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On the Theory of Gene-Culture Co-Evolution in a Variable Environment
AIWWLCOGNUTONAM, BEh!4 WOR Row L.Mellgren, editor 0 North-HolIand fiblkhing C b m p y , 1983
421
ON THE THEORY OF GENE-CULTURE CO-EVOLUTION IN A VARIABLE ENVIRONMENT
H. Ronald Pulliam State University of New York
Though some social scientists have appreciated the interactions between genetic and cultural evolution (e.g , Campbell, 1965 and hrham, 19761, the genetical evolution of behavior and the cultural evolution of human societies have been, for the most part, treated as distinct fields of inquiry. In their recent book Genes, Mind, and Culture, Charles Lumsden and E. 0. Wilson ( 1 9 8 1 ~ ~ e ~ w e ~ , t h a t e n eand t icultural c evolution are tightly coupled one to another. The basic premise of Lumsden and Wilson's argument is both simple and compelling. An individual's chances of survival and reproduction depend on his or her behavior, but the decision to adopt one behavior or another is influenced by both the individual's genotype and his or her social environment. Thus, the social environment influences the relative Darwinian fitness of individuals and, thereby, influences the course of genetic evolution. Furthermore, the genetic composition of a population influences the social environment and, thereby, influences the course of cultural evolution. Starting from this simple premise, Lumsden and Wilson construct a complicated mathematical model of the process of gene-culture co-evolution and then use their model to deduce hitherto hidden features of the human mind and of human societies.
.,
The purpose of this paper is to extend the analysis of Lumsden and Wilson by addressing what I see as three serious shortcomings of their model of gene-culture co-evolution. First, their model is so complex as, on the one hand, to discourage all but the most mathematically adept readers. In this paper, I attempt to develop a simplified version of the Lumsden and Wilson model which retains the biological and cultural richness of their original model but is nonetheless easier to understand and more amenable to analysis. Secondly, despite the fact that many authors have argued that culture is an adaptation to a rapidly changing environment, Lumsden and Wilson consider genecultural co-evolution only in a constant environment where a particular behavior always has the same fitness consequences.
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I allow the environment to change between generations and show that this substantially changes the conclusion that can be drawn concerning the importance of genetic constraints on behavior. Finally, Lumsden and Wilson consider only the situation where an individual's decision to adopt one behavior or another is influenced by the relative numbers of behavior users in the social environment and not at all by the relative success of individuals that adopt different behaviors. I argue that humans selectively imitate those individuals that they perceive as successful, and that this greatly alters the course of gene-culture co-evolution. The Lumsden-WilsonModel Lumsden and Wilson envision a co-evolutionary circuit according to which genes and culture interact to influence individual decisions. In turn, individuals decisions ultimately effect both cultural and genetic changes. In the words of Lwnsden and Wilson, "The epigenetically guided actions of the individual members create the cultural patterns, but the patterns influence the actions and, ultimately, the frequencies of the underlying genes themselves" (p. 265). Lumsden and Wilson make an important contribution to social theory by speciQing the numerous steps involved in going from genes to culture and back to genes again. At the heart of the Lumsden and Wilson model of gene-culture co-evolution is a submdel of the life cycle (Figure 1). Each individual begins life as a zygote with a certain genotype inherited from his or her parents. During early development, each individual is exposed to alternative modes of behavior, or culturgens as they are called by Lumsden and Wilson. A representation of each culturgen is stored in each individual's long-term memory and each individual evaluates the culturgens according to innate biases specific to his or here genotype and to his or her perceptions of the usage and evaluations of the same culturgens by other individuals in his or her own or parental generations. In the words of Lumsden and Wilson, the juveniles "record impressions of how many adults use each of the two culturgens" and during "exploration and play they access the culturgens still further by means of lessons, games, practice, and conversations" (p. 267). After the juvenile socialization period, each individual enters a prereproductive forage period during which tine he or she has many opportunities to make decisions concerning culturgen usage and at each decision point, may reevaluate the culturgens and may shift usage, as illustrated by the arrows between culturgens in Figure 1. The decisions made during this prereproductive period determine the amount of resources gathered
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Parental influence
@--
Prereproductive forage period
Reproductive period Peer influence
Figure 1. The co-evolutionary c i r c u i t (adapted from Lumsden and Wilson 1981). Gametes (G) carry genetic information that controls the epigenetic development of the zygotes ( Z ) . Developing individuals a r e exposed early i n l i f e t o alternative behaviors (C1 and C2) which they subsequently evaluate under parental and peer influences. The behavior f i n a l l y adopted determines success during the prereproductive "forage" period, which, in turn, l i m i t s individual contributions t o the gene pool of the next generation. Adults l i v e long enough t o enculturate the new generation but die before the next reproductive phase.
and, thereby, the individual's subsequent Darwinian fitness. According t o Lumsden and Wilson, t o "gather a resource means e i t h e r l i t e r a l l y t o accumulate food i n a d i r e c t manner o r e l s e t o secure a richer subsequent harvest through the establishment of t e r r i t o r y , attainment of rank i n a hierarchy, formation of economic and p o l i t i c a l alliances, o r other devices" (p. 2 7 0 ) .
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The first phase of adult life, is the reproductive period dur-
ing which time the resources gathered in the prereproductive forage period are converted into gametes which contribute to the zygotes of the next generation according to a fixed fertility rule involving random mating. Again, according to Lumsden and Wilson, the "variation in fertility due to alternative culturgen usage is the sole cause of variation in absolute fitness among the genotypes in the population" (p. 270). After reproduction, the adults live long enough to guard their offspring and to participate in their socialization. The adults, however, die before the beginning of the next reproductive phase, making the generations "quasi-disCrete".
