Gene-Culture Coinheritance of a Behavioral Trait

vol. 192, no. 3 the american naturalist september 2018

Elliot G. Aguilar* and Erol Akçay

University of Pennsylvania, Philadelphia, Pennsylvania 19104 Submitted October 5, 2017; Accepted April 5, 2018; Electronically published July 16, 2018 Online enhancements: appendix. abstract: Many physical and behavioral traits in animals, including havior (Pérusse et al. 1994), handedness (Laland 2008), fer- humans, are inherited both genetically and culturally. The presence of tility (Kosova et al. 2010; Alvergne et al. 2011; Colleran and different inheritance systems affecting the same trait can result in com- Mace2015;Colleran2016),andAlzheimer’sdiseasebiomark- plex evolutionary dynamics. Here, we present a general model that elu- ers (Levy et al. 2016) in humans as well as song form in pas- cidates the distinct roles of cultural and genetic inheritance systems and serine birds (Freeberg 2000; Feher et al. 2009), mate choice their interaction in driving the evolution of complex phenotypes. In par- in Trinidadian guppies (Dugatkin 1992), and foraging be- ticular, we derive a Price equation that incorporates both cultural and havior in bottlenose dolphins (Krŭtzen et al. 2005). In each genetic inheritance of a phenotype where the effects of genes and cul- fi ture are additive. We then use this equation to investigate whether a of these cases, an important tness-related trait or behavior genetically maladaptive phenotype can evolve under dual transmission. is determined by not only genetic inheritance but also cul- We examine the special case of altruism using an illustrative model and tural transmission from individuals that may not have con- show that cultural selection can overcome genetic selection when the tributedanygeneticmaterial.Giventheimportanceofgenetic variance in culture is sufficiently high with respect to genes. We also and nongenetic inheritance in determining so many behav- show that the presence of cultural transmission can modify genetic se- ioral traits, it is imperative to develop a better theoretical un- lection itself, making genetic selection more favorable to a trait than derstanding of how such coinheritance affects the evolution under purely genetic inheritance. Last, we consider the effect of different timescales of genetic and cultural transmission. We discuss the im- of behavioral traits. plications of our results for understanding the evolution of important In recent years, evolutionary theorists have begun to in- coinherited behaviors, including how our framework can be used to vestigate the consequences of multiple inheritance systems generate quantitative estimates of selection pressures required for a ge- (Otto et al. 1995; Bonduriansky and Day 2009; Day and Bon- netically maladaptive trait to evolve. duriansky 2011). In a pair of articles, Day and Bondurianski Keywords: gene-culture coevolution, altruism, multiple inheritance, used the Price equation to construct a general framework for Price equation. modeling genetic and nongenetic traits that jointly determined phenotype. However, their approach was limited to vertical transmission of the nongenetic trait and thus kept Introduction track of only the reproductive fitness consequences of both systems of inheritance. While this approach gives a mathe- Behavioral traits are among the most complex phenotypes matically valid description of evolutionary change in a trait, under study in evolutionary biology. At the heart of that com- it obscures the separate roles of genetic and nongenetic in- plexity is the interaction between genetic inheritance and the heritance and selection in causing that change. In another environment (Turkheimer 2000). In organisms with social recent article, El Mouden et al. (2014) developed a Price equa- learning, a significant component of the environment can tion for cultural evolution and addressed the question of how be conspecific individuals who serve as models for socially potential conflicts between cultural and genetic selection might learned behaviors, leading to cultural transmission. Differ- be resolved. However, their work considered cultural and ge- ential cultural transmission of behaviors or traits can lead netic transmission of (and selection on) a trait as mutually ex- to an evolutionary process that operates in tandem with ge- clusive alternatives and did not attempt to model the cotrans- netic evolution. Examples of behaviors that are influenced by mission of a single trait through both culture and genetics both genetic and cultural transmission span a wide range, (for more on this point, see “Discussion”). such as antisocial behavior (Maes et al. 2007), parental be- To account for the distinct causal roles of cultural and genetic selection, one needs to consider fitness measures in both * Corresponding author; email: [email protected]. ORCIDs: Akçay, http://orcid.org/0000-0001-8149-7124. systems of inheritance simultaneously. This is ultimately be- – q cause ancestors in one system may not be identical to the Am. Nat. 2018. Vol. 192, pp. 000 000. 2018 by The University of Chicago. fi 0003-0147/2018/19203-57995$15.00. All rights reserved. ancestors in another. A tness measure implies a mapping DOI: 10.1086/698872 from ancestral to descendant individuals: ancestors who map

