals. De- Such individuals might be expected to adjust their behavior spite their complexity relative to other linear models of herit- to the contingencies of their immediate surroundings, but ability41,4*,Otto et d’s models are nonetheless forced to they might pay a fitness cost in the mean time. Experimental make extremely simple assumptions about the etiology of studies are required to investigate the conditions under behavior. The significance of this analysis is not that the which social learning increases or decreases an animal’s results can tell us how to manipulate environmental factors ability to track changing environmental resources, so that to enhance a person’s intelligence or scholastic achieve- the predictions of the models can be put to the test. ment. Rather, the analysis illustrates the sensitivity of herit- Several other studies that employ gene-culture coevolu- ability estimates to the model assumptions. Otto et al. tionary methods deserve mention: Aoki and Feldman13have illustrate how a variety of simple models may fit the investigated the coevolution of recessive hereditary deaf- observed data, irrespective of whether or not they capture ness and the transgenerational inheritance of sign language. the paths of influence on a trait, leading to quite different Laland et al.4develop a gene-culture model of handedness, estimates for genetic and cultural heritability. which gives a better fit to familial and twin data than estab- Otto et al. fitted their models to familial correlations for lished genetic models. This review is necessarily incomplete, IQ collated by Bouchard and McCue43from 111 studies and since the body of gene-culture coevolutionary theory rep- found that no models gave a good fit to all the data without resents over 20 years research, by practitioners in a variety a parameter that measured the degree of common environ- of disciplines, addressing numerous different questions. ment in monozygotic twins raised apart (see also Cloninger More-comprehensive descriptions of gene-culture meth- et ~1.44).This finding, which strongly implies that mono- ods and related approaches can be found elsewheredg-51. zygotic twins raised apart share common cultural and non- The models make a variety of testable predictions: Aoki transmitted experiences, questions the validity and applic- eta/.39detail the conditions under which the spread of farm- ability of heritability estimates based solely on twin data41145. ing will generate gene frequency clines. Laland’siGmodel of In general, the best-fitting models to the IQ data include a implies that there should be society-specific large influence of common environment parameters, and correlations for anatomical traits and learned preferences for ignoring these parameters, as is common in the behavior such traits in the opposite sex. Soltis, Boyd and Richersons genetics literature, leads to a significant drop in the good- have used data on rates of population extinction among New ness of fit, and a marked increase in heritability estimates. Guinea communities to test Boyd and Richerson’s group The obtained heritability estimates for IQ are around 0.3, selection hypothesis. The models also generate insights of which contrast starkly with the inflated estimates generated relevance to other bodies of theory. For instance, Feldman using twin data alone, which range from 0.5 to 0.8. Similar and Cavalli-Sforzaio developed models of uniparental cul- findings surrounded estimates of heritability when the mod- tural transmission, which anticipated many of the findings els were applied to personality traits. Inclusion of common of quantitative genetics models of maternal inheritancezo. environment parameters uniformly lowered estimates of The clear conclusion of gene-culture coevolutionary analy- heritability, sometimes increasing the estimated influence of ses is that cultural transmission can transform evolutionary cultural transmission, and for psychoticism and neuroti- dynamics in numerous ways, implying that, for many cism data, significantly improved the fit of the model. Once questions related to or human behavior again, heritability estimates relying exclusively on twin or genetics, traditional methods and models are no longer parent-offspring correlations were inflated. In the case of appropriate.