A central concept in the co-evolutionary circuit is the socialization of children by members of both their own and their parent's generations. According to the Lumsden-Wilson model, at each decision point, each individual reevalutes its culturgen usage according to a transition matrix that gives the probability that an individual adopts culturgen i given that he or she last preferred culturgen j. The actual values of the transition probabilities used in making a particular decision depend on both the individual's genotype and on his or her social environment, The genotypic influence is via the specification of innate biases that determine the transition probabilities prior t o specific social influence. The Lumsden and Wilson models are greatly complicated by the fact that each individual may change his or her mind about culturgen usage many times. The result is a very complicated set of equations describing the time between decision points and the integration of innate biases and social influence into each decision. In order to simplify their model, Lumsden and Wilson assume that the prereproductive forage period is long enough that the distribution of behavioral decisions is in a steady state for all but a negligible fraction of the prereproductive period. Still the equations are so complex as to defy simple interpretation and analytic solution. In the models that follow, I assume that each individual makes only one decision regarding culturgen usage. That decision may be influenced by both the behavioral usage patterns of the adult generation and the peer generation but once it is made it is fixed f o r life. The result of this single change is to simplify greatly the mathematics without greatly altering the model's biological and cultural assumptions.
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A Simple Model of Gene-Culture Co-evolution
Following Lumsden and Wilson, I assume a large, randomly mating population with quasi-discrete generations, meaning "the adults p e r s i s t long enough t o enculturate the juveniles but die before the next breeding phase takes place" (p. 266). Also, I assume t h a t the only genetic influence on variation i n individual behavior is due t o a l l e l i c variation a t a single autosomal locus with two a l l e l e s , A and B. As do Lumsden and Wilson, I assume t h a t an individual's r e productive success i s determined solely by the individual's behavior, though variation i n behavior i s influenced by both genetic and cultural factors. In the simplest case (and the only one e x p l i c i t l y considered by Lumsden and Wilson), there is but a single habitat, and an individual who uses behavior 1 has fitness W 1 as compared t o an individual who chooses behavior 2 who has f i t n e s s W 2 . Thus, the mean fitness of individuals of genotype i j depends on the fraction (Ui.) o f such individuals using behavior 1 and the fraction (1-Ui-j using behavior 2 . In particular, the mean fitnesses of the three genotypes are given by the following equations:
The t o t a l number of individuals using behavior 1 i n generation
t i s given by:
N1t
=
UMtNMt
+
UABtNABt
+
UBCNBB t ,
where N - . gives the number o f individuals of genotype i j . The fractioi'of the population a t large using behavior 1 in generation t is given by Ut = N l t / N t , where N t i s the t o t a l population size. The fractions u u t , Umt, and U B B ~ can be thought of as genotype specific functions of the social environment experienced by individuals i n generation t. To simplify the model, I assume t h a t a l l individuals a r e socialized early in l i f e and make only one decision concerning the fitness determining behavior. In the version of the model discussed, I assume t h a t the behavioral decisions of the generation being socialized a r e influenced primarily by the behavior usage pattern of the parental generation. This assumption can be easily modified t o allow f o r both parental and peer influence on individual decisions.
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H. RDnald Pulliam
Following Lumsden and Wilson, I use the term assimilation function t o r e l a t e individual behavioral decisions t o the social environment experienced by the individual. An assimilation function U t specifies the probability t h a t an individual of genot3e i j i n generation t adopts behavior 1. In general, t h i s probability is thought t o be influenced by the usage patterns of both the parental and peer generations. In the very simplest case, however, the probability of adopting behavior 1 is given by a constant value Ui .O, regardless of the social environment experienced by the indlaidual Throughi s referred t o as the "innate bias" toout t h i s paper, wards adopting be vior 1. In the extreme case where U i - O = 1.0 and there is no social influence, it can be said thag behavior 1 is genetically determined for individuals of genotype ij Furthermore, i n any case where Uijo > 0.5, it can be said that individuals of genotype i j have a genetic predisposition i n favor of adopting behavior 1.
?:
.
.
In contrast t o an individual with a fixed probability of adopting a particular behavior, a saturable trend watcher (Lumsden and Wilson, p. 135) is more likely t o adopt whichever behavior i s most prevalent i n h i s o r her social environment. For the example discussed here, I assume that individuals i n generation t are influenced only by the usage pattern, U t - 1 , of t h e i r parental generation. In particular, I use the function
%t
=A1-
t o specify the probability that a saturable trend watcher adopts behavior 1. For a l l examples presented, I have set A1 = A2 = 0.5. As shown in Figure 2 , with these parameter values, a trend watcher i s equally l i k e l y t o adopt behavior 1 o r behavior 2 i f the parental generation i s s p l i t 50:50 i n behavior usage; however, i f most of the parental generation uses behavior 1, a trend watcher adopts behavior 1 with a probability of almost 90%. Innate bias and trend watching can be combined i n various degrees by specifying a parental socialization factor, a i j , which averages the two. In general, the probability t h a t an individual of genotype i j i n generation t adopts behavior 1 is given by the assimilation function
The parental socialization factor can take on values from 0.0 t o 1 . 0 and specifies the r e l a t i v e s e n s i t i v i t y of the adoption
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433
decision to the usage pattern of the parental generation. Figure 2 illustrates assimilation functions for various values of U . . O and a i j . 1J
0
x Jr
1.0-
._
n
% L
0.0
0.2
0.4
0.6
0,8
I,O
a
I
I.0C
Percent of parental generation using behavior 1
Figure 2 . Assimilation functions. The probability that an individual adopts a particular behavior is taken to be a function of both the social environment experienced by the individual and the individual's genotype. Each assimilation function depicted is of the form U = cii' 4 + (1-clij)Uij all three cases (see text for details). = 1.0. In Case A, UBBO = 1.0 and "BB = 0.0; in case B, UBBO = 1.0 and ciBB = 0 . 7 ; and in case C, UBBO =
&!
0.5, and
~ 1 ' -=
13
0.5.
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H. Ronald Pulliam
Under the assumption of random mating and approximate HardyWeinberg equilibrium, the mean fitness of an individual in the population is
wt = pt2w<
+
2Pt(l-Pt)
wmt +
2 t (l-pt) WBB ,
(5)
where pt is the frequency of gene A in generation t. The gene frequency in the next generation is given by the standard equation
Finally, the usage of behavior 1 in the next generation is given by
Since the fitness terms (Wij) depend on usage frequencies and the total usage depends on gene frequencies, equations 6 and 7 are tightly coupled justifying the term gene-culture coevolution. Lumsden and Wilson assume a constant foraging environment in which an individual's behavioral decision "determines both the strategy of exploitation and the reproductive success" of foragers (p. 270). I assume that the environment may change and that the behavior that results in greater fitness in one environment results in lower fitness in the second environment. In the examples to follow, the environment changes between generations according to the Markov transition matrix T =
b 2 l T22j where T i j is the probability of a transition from environment j to environment i during the time between two generations, and the probability of no change is Tjj = l-Tij.