(i.e., contribute hereditary material) to more descendants ple forms of inheritance are present. This point was high- have higher fitness. Multiple inheritance systems mean the lighted nearly 40 years ago by Richerson and Boyd (1978), possibilityofmultiplemappings.Forexample,imagineapop- who remarked that when both genes and culture determine ulation of asexual organisms (as in fig. 1) with a phenotype a single phenotype, the value of the phenotype that maximizes fi p determined by genetic and cultural inheritance. Let pa be genetic tness may differ from the value that maximizes cul- fi fl the phenotype of an ancestor and pd the phenotype of her ge- tural tness, leading to con icts between the two inheritance netic descendant. If both genes and culture are inherited from systems. Modeling phenotype as the outcome of a nonzero the same ancestor and we assume no flaws in transmission sum game between cultural and genetic inheritance, they p and identical environmental effects, then pa pd. However, showed the conditions under which the Nash equilibrium if one’s genetic parent and cultural role model are not the phenotype would be the cultural fitness optimum and not ( fi same individual, then it is possible that pa pd.Ifwecon- the optimum value for genetic tness. In the ensuing de- sider the mapping solely from genetic parents to offspring, cades, cultural evolution theory has largely focused on the this discrepancy will appear simply to be an unexplained de- case when the genetic trait encodes a learning rule that deviation between parents and offspring. However, also keep- termines how a cultural trait is acquired (Cavalli-Sforza and ing track of the mapping between cultural role models and Feldman 1981; Boyd and Richerson 1988; Boyd et al. 2003; pupils, we might find that certain individuals map to more Guzmán et al. 2007; Lehmann et al. 2008). By contrast, the cultural descendants as a result of their phenotype because problem of conflict between inheritance systems that affect of selection in the cultural domain. Thus, what appears un- the same trait has received surprisingly little attention, with der one mapping to be an unexplained deviation between the notable exception of the model of Findlay (1992), which parent and offspring is revealed under another mapping to treated only vertical cultural transmission. This dearth of at- be a force of selection in its own right. tention is particularly surprising, given the anthropological The argument above underscores the importance of con- evidence for behavioral and social practices in humans that sidering fitness in each domain of inheritance when multi- reduce reproductive fitness (Glanville 1987; Logan and Qirko

a A1 A2 A3

D1 D2 D3

b gcPhenotypes Reproductive ﬁtness Cultural ﬁtness 10 = 1 = 1 = 0 A1 pa1 w1 s1 10 = 1 = 2 = 0 A2 pa2 w2 s2 11 = 2 = 0 = 3 A3 pa3 w3 s3 11 = 2 D1 pd1 11 = 2 D2 pd2 11 = 2 D3 pd3

Figure 1: a, Diagram shows the hereditary relationships between ancestors (A1, A2, A3) and descendants (D1, D2, D3). Solid lines indicate reproductive relationships, while dashed lines show cultural learning. While A3 sired no offspring, he is the cultural learning model for all descendants. b, Genotype, culture type, phenotypic, and ﬁtness values for each ancestor and descendant (excepting ﬁtness values). Each p descendant has only one genetic and cultural ancestor; thus, each solid edge corresponds to vij 1, and each dashed edge corresponds to p gij 1.

1996). Examples include clubbing pregnant women to in- ness, conscientiousness; Goldberg 1993), or a morphological duce birth in Colombia (Reichel-Dolmatoff and Reichel- one such as body size. We assume that the effects of genetic Dolmatoff 2013), unhygienic neonatal care practices in Ban- and cultural inheritance are additive; that is, we express an gladesh (McConville 1988), and folk medical practices such individual’s phenotype as the following: as ingesting rhino horn (Ayling 2013) or bloodletting (Woot- p 1 1 : ton 2007). While these practices are undoubtedly inherited pj cj gj e ð1Þ through cultural transmission, they are very likely also influenced by genetic inheritance, at the very least via broader The final term, e, is the effect of the environment that does behavioral traits with a significant genetic component, such not include cultural transmission (i.e., is not heritable). The as risk-taking, a trait that itself shows cross-cultural varia- two terms cj and gj will be referred to as the culture type and tion (Weber and Hsee 1998; Hsee and Weber 1999; Cesarini genotype, respectively. These terms only describe continuous et al. 2009). Conflict between selection in the two inheritance variables and are not meant to imply any particular mode of domains provides a potential explanation for the spread of inheritance (e.g., haploidy, diploidy). If we take extraversion such maladaptive traits. Recent work (El Mouden et al. 2014; as an example, gj might represent a genetic predisposition Morin 2014) has claimed that such conflicts will always be toward extraversion (e.g., a polygenic score), while cj might resolved in favor of reproductive fitness in the long term. represent the overall exposure j has had to individuals of Yet because this work has not explicitly modeled both types varying levels of extraversion, including the relative influ- of selection acting on a trait simultaneously, the authors did ence they have had on j. Equation (1) is similar to the quan- not actually address the question of what happens to a trait titative genetic formulation of Otto et al. (1995). The culture that is under simultaneous, conflicting selection through types and genotypes are determined by the corresponding genetic and cultural transmission. We take up this precise values in j’s genetic and cultural ancestors. We assume that question, which reveals a more complex picture than previ- a descendant’s culture type and genotype are linear functions ously recognized. of her ancestors’ values given by