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Acknowledgements 25 Aoki, K. (1986) A stochastic model of gene-culture coevolution Research supported in part by NIH grant GM28016 to suggested by the ‘culture historical hypothesis’ for the evolution Marc Feldman and by a Royal Society University Research of adult lactose absorption in humans, Proc.Nat/. Acad. Sci. U. S. A. Fellowship to Kevin Laland. We are grateful to Peter 83,2929-2933 Richerson for comments on this manuscript. 26 Aoki, K. (1987) Gene-culture waves of advance, J. Math. Biol. 25, 453-464 27 Dickeman, M. (1975) Demographic consequences of infanticide in References man, Annu. Rev. Ecol. Syst. 6, 107-137 1 Wiesenfeld, S.L. (1967) Sickle-cell trait in human biological and 28 Johansson, S.R. (1984) Deferred infanticide: Excess female mortal@ , Science 157,1134-1140 during childhood, in infanticide: Comparative and Evolutionary 2 Durham, W.H. (1991) &evolution: Genes, Culture andHuman Perspectives (Haufater, G. and Blaffer Hrdy, S., eds), pp. 463-485, Aldine Diversity, Stanford University Press 29 Mitra, A. (1979) Implications of Declining Sex-Ratio in India? 3 Cavalli-Sforza, L.L. and Feldman, M.W. (1973) Culti versus Population, Allied Press biological inheritance: Phenotypic transmission from parent to 30 Das Cupta, M. (1987) Selective discrimination against female children (a theory of the effect of parental phenotypes on children in rural Punjab, India, Popul. Dev. Rev. 13,77-100 children’s phenotype), Am. J. Hum. Genet. 25,618-637 31 Tuljapurkar, S., Li, N. and Feldman, M.W. (1995) High sex ratios in 4 Laland, K.N. et al. (1995) A gene-culture model of human China’s future, Science 267,874-876 handedness, Behav. Genet. 25,433-445 32 Angier, N. (1994) hot on track of gene for femaleness, 5 Otto, S., Christiansen, F. and Feldman, M.W. (1995) Genetic and cul- Neu, York Times, August 30 tural inheritance of continuous traits, Morrison Institute for 33 Am, P. et al. (1994) SRVX,a sex reversing locus in Xp21.2 + Population and Studies, Working Paper No. 64 p22.11.,Hum. Genet. 93, 389-393 6 Aoki, K. and Feldman, M.W. (1987) Toward a theory for the 34 Kumm, J. and Feldman, M.W.Gene-culture coevolution and sex evolution of cultural : Coevolution of signal ratios: II. Sex-chromosomal distorters and cultural preferences for Son and reception, Proc.Natl. Acad. Sci. U S. A. 84,7164-7168 offspring sex, Theor. Popul. Biol. (in press) 7 Aoki, K. and Feldman, M.W.(1989) Pleiotropy and preadaptation in 35 Darwin, C. (1991/1871) The Descent of Man, and Selection in Relation the evolution of human language capacity, Theor. PO@. BioL 35, to Sex, Princeton University Press 207-225 36 Cavalli-Sforza, L.L. and Feldman, M.W.(1983) Cultural versus 8 Boyd, R. and Richerson, P.J. (1985) Culture and the Evolutionary genetic , J’roc.Nat/ Acad. Sci. U S. A. 79,1331-1335 Process, University of Chicago Press 37 Laland, K.N., Richerson, P.J. and Boyd, R. (1996) Developing a 9 Feldman, M.W.,Aoki, K. and Kumm, J. Individual versus of anbnal social learning, in Social Learning in Animals: The learning: Evolutionary analysis in a fluctuating environment, Roots of Culture (Heyes, CM. and Galef, B.G.,Jr, eds), pp. 129-154, Anthropol. Sci. (in press) Academic Press 10 Feldman, M.W. and Cavalli-Sforza, L.L. (1976) Cultural and 38 Ciraldeau, L.A., Caraco, T. and Vafone, T.J. (1994) !%~cialforaging: biological evolutionary processes, selection for a trait under Individual learning and cultural transmission of innovations, complex transmission, Theor. Popul. Biol. 9,238-259 Behav. Ecol. 5,35-43 11 Cavalli-Sforza, L.L. and Feldman, M.W. (1981) Cu/tura/ Transmission 39 Aoki, K., Shida, M. and Shigesada, N. 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