"Gene-culture Co-evolution
43 5
The Evolution of Assimilation Functions Using equations 6 and 7 , the evolution of assimilation functions can be studied by specifying an assimilation function for each genotype and following changes in gene frequency through time. In the case of a constant environment, equations 6 and 7 can be solved directly, giving the conditions for a rare gene to increase in frequsncy. In the case of a varying environment, the evolution of assimilation functions can be studied using computer simulation. Assuming no dominance (i.e., Urn = (Urn + UBB)/~) and following the convention that in a constant environment individuals using behavior 1 have greater mean fitness, gene A increases in fitness so long as W m t > W B B ~ ,which is the case if U M ~ > U B B ~ . Thus, if one genotype has a probability of using behavior 1 which is strictly greater than that of the other genotype (e.g. Figures 2a and 2b), genes resulting in more genetically determined behavioral responses (higher UijO and lower aij) are favored by natural selection. The dynamics of gene-culture co-evolution in a constant environment can be analyzed with a simple graph whose axes are gene frequency in generation t (pt) and usage frequency in the parental generation (Ut-1). Using equations 6 and 7 , for any point (pt, Ut-1) on this graph, the changes p and U can be plotted as a single change vector indicating the direction and magnitude of co-evolutionarychange. This is illustrated in Figure 3 using the assimilation functions shown in Figure 2a and the fitness values W1 = 1.50 and W2 = 0.50. As for any situation in a constant environment where U u is strictly greater than UBB, the result is complete fixation of gene A which promotes greater usage of the more fit behavior. This result can be generalized as the statement that gene-culture co-evolution in a constant environment favors lower responsiveness to the socialization and greater genetic control of behavior. This result is similar to that of Lumsden and Wilson who argue that the "tabula rasa state, in which no innate bias exists in culturgen choice, is shown to be unstable" (p. 304) and in "all cases examined, directed cognition due to genetically biased epigenetic rules replaced undirected cognition". I argue that this generality holds on1 in a constant environas greater mean fitness ment in which one behavior alwaysl? than the other.
H. Fanald Pulliam
436
0,o
012
0,4 0,6 0,8 Gene frequency (generation t
Figure 3. Gene-culture co-evolution in a constant environment. For any gene frequency in generation t (pt), and the usage frequency of the appropriate parental generation (Ut-l), the change vector , (Ap, AU) can be calculated. For this example, UAA and UBB are as given in Case A of Figure 2.
I,o
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For gene-culture co-evolutionin a variable environment, a gene will be selected only if its geometric mean fitness exceeds that of other genes in the population. The geometric mean fitnesses depend on 1) the proportion of the time the environment favors one behavior over the other and 2) the extent to which individuals of each genotype track their changing environments.
Figure 4. Gene frequency change for gene-culture coevolution in a variable environment. In each example, the genotypes contrasted are those shown in case A of Figure 2 . For Tii = 1.0, the environment is constant and genes favoring more fixed behavioral responses are favored. In a variable environment (Tii = 0.9 and O.S), however, genes favoring greater responsiveness to the social environment are favored, on average. Figure 4 compares gene-culture co-evolution in constant and variable environments. In all three examples, all parameter values except habitat autocorrelation, are the same. As in the last example, in a constant environment, gene A which promotes greater usage of behavior 1 gradually replaces gene B which promotes greater sensitivity to the social environment. Gene-culture co-evolution in a variable environment is'shown
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H. Fbnald Pulliam
in the other two examples, where the habitat autocorrelations (Ti1 = T22) are 0.9 and 0.5, respectively. In both cases the gene promoting more variable behavioral responses gradually replaces the gene promting more fixed responses. For the two examples of gene-culture co-evolution in a variable environment shown in Figure 4, the usage frequencies did not track environmental changes but rather gradually declined to 0.5. This suggests that the evolution of moTe variable behavioral responses was not due to social learning per se. This can be shown to be-e case by comparing assimilation functions such as those shown in Figure 2c, which differ in their responsiveness to the social environment but not in their mean predisposition towards either behavior. Either of the assimilation functions shown in Figure 4c will replace the function U%in Figure 4b. However, when two functions such as those in igure 4c are compared directly, the usage frequencies of all three genotypes converge to 0.5. Once this has happened, individuals of all three genotypes are equally likely to adopt either behavior and, therefore, are equally fit. For example, a genotype which uses behavior 1 with probability 0.5 regardless of the social environment is equally fit as a trend watcher genotype that uses behavior 1 with probability 0.5 when the parental generation is split 50:SO but otherwise uses whichever behavior is more frequently used by the parental generation. In order for usage frequencies to track changes in the environment in an adaptive manner, there must be social transmission of some information about which behavior is better adapted to current conditions. This can be accomplished in one of two ways. First, social learning can be highly structured with, for example, offspring only, or at least primarily, learning from their parents (e.g. , see Cavalli-Sforza and Feldman, 1981 and Boyd and Richerson, 1976). In this situation, parents who use maladaptive behaviors have fewer offspring who learn from them. This leads to a gradual shift in usage frequency without any necessity of actual perception of the relative fitness consequences of the behaviors in question (Pulliam and Dunford 1981). Alternatively, offspring might be more likely to learn from particularly successful adults of the parental generation, regardless of their biological relatedness to those adults. This is m s t likely to occur if the costs and benefits of the various behaviors can be perceived and compared. Selective imitation of successful adults can be modeled in the following simple manner. Social learning is viewed as a two step process. First, offspring are exposed to the behaviors of the parental generation and acquire tentative usage
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439
probabilities (Vi .t, according to the assimilation functions previously given in equations 3 and 4 . The tentative usage probability is, thus,
and, if there were no further evaluations of the alternative behaviors, this would be the probability of using behavior 1. However, the new generation does not merely acquire behaviors passively from the parental generation; rather, they partially perceive and compare the relative costs and benefits of the behaviors in question. Perhaps, this is accomplished through peer contact and discussions of the successes and failures of the parental generation. The magnitude of selective imitation is specified by the genotype specific constants Sm, Sm and SBB. If in the parental generation, behavior 1 is the more successful behavior, the probability that an individual of genotype ij adopts behavior 1 is given by
u . . t = s . . + (1-s.. ) v..t. 1J
13
11
11
If however, behavior 2 is the more successful genotype, the usage probability for behavior 1 is given by Uijt =
(1-s. .) vijt . 1J
The selective imitation constants can range from 0.0, where there is no selective imitation, to 1.0, where each individual adopts with probability 1.0 whichever behavior was more beneficial to the parental generation. Natural selection favors selective imitators. Even with very modest values of selective imitation, in the range of 0.1 to 0.2, selective imitators quickly replace non-selective imitators. Furthermore, selective imitation greatly enhances the value of the social transmission of behavioral preferences from the parental generation. Recall that in the absence of selective imitation, selection is neutral with respect to a genotype that always chooses behavior 1 with probability 0.5 versus a trend watcher that chooses whichever behavior is used most frequently by the parental generation.