We derive a Price equation that explicitly incorporates XN both genetic and cultural inheritance. The Price equation is p 1 gj nijgi Dgj, ð2aÞ an exact description of an evolutionary process under a cer- ip1 tain set of minimal assumptions (Price 1970; Frank 1998; XN Rice 2004). Soon after its introduction, Hamilton (1975) c p g c 1 Dc , ð2bÞ pointed out that the Price equation can apply equally well j ij i j ip1 to cultural transmission, and recent authors have developed it exclusively for that purpose (Henrich 2004a; El Mouden where ancestral individuals are indexed by i and descendant fi et al. 2014). Others have also extended the Price equation to individuals by j. The coef cients vij and gij are the weights include multiple forms of inheritance (Helanterä and Uller that describe the degree of influence an ancestor i has on de- 2010; Day and Bonduriansky 2011), although with the limi- scendant j in the genetic and culturalP domain, respectively.P fi N p N p tation of a single tness measure. Here, we use a simple addi- These weights are normalized so that ip1nij ip1gij tive model to derive a Price equation that incorporates both 1. For example, in a haploid organism, for an ancestor i, all domains of inheritance and their relevant fitness measures vij are either 1 (if j is a descendant of i) or 0 (if j is not a de- p directly. We then analyze the condition for the evolution of scendant of i). In the diploid, sexually reproducing case, nij = a phenotype when selection in the two domains is in conflict, f0, 1 2g, if we assume codominance. Similarly, the gij can taking altruistic behavior as a special case and extending our accommodate any particular mode of information transfer result to differing timescales of genetic and cultural transmis- from cultural parents to offspring. By normalizing these sion. Our model elucidates the conditions under which se- weights, we have assumed that all individuals have at least lection in one domain can overcome counterselection in the one genetic and cultural ancestor. While this assumption is other domain. We end with a discussion of the implications perfectly natural for genetic reproduction, one can imagine of our results for understanding the evolution of potentially traits for which some individuals might receive no cultural maladaptive behaviors. input or more cultural input than genetic. The delta terms

Dgj and Dcj represent departures in j from the inherited genetic and cultural values. As an example, Dg may be nonzero Gene-Culture Price Equation j in the event of mutation or recombination, while Dcj may be We model the change in a continuous phenotype, denoted nonzero because of individual learning or experience. This by p, that results from both genetic and cultural inheritance. model generalizes that presented by El Mouden et al. (2014) We can take p to represent a behavioral trait, such as one to multiple inheritance, although our analysis and some con- of the big ﬁve personality traits (e.g., extraversion, agreeable- clusions differ.