H. Wnald Pulliam
440
ox)
0, I
0,2
0.3
0.4
05
0,6
Gene frequency (P,)
Figure 5. The influence of imitating successful individuals on gene-culture co-evolution. The parameter values used here and in Figure 6 are U r n 0 = 0.5, = 0.0, Sm= 0.2, U 0 = 0.5, social QBB = 1.0, and SBB = 1.0. Notice imitation of successful individuals allows the usage pattern to track environmental changes in an adaptive manner, even as gene frequencies change.
8%
Figure 5 shows gene-culture co-evolution in a variable environment for the situation where all three genotypes have the same parameter values for innate bias (U O = U BO = 0.5) and selective imitation (S = SBB = 0 . 8 but Lffer in their parental socializationqactors (aM = 0.0 and cx = 1.0). Gene B quickly increases in frequcy and eventuaffy completely replaces gene A. Furthermore, usage frequencies track the environmental changes in an adaptive manner. Figure 6 indicates that the selective advantage of the trend watching genotypes is due to their greater ability to track environmental changes. After Gene B is fixed in the population, individuals
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441
have greater than an 80 percent chance of adopting whichever behavior did better in the parental generation.
t 0
20
40 60 Time ( t )
100
80
Figure 6 . Tracking a variable environment. The two genotypes differ in their responsiveness to the social environment (aAA = 0.0 and aBB = 1.0) though individuals of both genotypes imitate successful individuals in the parental generation (SM = 0.2 = SBB) As depicted in Figure 5, the greater tracking ability of genotype BB, results in a gradual fixation of gene B in the population.
.
Discussion and Conclusions The model presented above suggests that natural selection favors genetically fixed behavioral responses in a constant environment where the same response always confers greater fitness than other possible responses. However, in a variable environment, where one behavior works best in some generations and another works best in other generations, natural selection may favor less fixed behavioral responses. In particular, in a variable environment, natural selection may favor social transmission of behavior between generations. Furthermore, the value of social transmission of behavior is greatly enhanced by the ability to imitate selectively those individuals of the
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H. Wnald Pulliam
parental generation that are particularly successful. Even a moderate ability at selective imitation allows substantial intergenerational tracking of environmental changes. Lumsden and Wilson concluded that natural selection normally favors strong innate biases in behavioral choices. I have suggested that this conclusion does not generally hold for evolution in rapidly changing environments. Did the environment faced by early hominids change rapidly enough to favor social transmission of behavior over innately fixed behavior? In particuzar, did the hominid environment change so much more rapidly than that of other species so as to explain the greater role of social transmission for humans than for other species? Rose (1980) suggests that the rapid increase in hominid brain size over the last few million years is best explained as an unprecedented "mental arms race". According to this hypothesis, both the requirements of ecologieal adaptation and intraspecific competition favor increased generalized calculating ability, which, in turn, allows organisms to generate novel behavioral responses to unanticipated fitness contingencies. Since among the most complex of problems faced by an intelligent animal are those generated via intraspecific competition, the greater the mental abilities of one's competitors, the greater the utility of increased personal calculating ability. Thus, according to Rose's hypothesis what has distinguished hominid evolution is an unprecedented feedback loop whereby the evolution of intelligence created the need for yet greater intelligence. If Rose's hypothesis is essentially correct, the hominid social environment may have indeed changed very rapidly. If the evolution of intelligence effectively accelerated the pace of environmental change, it would also have increased the utility of the social transmission of behavior. Moreover, the socially transmitted information would itself have become yet more weaponry to be employed in the mental arms race. The genetic evolution of hominid intelligence may have quickly passed into a self-acceleratingperiod of gene-culture coevolution. According to the model of gene-culture co-evolution developed here, during this period, hominid mental evolution was probably characterized by a progressive eroision of genetic constraints on behavior. However, given a limited source of genetic variability, this self-accelerationphase may have been relatively short-lived, quickly passing to a phase of purely cultural evolution with little or no subsequent genetic change. Just how far gene-culture co-evolutionmay have proceeded towards the evolution as a true human tabula rasa will no doubt be debated for some time to come.
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References 1 Boyd, R. Fr Richerson, P. J. A simple dual inheritance model of the conflict between social and biological evolution. Zygon, 1976, 11, 254-262. 2
Campbell, D. T. Variation and selective retention in socio-culturalevolution. In H. R. Barringer, G. I. Blanksten E R. W. Mack, eds., Social change in developing areas. Cambridge, Mass.: Schenlanan Publishing Co., 1965.
3
Cavalli-Sforza,L. L. F, Feldman, M. W. Cultural transmission and evolution: a quantitative approach. Monographs in Population Biology (16), - Princeton, N.J.: Princeton University Press, 1981.
4 Durham. W. The adaptive significance of cultural behavior. H ~ o n a nEcology, 1976, 4, 89-121.
5 Lmden, C. J. Fr Wilson, E. 0. Genes, mind, and culture: the coevolutionary process. Cambridge, Mass., Harvard University Press, 1981. 6 Pulliam, H. R. 6 Dunford, C. Programmed to learn: an essay on the evolution of culture. New York: Cambridge University Press, 1980.
7 Rose, M. R. The mental arms race amplifier. Human Ecology, 1980, 8, 285-293.
421
ON THE THEORY OF GENE-CULTURE CO-EVOLUTION IN A VARIABLE ENVIRONMENT
H. Ronald Pulliam State University of New York
Though some social scientists have appreciated the interactions between genetic and cultural evolution (e.g , Campbell, 1965 and hrham, 19761, the genetical evolution of behavior and the cultural evolution of human societies have been, for the most part, treated as distinct fields of inquiry. In their recent book Genes, Mind, and Culture, Charles Lumsden and E. 0. Wilson ( 1 9 8 1 ~ ~ e ~ w e ~ , t h a t e n eand t icultural c evolution are tightly coupled one to another. The basic premise of Lumsden and Wilson's argument is both simple and compelling. An individual's chances of survival and reproduction depend on his or her behavior, but the decision to adopt one behavior or another is influenced by both the individual's genotype and his or her social environment. Thus, the social environment influences the relative Darwinian fitness of individuals and, thereby, influences the course of genetic evolution. Furthermore, the genetic composition of a population influences the social environment and, thereby, influences the course of cultural evolution. Starting from this simple premise, Lumsden and Wilson construct a complicated mathematical model of the process of gene-culture co-evolution and then use their model to deduce hitherto hidden features of the human mind and of human societies.
.,
The purpose of this paper is to extend the analysis of Lumsden and Wilson by addressing what I see as three serious shortcomings of their model of gene-culture co-evolution. First, their model is so complex as, on the one hand, to discourage all but the most mathematically adept readers. In this paper, I attempt to develop a simplified version of the Lumsden and Wilson model which retains the biological and cultural richness of their original model but is nonetheless easier to understand and more amenable to analysis. Secondly, despite the fact that many authors have argued that culture is an adaptation to a rapidly changing environment, Lumsden and Wilson consider genecultural co-evolution only in a constant environment where a particular behavior always has the same fitness consequences.
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H. Fbnald Pulliam
I allow the environment to change between generations and show that this substantially changes the conclusion that can be drawn concerning the importance of genetic constraints on behavior. Finally, Lumsden and Wilson consider only the situation where an individual's decision to adopt one behavior or another is influenced by the relative numbers of behavior users in the social environment and not at all by the relative success of individuals that adopt different behaviors. I argue that humans selectively imitate those individuals that they perceive as successful, and that this greatly alters the course of gene-culture co-evolution. The Lumsden-WilsonModel Lumsden and Wilson envision a co-evolutionary circuit according to which genes and culture interact to influence individual decisions. In turn, individuals decisions ultimately effect both cultural and genetic changes. In the words of Lwnsden and Wilson, "The epigenetically guided actions of the individual members create the cultural patterns, but the patterns influence the actions and, ultimately, the frequencies of the underlying genes themselves" (p. 265). Lumsden and Wilson make an important contribution to social theory by speciQing the numerous steps involved in going from genes to culture and back to genes again. At the heart of the Lumsden and Wilson model of gene-culture co-evolution is a submdel of the life cycle (Figure 1). Each individual begins life as a zygote with a certain genotype inherited from his or her parents. During early development, each individual is exposed to alternative modes of behavior, or culturgens as they are called by Lumsden and Wilson. A representation of each culturgen is stored in each individual's long-term memory and each individual evaluates the culturgens according to innate biases specific to his or here genotype and to his or her perceptions of the usage and evaluations of the same culturgens by other individuals in his or her own or parental generations. In the words of Lumsden and Wilson, the juveniles "record impressions of how many adults use each of the two culturgens" and during "exploration and play they access the culturgens still further by means of lessons, games, practice, and conversations" (p. 267). After the juvenile socialization period, each individual enters a prereproductive forage period during which tine he or she has many opportunities to make decisions concerning culturgen usage and at each decision point, may reevaluate the culturgens and may shift usage, as illustrated by the arrows between culturgens in Figure 1. The decisions made during this prereproductive period determine the amount of resources gathered
"Gene-culture Cc-evolution"
429
Parental influence
@--
Prereproductive forage period
Reproductive period Peer influence
Figure 1. The co-evolutionary c i r c u i t (adapted from Lumsden and Wilson 1981). Gametes (G) carry genetic information that controls the epigenetic development of the zygotes ( Z ) . Developing individuals a r e exposed early i n l i f e t o alternative behaviors (C1 and C2) which they subsequently evaluate under parental and peer influences. The behavior f i n a l l y adopted determines success during the prereproductive "forage" period, which, in turn, l i m i t s individual contributions t o the gene pool of the next generation. Adults l i v e long enough t o enculturate the new generation but die before the next reproductive phase.
and, thereby, the individual's subsequent Darwinian fitness. According t o Lumsden and Wilson, t o "gather a resource means e i t h e r l i t e r a l l y t o accumulate food i n a d i r e c t manner o r e l s e t o secure a richer subsequent harvest through the establishment of t e r r i t o r y , attainment of rank i n a hierarchy, formation of economic and p o l i t i c a l alliances, o r other devices" (p. 2 7 0 ) .
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H. Rcnald Pulliam
The first phase of adult life, is the reproductive period dur-
ing which time the resources gathered in the prereproductive forage period are converted into gametes which contribute to the zygotes of the next generation according to a fixed fertility rule involving random mating. Again, according to Lumsden and Wilson, the "variation in fertility due to alternative culturgen usage is the sole cause of variation in absolute fitness among the genotypes in the population" (p. 270). After reproduction, the adults live long enough to guard their offspring and to participate in their socialization. The adults, however, die before the beginning of the next reproductive phase, making the generations "quasi-disCrete".