Fitness captures the contribution of an ancestor to the results from the fact that we are measuring the differences ’ next generation. In this model, that contribution, whether (Dgj, Dcj) between an individual offspring s type and its an- genetic or cultural, is determined by the weights given to an cestral contribution and then averaging over descendants. ancestor by her descendants, a formulation introduced by El The standard Price equation uses a single fitness mea- Mouden et al. (2014). Thus, the fitness of an individual in ei- sure and provides a mathematically valid description of ther domain of inheritance is simply the sum of the weights evolutionary change. But in order to understand the effect given to an ancestor by all descendants. Specifically,P we de- of nongenetic inheritance, we need to keep track of two fi fi p N0 fi fi ne the genetic tness of anP ancestor i as wi jp1nij and kinds of tness. To see why, consider gure 1, which de- fi p N0 the cultural tness as si jp1gij, where the sums are taken picts an asexually reproducing population where descendants over the descendant generation and N0 is the number of de- receive both genes and culture from ancestors, although not scendants. If we recall the haploid case from above for vij, necessarily the same ancestors. Arrows with solid lines indi- ’ then wi is just the sum of i s offspring. For si, the values can cate parent-offspring relationships, and arrows with dashed range from 0 to a maximum of N0, which occurs when i is lines indicate social learning relationships. Using only repro- the sole cultural ancestor of all descendants in the popula- ductive fitness (arrows with solid lines), we could capture fi tion. In the cultural domain, the de nition of si shows that the evolutionary change with the standard Price equation: fl p = 1 p 2 = 1 p = the total amount of in uence an ancestor i has on descen- Dp (1 w)cov(wi, pi) E[wDp] 1 3 1 2 3. This dant phenotypes is what matters most, not just the number expression indicates that the effect of natural selection is to of individuals over which i has had some nonzero influence. oppose increases in the phenotype, but it leads us to conclude Using these definitions and equation (1), we can derive that the transmission term, for reasons that are obscure, the following Price equation to describe the evolutionary more than compensates for natural selection. Thus, it ap- change in the mean value of the phenotype (see app. sec. A1; pears that natural selection has been overtaken by a faulty in- appendix is available online): heritance system. However, computing the terms in equa- p p = 〈 〉 p tion (3), we have cov(wi, gi) 0, cov(si, ci) 2 3, Dgj 0, p 1 1 1 1 〈 〉 1 〈 〉: 〈 〉 p p 1 = 1 1 p = Dp cov(wi, gi) cov(si, ci) Dgj Dcj ð3Þ Dcj 0,andsoDp 0 2 3 0 0 2 3.Consider- w w ing both genetic and cultural mappings, we see that there Note that angled brackets indicate averages over the descen- is in fact no natural selection on the phenotype in the genetic dant population, indexed by j.JustasinthestandardPrice domain and no flaws in either inheritance system; however, equation, the covariance terms represent the effects of selec- there is positive selection in the cultural domain that pro- tion and drift on evolutionary change (Rice 2004). Impor- duces evolutionary change. This is a distinctly different cause tantly, we can separate the effects of differential reproduction, than was revealed by considering only the reproductive fitness mapping. In summary, if the two modes of inheri- 1 cov(wi, gi), tance were not explicitly described as in equation (1), then w a departure in phenotype from one’s genetic ancestors would and differential influence in cultural transmission (e.g., due include the effect of cultural inheritance, while a departure in to content bias, model bias), phenotype from one’s cultural ancestors would include genetic inheritance. By explicitly accounting for both inheri- 1 : cov(si, ci) tance mechanisms, our approach avoids confounding their w evolutionary effects. In the remainder of the article, we explore Note also the mean fitness, the consequences of accounting for both cultural and genetic fitness explicitly. N0 w p p s, It is worth noting that the distinction between ancestral N and descendant individuals in this context is not meant to which is a direct result of the normalization conditions on gij imply a nonoverlapping generations model. The Price equa- and vij and again implies that everyone receives the same tion examines evolutionary change over an arbitrary time amount ofcultural inputasgeneticinputandthatcultural de- step (Rice 2004); ancestors and descendants are simply the scendants must be equal to the total number of genetic off- members of the same population separated by the given time spring.Theremainingtermsaretheeffectsduetospontaneous step that can be mapped to one another. For example, if the departure from one’s inherited information, such as mutation time step is within a (reproductive) generation, an individual or recombination in genes or individual trial and error learn- may serve as her own ancestor if she has simply persisted ing in culture. These terms differ somewhat from the trans- in the population. When the time step represents multiple mission term in the standard Price equation, which is the generations, we can take ancestors and descendants to have fitness-weighted average departure of mean offspring phe- their colloquial meanings. In a later section, we examine the notype from parental phenotype (E[wDp]). This difference consequences of assuming an explicitly nonoverlapping gen-

This content downloaded from 165.123.034.086 on August 14, 2018 21:07:50 PM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). Gene-Culture Coinheritance of a Trait 000 erations model when genes and culture are transmitted on others on the focal individual are ignored (Hamilton 1964a; different timescales. Rousset 2013). We start by examining the most stringent case where fitness cost is both genetic and cultural, although there is no necessity for altruism to be costly with respect to Conflict between Cultural and Genetic Selection both domains of inheritance. Let p now represent the level of We can use equation (3) to examine evolutionary change altruistic behavior and the cultural and genetic fitnesses be when there are conflicts between cultural and genetic selection given by the following equations: 1 forces, that is, when Dp 0, even though cov(si, pi) and p 1 b 1 b ~ ~ cov(wi, pi) have opposite signs. For example, consider a so- si s0 sppi sp pi, ð5Þ cially acquired preference that leads to decreased reproduc- p 1 b 1 b ~ : tion, as in some cultural evolution models of the demographic wi w0 wppi wp~ pi ð6Þ transition (Ihara and Feldman 2004; Kolk et al. 2014). Let The tilde over a variable indicates the mean value of that higher values of p reduce fitness (i.e., cov(w , p ) ! 0). Then i i variable across i’s neighbors (i.e., the individuals with whom the mean phenotype in the population will increase when the focal can potentially interact). We have assumed that 1 2 1 〈 〉 fi ’ cov(si, ci) (cov(wi, gi) w Dcj ), ð4Þ both kinds of tness are linear functions of an individual s own phenotype and the phenotypes of her neighbors, where 〈 〉 where we have ignored the genetic transmission term Dgj fi s0 and w0 are the baseline tnesses. As in the standard deri- under the assumption that mutation and recombination ef- vation of Hamilton’s rule using the Price equation, it is cus- fects are unbiased with respect to genotypic value. If the mag- b b tomary to identify wp and w~p as the cost (C) to an altruist nitude of cultural selection exceeds that of genetic selection and benefit(B) to recipients of altruism, respectively (Frank (plus the effect of genetic transmission), then p can increase, 1998; Rice 2004; McElreath and Boyd 2008). We will use despite being opposed by natural selection. In essence, a loss the same convention but add subscripts to indicate costs in reproductive fitness can be compensated for by increased fi fi b p 2 and bene ts to genetic and cultural tnesses: wp Cg , importance as a learning model. However, the cultural trans- b p 2 b p b p sp Cc, w~p Bg , s~p Bc. By labeling these terms, mission term means that this condition will be harder to we will be able to more clearly interpret our key results. We meet if social learning biases individuals toward lower cul- can then derive the following condition (see app. sec. A2), tural values than their learning models, for example, as a re- b 1 b 2 1 b 1 sult of biased learning error (Henrich 2004b). Bc( ~cc g~c) Cc(1 gc) ð7Þ 2 b 1 b 2 1 b var(gi) [Bg ( g~g ~cg ) Cg (1 cg )] , ð7Þ Cultural Evolution of Altruism var(ci) Hamilton’s rule (Hamilton 1964a, 1964b)statesthatanal- where we have ignored the transmission terms. The left-hand truistic allele will spread in the population when rB 1 C, side of equation (7) gives the cultural selection coefficient, where B is the fitness benefit to a recipient of altruism, C while the term in brackets on the right-hand side is the genetic is the fitness cost to an altruist, and r measures the assort- selection coefficient. It is immediately apparent that the ge- ment between altruists (often interpreted as a relatedness netic selection coefficient is different than it would be under fi b 2 coef cient). Cultural evolution theorists have claimed that purely genetic transmission of the phenotype (i.e., Bg ~gg ’ altruism is more likely to evolve under cultural evolution be- Cg , as follows from the canonical form of Hamilton s rule) cause this relatedness parameter for culture is likely to be because of the presence of the additional regression coeffi- b b higher than for genes (Fehr and Fischbacher 2003; Henrich cients ~cg and cg . The same is true for the cultural selection fi b 2 2004a; Boyd and Richerson 2010). This claim implies that coef cient, which would be Bc ~cc Cc under purely cultural cultural evolution makes the spread of altruism possible even transmission (El Mouden et al. 2014). when the classical form of Hamilton’s rule does not hold (El Of the three regression coefficients on the left-hand side, fi b Mouden et al. 2014), that is, when genetic selection is op- the rst, ~cc, is the cultural relatedness term, and it describes posed to altruism. To investigate this claim, the effect of evo- how likely actors are to behave altruistically toward individ- b lutionary forces in the cultural and genetic domains must be uals with similar culture types. The second, ~gc, is one of the compared directly, which has not been done before. Here we gene-culture relatedness terms and captures the correlation use our framework to derive the precise conditions under between an actor’s culture type and neighbor’s genotype. which cultural selection can favor altruism, despite being op- Thus, if individuals with higher culture type values are more posed by genetic selection. likely to direct their altruism toward those with higher geno- By altruism we mean here a behavior that reduces the typic values, the cultural fitness benefit is greater. The final fi fi b tness (genetic and/or cultural) of a focal individual while regression coef cient, gc, captures the correlation between increasing the fitness of others, when the fitness effects of an actor’s genotype and her culture type. The higher the cor-