A central concept in the co-evolutionary circuit is the socialization of children by members of both their own and their parent's generations. According to the Lumsden-Wilson model, at each decision point, each individual reevalutes its culturgen usage according to a transition matrix that gives the probability that an individual adopts culturgen i given that he or she last preferred culturgen j. The actual values of the transition probabilities used in making a particular decision depend on both the individual's genotype and on his or her social environment, The genotypic influence is via the specification of innate biases that determine the transition probabilities prior t o specific social influence. The Lumsden and Wilson models are greatly complicated by the fact that each individual may change his or her mind about culturgen usage many times. The result is a very complicated set of equations describing the time between decision points and the integration of innate biases and social influence into each decision. In order to simplify their model, Lumsden and Wilson assume that the prereproductive forage period is long enough that the distribution of behavioral decisions is in a steady state for all but a negligible fraction of the prereproductive period. Still the equations are so complex as to defy simple interpretation and analytic solution. In the models that follow, I assume that each individual makes only one decision regarding culturgen usage. That decision may be influenced by both the behavioral usage patterns of the adult generation and the peer generation but once it is made it is fixed f o r life. The result of this single change is to simplify greatly the mathematics without greatly altering the model's biological and cultural assumptions.
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A Simple Model of Gene-Culture Co-evolution
Following Lumsden and Wilson, I assume a large, randomly mating population with quasi-discrete generations, meaning "the adults p e r s i s t long enough t o enculturate the juveniles but die before the next breeding phase takes place" (p. 266). Also, I assume t h a t the only genetic influence on variation i n individual behavior is due t o a l l e l i c variation a t a single autosomal locus with two a l l e l e s , A and B. As do Lumsden and Wilson, I assume t h a t an individual's r e productive success i s determined solely by the individual's behavior, though variation i n behavior i s influenced by both genetic and cultural factors. In the simplest case (and the only one e x p l i c i t l y considered by Lumsden and Wilson), there is but a single habitat, and an individual who uses behavior 1 has fitness W 1 as compared t o an individual who chooses behavior 2 who has f i t n e s s W 2 . Thus, the mean fitness of individuals of genotype i j depends on the fraction (Ui.) o f such individuals using behavior 1 and the fraction (1-Ui-j using behavior 2 . In particular, the mean fitnesses of the three genotypes are given by the following equations:
The t o t a l number of individuals using behavior 1 i n generation
t i s given by:
N1t
=
UMtNMt
+
UABtNABt
+
UBCNBB t ,
where N - . gives the number o f individuals of genotype i j . The fractioi'of the population a t large using behavior 1 in generation t is given by Ut = N l t / N t , where N t i s the t o t a l population size. The fractions u u t , Umt, and U B B ~ can be thought of as genotype specific functions of the social environment experienced by individuals i n generation t. To simplify the model, I assume t h a t a l l individuals a r e socialized early in l i f e and make only one decision concerning the fitness determining behavior. In the version of the model discussed, I assume t h a t the behavioral decisions of the generation being socialized a r e influenced primarily by the behavior usage pattern of the parental generation. This assumption can be easily modified t o allow f o r both parental and peer influence on individual decisions.
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H. RDnald Pulliam
Following Lumsden and Wilson, I use the term assimilation function t o r e l a t e individual behavioral decisions t o the social environment experienced by the individual. An assimilation function U t specifies the probability t h a t an individual of genot3e i j i n generation t adopts behavior 1. In general, t h i s probability is thought t o be influenced by the usage patterns of both the parental and peer generations. In the very simplest case, however, the probability of adopting behavior 1 is given by a constant value Ui .O, regardless of the social environment experienced by the indlaidual Throughi s referred t o as the "innate bias" toout t h i s paper, wards adopting be vior 1. In the extreme case where U i - O = 1.0 and there is no social influence, it can be said thag behavior 1 is genetically determined for individuals of genotype ij Furthermore, i n any case where Uijo > 0.5, it can be said that individuals of genotype i j have a genetic predisposition i n favor of adopting behavior 1.
?:
.
.
In contrast t o an individual with a fixed probability of adopting a particular behavior, a saturable trend watcher (Lumsden and Wilson, p. 135) is more likely t o adopt whichever behavior i s most prevalent i n h i s o r her social environment. For the example discussed here, I assume that individuals i n generation t are influenced only by the usage pattern, U t - 1 , of t h e i r parental generation. In particular, I use the function
%t
=A1-
t o specify the probability that a saturable trend watcher adopts behavior 1. For a l l examples presented, I have set A1 = A2 = 0.5. As shown in Figure 2 , with these parameter values, a trend watcher i s equally l i k e l y t o adopt behavior 1 o r behavior 2 i f the parental generation i s s p l i t 50:50 i n behavior usage; however, i f most of the parental generation uses behavior 1, a trend watcher adopts behavior 1 with a probability of almost 90%. Innate bias and trend watching can be combined i n various degrees by specifying a parental socialization factor, a i j , which averages the two. In general, the probability t h a t an individual of genotype i j i n generation t adopts behavior 1 is given by the assimilation function
The parental socialization factor can take on values from 0.0 t o 1 . 0 and specifies the r e l a t i v e s e n s i t i v i t y of the adoption
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decision to the usage pattern of the parental generation. Figure 2 illustrates assimilation functions for various values of U . . O and a i j . 1J
0
x Jr
1.0-
._
n
% L
0.0
0.2
0.4
0.6
0,8
I,O
a
I
I.0C
Percent of parental generation using behavior 1
Figure 2 . Assimilation functions. The probability that an individual adopts a particular behavior is taken to be a function of both the social environment experienced by the individual and the individual's genotype. Each assimilation function depicted is of the form U = cii' 4 + (1-clij)Uij all three cases (see text for details). = 1.0. In Case A, UBBO = 1.0 and "BB = 0.0; in case B, UBBO = 1.0 and ciBB = 0 . 7 ; and in case C, UBBO =
&!
0.5, and
~ 1 ' -=
13
0.5.
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H. Ronald Pulliam
Under the assumption of random mating and approximate HardyWeinberg equilibrium, the mean fitness of an individual in the population is
wt = pt2w<
+
2Pt(l-Pt)
wmt +
2 t (l-pt) WBB ,
(5)
where pt is the frequency of gene A in generation t. The gene frequency in the next generation is given by the standard equation
Finally, the usage of behavior 1 in the next generation is given by
Since the fitness terms (Wij) depend on usage frequencies and the total usage depends on gene frequencies, equations 6 and 7 are tightly coupled justifying the term gene-culture coevolution. Lumsden and Wilson assume a constant foraging environment in which an individual's behavioral decision "determines both the strategy of exploitation and the reproductive success" of foragers (p. 270). I assume that the environment may change and that the behavior that results in greater fitness in one environment results in lower fitness in the second environment. In the examples to follow, the environment changes between generations according to the Markov transition matrix T =
b 2 l T22j where T i j is the probability of a transition from environment j to environment i during the time between two generations, and the probability of no change is Tjj = l-Tij.