This content downloaded from 165.123.034.086 on August 14, 2018 21:07:50 PM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). 000 The American Naturalist relation between genes and culture, the more likely it is that a ple times during a reproductive generation. We imagine a costly genotype will be paired with a costly culture type, mak- fixed population of size N with nonoverlapping reproductive ing it more difficult for altruism to evolve. generations. Within a reproductive generation, there are n Turning to the term in brackets on the right-hand side, the nonoverlapping stages of cultural transmission. A cohort is fi b regression coef cient, ~cg, is the regression of neighbor cul- born at the beginning of a reproductive generation and re- b ture type on focal genotype. The term cg is the regression ceives its initial cultural and genetic input from the outgoing of focal culture type on focal genotype. Both of these terms generation. This cohort then moves through the n stages up- mean that the presence of cultural transmission changes ge- dating its culture types on the basis of the values of other co- netic selection on altruism (i.e., genetic selection is no longer hort members in the previous stage. In effect, while the stages b 2 given by Bg ~gg Cg ), since there are now gene-culture relat- are nonoverlapping, all stages after the initial stage allow for edness terms to be taken into account. For example, if indi- horizontal transmission that alters the cohort’s culture types viduals with an altruistic genotype are more likely to direct from its initial inheritance from the previous generation. Ig- their altruism toward those with an altruistic culture type, noring the effects of both genetic and cultural transmission, then genetic selection can favor altruism even with low ge- we can derive the following Hamilton’srule–like condition b netic relatedness ( ~gg); this suggests that a locus that causes (for model details and full results, see app. sec. A4): individuals to preferentially interact with culturally similar Xn var(g) t 1 2 individuals can be favored by natural selection even when Sc Sg , ð9Þ 〈St var(ct21)〉 it is costly. tp1 c k t When there is complete statistical independence of genetic where and cultural transmission, all gene-culture correlations are 0 (b p b p b~ p b~ p 0), and equation (7) reduces to t 1 t t t t t gc cg cg gc S p [b (1 1 b ) 1 b ~ (b~ 1 b~ )] c z zp gc zp cc gc b 2 1 2 b 2 var(gi) : Bc ~cc Cc (Bg gg~ Cg ) ð8Þ and var(ci) p 1 b 1 b 1 b b 1 b The term in parentheses on the right-hand side is the genetic Sg [ hp(1 〈c〉g ) h~p( 〈~c〉g ~gg)] inclusive fitness from the canonical form of Hamilton’s rule, h while the left-hand side is the corresponding expression for are the cultural and genetic selection coefficients, respectively culture. Thus, when there are no gene-culture correlations, (for details on the scaling factors 1=z and 1=h, see app. sec. A4). altruism will spread as long as cultural inclusive fitness only The cultural selection coefficients are identified by super- exceeds genetic inclusive fitness scaled by the ratio of the script t to indicate the selection coefficient at each of the n variances in the two domains. When the variance in culture stages of cultural transmission. The denominator on the right- types is sufficiently high with respect to variance in geno- hand side is the average cultural variance over the n stages, types, cultural selection can overcome even considerable ge- weighted by the selection coefficient relevant to that stage. netic selection. If we further consider the case when altruism It is easy to see that when n p 1, we have equation (7). is costly to genetic fitness but beneficial to cultural fitness, For n 1 1, we see that cumulative cultural selection must b 1 the left-hand side becomes Bc ~cc Cc, and the condition be- overcome the genetic selection coefficient scaled by a new ra- comes even easier to meet. tio: that of genetic variance to the selection weighted average From examination of equation (7), we see that cultural cultural variance over the n stages of cultural transmission. transmission affects the evolution of altruism in two impor- This selection weighted variance term is complex in that se- tant ways: (1) by introducing a cultural selection force that lection may vary over the n stages of cultural transmission, may overcome genetic selection and (2) by changing the na- which will affect how the different variances are weighted, ture of genetic selection itself. This latter effect means that for but those variances too will be affected by the magnitude of given values of Bg and Cg , genetic selection may be positive in selection at the previous stage. A more explicit model will the presence of joint cultural and genetic transmission when be required to explore how different selection trajectories t it would have been negative under purely genetic transmis- (i.e., the sequence of Sc values) affect the overall effect on phe- sion. notypic evolution. Differing timescales of transmission. Up to now we have considered evolutionary change over a single time step for Discussion both genetic and cultural transmission. However, measuring Coinherited Behaviors the effect of two selection processes operating under incon- gruent timescales over a single time period can cause prob- Our model is inspired by the fact that many complex traits lems of interpretation of the Price equation terms. Here we (from psychological traits to disease risk) are likely affected consider a model where cultural transmission occurs multi- by both genetic and cultural transmission. We use a gene-

This content downloaded from 165.123.034.086 on August 14, 2018 21:07:50 PM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). Gene-Culture Coinheritance of a Trait 000 culture Price equation to investigate the effect of conflicts Related Work between selection in the two domains of inheritance. Our Price equation framework provides a simple condition for Nearly 40 years ago, Richerson and Boyd (1978) used a game when cultural selection can overcome genetic selection and theoretic model to show that the Nash equilibrium value of a steer the evolution of a phenotype. trait that is both genetically and culturally inherited could be This framework can be useful for making both quantita- that which optimizes cultural fitness. But surprisingly, given tive and qualitative predictions. For instance, educational at- the intense attention gene-culture coevolution received, very tainment is a complex trait that is clearly influenced by so- little theoretical work has been done to follow up on the evo- cial learning. Epidemiological studies suggest a narrow-sense lution of phenotypes that are directly coinherited, as opposed heritability of 0.4 (Branigan et al. 2013), while Kong et al. to culturally inherited behavioral phenotypes and genetically (2017) recently showed evidence for selection against genetic inherited learning rules (e.g., Lehmann and Feldman 2008). variants associated with higher educational attainment in an Findlay (1992) modeled gene-culture transmission of a phe- extensive data set from Iceland. If we assume that the remain- notype in a structured population but limited his analysis ing trait variance is due to culture, equation (4) can be used to to vertical transmission. Another article close to our model calculate a threshold cultural selection value for the increase is that of Lehmann et al. (2008), who model the evolution in educational attainment. In another example, Levy et al. of a purely culturally inherited altruistic behavior in a sub- (2016) found that culturally transmitted negative stereotypes divided population. In their model, Lehmann et al. (2008) about aging predicted later biomarkers of Alzheimer’s dis- consider the phenotype to be affecting either only cultural ease (reduced hippocampal volume and increased amyloid or only reproductive fitness and assume no genetic contribu- plaque development). Our model indicates that if these neg- tion to the phenotype. As such, their model can be recovered — p ative stereotypes are culturally selected for perhaps because by modifying our Price equation (7) by setting pi ci, which a rapidly changing environment makes older individuals seem replaces the right-hand side of the condition with 0. Impor- less valuable as cultural role models—then cultural selection tantly, biological offspring in Lehmann et al.’s (2008) model can increase the incidence and severity of Alzheimer’sbio- serve as vectors of the cultural types of their parents, which markers, especially because natural selection is likely to be means that even when their cultural trait affects only repro- fi very weak in this case. ductive tness, our corresponding Bc and Cc terms would be Our results show the importance of the ratio of genetic to nonzero. That means that the transmission rate of different cultural variance in determining the relative strength of ge- cultural types are not the same over the entire life cycle, and netic and cultural selection. Although several studies have there is cultural (but no genetic) selection. looked at genetic and cultural variation in humans, they cur- More recently, El Mouden et al. (2014, p. 235), using a rently do not report the necessary information to measure Price equation to describe cultural evolution, claimed that this ratio for a particular trait. Bell et al. (2009) compared cultural selection can increase genetic fitness (e.g., through fi FST values for culture and genes in populations using the altruism that bene ts others) of a population only if genetic World Values Survey. Their results suggested greater between- and cultural fitness is positively correlated. Our results con- population variation in culture than in genes, although these tradict this claim: instead, we show that coinherited altruistic were across genomes and cultures and not with respect to a behaviors that increase mean genetic fitness of the popula- particular trait. Other studies have shown parallels in the pat- tion can evolve through cultural selection even when opposed terns of linguistic and genetic diversity (Hunley et al. 2008; by genetic selection. To give the simplest possible example, 1 Perreault and Mathew 2012; Creanza et al. 2015; Longobardi consider our equation (8) and an altruistic trait with Bg b ! et al. 2015) but again do not report the ratio of genetic to cul- Cg but ~ggBg Cg . This trait would be opposed by genetic se- tural variance for a particular trait. However, behavioral ge- lection (more altruistic phenotypes would have lower genetic netics is providing increasingly accurate heritability measures fitness). However, if it spreads through cultural selection b 2 fi for behavioral traits. These studies, in combination with cul- (which happens when ~ccBc Cc is suf ciently large, when tural measures (e.g., using cultural pedigrees), can offer em- more altruistic phenotypes have higher cultural fitness), it pirical estimates of this ratio for evolving behaviors. Non- would increase the mean genetic fitness, despite the fact that human animals provide even better prospects for measuring cultural and genetic fitness is negatively correlated. At the distinct genetic and cultural heritabilities, which we will show heart of this discrepancy is the fact that the mathematical relate directly to our variance ratio. Songbirds in particular framework of El Mouden et al. (2014) considers competing lend themselves to experimental designs where both genetic hypotheticals where a trait is transmitted either purely cul- and cultural pedigrees can be manipulated (Danchin et al. turally or purely genetically. Therefore, their model cannot 2011). Using an extended animal model, cultural and genetic directly address the question of which direction a trait will heritabilities could be measured and the ratio of genetic to evolve under conflicting selection pressures and what the cultural variance estimated. consequences of such evolution are for a population’s mean