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43 5
The Evolution of Assimilation Functions Using equations 6 and 7 , the evolution of assimilation functions can be studied by specifying an assimilation function for each genotype and following changes in gene frequency through time. In the case of a constant environment, equations 6 and 7 can be solved directly, giving the conditions for a rare gene to increase in frequsncy. In the case of a varying environment, the evolution of assimilation functions can be studied using computer simulation. Assuming no dominance (i.e., Urn = (Urn + UBB)/~) and following the convention that in a constant environment individuals using behavior 1 have greater mean fitness, gene A increases in fitness so long as W m t > W B B ~ ,which is the case if U M ~ > U B B ~ . Thus, if one genotype has a probability of using behavior 1 which is strictly greater than that of the other genotype (e.g. Figures 2a and 2b), genes resulting in more genetically determined behavioral responses (higher UijO and lower aij) are favored by natural selection. The dynamics of gene-culture co-evolution in a constant environment can be analyzed with a simple graph whose axes are gene frequency in generation t (pt) and usage frequency in the parental generation (Ut-1). Using equations 6 and 7 , for any point (pt, Ut-1) on this graph, the changes p and U can be plotted as a single change vector indicating the direction and magnitude of co-evolutionarychange. This is illustrated in Figure 3 using the assimilation functions shown in Figure 2a and the fitness values W1 = 1.50 and W2 = 0.50. As for any situation in a constant environment where U u is strictly greater than UBB, the result is complete fixation of gene A which promotes greater usage of the more fit behavior. This result can be generalized as the statement that gene-culture co-evolution in a constant environment favors lower responsiveness to the socialization and greater genetic control of behavior. This result is similar to that of Lumsden and Wilson who argue that the "tabula rasa state, in which no innate bias exists in culturgen choice, is shown to be unstable" (p. 304) and in "all cases examined, directed cognition due to genetically biased epigenetic rules replaced undirected cognition". I argue that this generality holds on1 in a constant environas greater mean fitness ment in which one behavior alwaysl? than the other.
H. Fanald Pulliam
436
0,o
012
0,4 0,6 0,8 Gene frequency (generation t
Figure 3. Gene-culture co-evolution in a constant environment. For any gene frequency in generation t (pt), and the usage frequency of the appropriate parental generation (Ut-l), the change vector , (Ap, AU) can be calculated. For this example, UAA and UBB are as given in Case A of Figure 2.
I,o
"Gene-culture Co-evolution"
43 7
For gene-culture co-evolutionin a variable environment, a gene will be selected only if its geometric mean fitness exceeds that of other genes in the population. The geometric mean fitnesses depend on 1) the proportion of the time the environment favors one behavior over the other and 2) the extent to which individuals of each genotype track their changing environments.
Figure 4. Gene frequency change for gene-culture coevolution in a variable environment. In each example, the genotypes contrasted are those shown in case A of Figure 2 . For Tii = 1.0, the environment is constant and genes favoring more fixed behavioral responses are favored. In a variable environment (Tii = 0.9 and O.S), however, genes favoring greater responsiveness to the social environment are favored, on average. Figure 4 compares gene-culture co-evolution in constant and variable environments. In all three examples, all parameter values except habitat autocorrelation, are the same. As in the last example, in a constant environment, gene A which promotes greater usage of behavior 1 gradually replaces gene B which promotes greater sensitivity to the social environment. Gene-culture co-evolution in a variable environment is'shown
43 8
H. Fbnald Pulliam
in the other two examples, where the habitat autocorrelations (Ti1 = T22) are 0.9 and 0.5, respectively. In both cases the gene promoting more variable behavioral responses gradually replaces the gene promting more fixed responses. For the two examples of gene-culture co-evolution in a variable environment shown in Figure 4, the usage frequencies did not track environmental changes but rather gradually declined to 0.5. This suggests that the evolution of moTe variable behavioral responses was not due to social learning per se. This can be shown to be-e case by comparing assimilation functions such as those shown in Figure 2c, which differ in their responsiveness to the social environment but not in their mean predisposition towards either behavior. Either of the assimilation functions shown in Figure 4c will replace the function U%in Figure 4b. However, when two functions such as those in igure 4c are compared directly, the usage frequencies of all three genotypes converge to 0.5. Once this has happened, individuals of all three genotypes are equally likely to adopt either behavior and, therefore, are equally fit. For example, a genotype which uses behavior 1 with probability 0.5 regardless of the social environment is equally fit as a trend watcher genotype that uses behavior 1 with probability 0.5 when the parental generation is split 50:SO but otherwise uses whichever behavior is more frequently used by the parental generation. In order for usage frequencies to track changes in the environment in an adaptive manner, there must be social transmission of some information about which behavior is better adapted to current conditions. This can be accomplished in one of two ways. First, social learning can be highly structured with, for example, offspring only, or at least primarily, learning from their parents (e.g. , see Cavalli-Sforza and Feldman, 1981 and Boyd and Richerson, 1976). In this situation, parents who use maladaptive behaviors have fewer offspring who learn from them. This leads to a gradual shift in usage frequency without any necessity of actual perception of the relative fitness consequences of the behaviors in question (Pulliam and Dunford 1981). Alternatively, offspring might be more likely to learn from particularly successful adults of the parental generation, regardless of their biological relatedness to those adults. This is m s t likely to occur if the costs and benefits of the various behaviors can be perceived and compared. Selective imitation of successful adults can be modeled in the following simple manner. Social learning is viewed as a two step process. First, offspring are exposed to the behaviors of the parental generation and acquire tentative usage
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439
probabilities (Vi .t, according to the assimilation functions previously given in equations 3 and 4 . The tentative usage probability is, thus,
and, if there were no further evaluations of the alternative behaviors, this would be the probability of using behavior 1. However, the new generation does not merely acquire behaviors passively from the parental generation; rather, they partially perceive and compare the relative costs and benefits of the behaviors in question. Perhaps, this is accomplished through peer contact and discussions of the successes and failures of the parental generation. The magnitude of selective imitation is specified by the genotype specific constants Sm, Sm and SBB. If in the parental generation, behavior 1 is the more successful behavior, the probability that an individual of genotype ij adopts behavior 1 is given by
u . . t = s . . + (1-s.. ) v..t. 1J
13
11
11
If however, behavior 2 is the more successful genotype, the usage probability for behavior 1 is given by Uijt =
(1-s. .) vijt . 1J
The selective imitation constants can range from 0.0, where there is no selective imitation, to 1.0, where each individual adopts with probability 1.0 whichever behavior was more beneficial to the parental generation. Natural selection favors selective imitators. Even with very modest values of selective imitation, in the range of 0.1 to 0.2, selective imitators quickly replace non-selective imitators. Furthermore, selective imitation greatly enhances the value of the social transmission of behavioral preferences from the parental generation. Recall that in the absence of selective imitation, selection is neutral with respect to a genotype that always chooses behavior 1 with probability 0.5 versus a trend watcher that chooses whichever behavior is used most frequently by the parental generation.
H. Wnald Pulliam
440
ox)
0, I
0,2
0.3
0.4
05
0,6
Gene frequency (P,)
Figure 5. The influence of imitating successful individuals on gene-culture co-evolution. The parameter values used here and in Figure 6 are U r n 0 = 0.5, = 0.0, Sm= 0.2, U 0 = 0.5, social QBB = 1.0, and SBB = 1.0. Notice imitation of successful individuals allows the usage pattern to track environmental changes in an adaptive manner, even as gene frequencies change.
8%
Figure 5 shows gene-culture co-evolution in a variable environment for the situation where all three genotypes have the same parameter values for innate bias (U O = U BO = 0.5) and selective imitation (S = SBB = 0 . 8 but Lffer in their parental socializationqactors (aM = 0.0 and cx = 1.0). Gene B quickly increases in frequcy and eventuaffy completely replaces gene A. Furthermore, usage frequencies track the environmental changes in an adaptive manner. Figure 6 indicates that the selective advantage of the trend watching genotypes is due to their greater ability to track environmental changes. After Gene B is fixed in the population, individuals
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have greater than an 80 percent chance of adopting whichever behavior did better in the parental generation.
t 0
20
40 60 Time ( t )
100
80
Figure 6 . Tracking a variable environment. The two genotypes differ in their responsiveness to the social environment (aAA = 0.0 and aBB = 1.0) though individuals of both genotypes imitate successful individuals in the parental generation (SM = 0.2 = SBB) As depicted in Figure 5, the greater tracking ability of genotype BB, results in a gradual fixation of gene B in the population.
.
Discussion and Conclusions The model presented above suggests that natural selection favors genetically fixed behavioral responses in a constant environment where the same response always confers greater fitness than other possible responses. However, in a variable environment, where one behavior works best in some generations and another works best in other generations, natural selection may favor less fixed behavioral responses. In particular, in a variable environment, natural selection may favor social transmission of behavior between generations. Furthermore, the value of social transmission of behavior is greatly enhanced by the ability to imitate selectively those individuals of the
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H. Wnald Pulliam
parental generation that are particularly successful. Even a moderate ability at selective imitation allows substantial intergenerational tracking of environmental changes. Lumsden and Wilson concluded that natural selection normally favors strong innate biases in behavioral choices. I have suggested that this conclusion does not generally hold for evolution in rapidly changing environments. Did the environment faced by early hominids change rapidly enough to favor social transmission of behavior over innately fixed behavior? In particuzar, did the hominid environment change so much more rapidly than that of other species so as to explain the greater role of social transmission for humans than for other species? Rose (1980) suggests that the rapid increase in hominid brain size over the last few million years is best explained as an unprecedented "mental arms race". According to this hypothesis, both the requirements of ecologieal adaptation and intraspecific competition favor increased generalized calculating ability, which, in turn, allows organisms to generate novel behavioral responses to unanticipated fitness contingencies. Since among the most complex of problems faced by an intelligent animal are those generated via intraspecific competition, the greater the mental abilities of one's competitors, the greater the utility of increased personal calculating ability. Thus, according to Rose's hypothesis what has distinguished hominid evolution is an unprecedented feedback loop whereby the evolution of intelligence created the need for yet greater intelligence. If Rose's hypothesis is essentially correct, the hominid social environment may have indeed changed very rapidly. If the evolution of intelligence effectively accelerated the pace of environmental change, it would also have increased the utility of the social transmission of behavior. Moreover, the socially transmitted information would itself have become yet more weaponry to be employed in the mental arms race. The genetic evolution of hominid intelligence may have quickly passed into a self-acceleratingperiod of gene-culture coevolution. According to the model of gene-culture co-evolution developed here, during this period, hominid mental evolution was probably characterized by a progressive eroision of genetic constraints on behavior. However, given a limited source of genetic variability, this self-accelerationphase may have been relatively short-lived, quickly passing to a phase of purely cultural evolution with little or no subsequent genetic change. Just how far gene-culture co-evolutionmay have proceeded towards the evolution as a true human tabula rasa will no doubt be debated for some time to come.
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References 1 Boyd, R. Fr Richerson, P. J. A simple dual inheritance model of the conflict between social and biological evolution. Zygon, 1976, 11, 254-262. 2
Campbell, D. T. Variation and selective retention in socio-culturalevolution. In H. R. Barringer, G. I. Blanksten E R. W. Mack, eds., Social change in developing areas. Cambridge, Mass.: Schenlanan Publishing Co., 1965.
3
Cavalli-Sforza,L. L. F, Feldman, M. W. Cultural transmission and evolution: a quantitative approach. Monographs in Population Biology (16), - Princeton, N.J.: Princeton University Press, 1981.
4 Durham. W. The adaptive significance of cultural behavior. H ~ o n a nEcology, 1976, 4, 89-121.
5 Lmden, C. J. Fr Wilson, E. 0. Genes, mind, and culture: the coevolutionary process. Cambridge, Mass., Harvard University Press, 1981. 6 Pulliam, H. R. 6 Dunford, C. Programmed to learn: an essay on the evolution of culture. New York: Cambridge University Press, 1980.
7 Rose, M. R. The mental arms race amplifier. Human Ecology, 1980, 8, 285-293.