fitness. In contrast, we allow both modes of inheritance to be For most of the article, we do not model population struc- present and make clear, direct comparisons between the ef- ture explicitly, instead dealing with statistics of population fects of those inheritance systems. This framework allows us structure, given by the gene-gene, culture-culture, and gene- to further consider the consequences of assortment between culturecorrelationtermsinequation(7)(whicharecalculated individuals genetically and/or culturally as well as the assort- explicitly in the assortment model described in app. sec. A3). ment of the genotypes and culture types within individuals. Findlay (1992) presented a model of explicit population struc- We find that some assortment patterns can cause genetic se- ture and found that when within- and between-group selec- lection to change direction to match cultural selection. Our tion had the same sign, gene-culture inheritance accelerated results show that there is more complexity to the interaction the rate of phenotypic evolution (vis-à-vis purely genetic in- of genetic and cultural selection, especially in structured pop- heritance) by increasing the correlation between parents and ulations. offspring as well as the heritable between-group variation. El Mouden et al. (2014) also conclude that natural selec- This result assumed vertical transmission of culture from ge- tion acting on the underlying learning rule that determines netic parent to offspring. A similarly explicit population struc- cultural selection will bring the two kinds of fitness into ture model in our framework may yield different results alignment. Specifically, El Mouden et al. (2014) consider a because of the fact that phenotypic correlations between par- trait evolving under purely cultural transmission and consider ents and offspring are likely to decrease when cultural and how the learning rule, itself genetically transmitted, would genetic parents differ. More generally, the effects of popula- evolve. In forthcoming work (E. Aguilar and E. Akçay, un- tion structure needs to be further explored for their implica- published manuscript), we extend the approach in this arti- tions for the literature on cultural group selection. cle to derive the conditions for the simultaneous (genetic) evolution of a learning rule with a gene-culture coinherited Limitations and Extensions trait. Our results in that work show that the conclusion of El Mouden et al. (2014) indeed holds in the special case when The Price equation derives its power from its generality. Re- the phenotype is transmitted only culturally. However, when sults derived from the Price equation will apply to all models the trait is coinherited, the picture becomes more complex: in the class defined by the Price equation’s basic assump- learning rules that support maladaptive phenotypes can be tions. Therefore, results for explicit models in the same class maintained in some cases. More generally, the coevolution can all be related to one another using the general results of of transmission rules for genetic and cultural systems for co- the Price equation. In this sense, our above results are general inherited traits needs to be explored further. for coinheritance models that respect additivity. However, Our results on the importance of the ratio of genetic to cul- this generality comes at a cost. On its own, the Price equation tural variance relates to a recent strand of work on extended cannot be used to iterate into the future and make statements inheritance. In a series of articles, Danchin et al. (2011, 2013) about the long-term dynamics of a process, a property re- and Danchin and Wagner (2010) introduced the idea of in- ferred to as dynamical insufficiency (Frank 1998). Viewed clusive heritability, which partitions the variance in the her- from this perspective, the Price equation is analogous to a itable component of phenotype into the contributions from derivative for a discretized system over arbitrary time steps. each system of inheritance. This allows for narrow-sense her- The variance and regression terms in the conditions derived itability to be expressed as the sum of the heritabilities in each above can evolve across time steps depending on the explicit domain (assuming no interactions between the inheritance dynamical model employed. Long-term behavior of coinheri- 2 p 2 1 2 2 fi systems). In our model, this means h hg hc (where hg tance systems will require examination of speci c dynamic 2 and hc are the genetic and cultural narrow-sense heritabilities). models; for this reason, we include results for an explicit dy- The relationship between these quantities and the term that namical model in the appendix (see app. sec. A3). However, appears in our results as the scaling factor of genetic selec- the Price equation does provide a recipe for model construction is tion and interpretation, which is especially important for considering multiple inheritance systems where there are more 2 var(gi) p var(gi)var(pi) p hg : degrees of freedom for choices of model assumptions. 2 ð10Þ var(ci) var(pi)var(ci) hc The additive model we used in this article is both the simplest model and a natural extension of the standard assump- Thus, it is the ratio of the narrow-sense heritabilities that tion in quantitative genetics (Falconer and Mackay 1996). It determines the relative importance of genetic selection in is also easily generalizable to an extended animal model, the evolution of a coinherited phenotype. This further dem- which would be of particular use in experimental setups in onstrates the relationship between inclusive heritability and nonhuman animals (Danchin et al. 2011). However, our frame- the effects of selection acting in different domains of inheri- work can also be expanded by a simple method to a wide tance. class of functions that determine phenotype and the effect

This content downloaded from 165.123.034.086 on August 14, 2018 21:07:50 PM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). Gene-Culture Coinheritance of a Trait 000 of the relative variances in the two domains still obtains (for Bell, A. V., P. J. Richerson, and R. McElreath. 2009. Culture rather than details, see app. sec. A5). genes provides greater scope for the evolution of large-scale human In the course of deriving our results on the effects of se- prosociality. Proceedings of the National Academy of Sciences of 〈 〉 the USA 106:17671–17674. lection, we often ignored the transmission terms Dcj and 〈 〉 Bonduriansky, R., and T. Day. 2009. Nongenetic inheritance and its evo- Dgj . In relatively simple genetic systems, it may be safe to lutionary implications. Annual Review of Ecology, Evolution, and Sys- assume that the expected difference between parents and off- tematics 40:103–125. spring is zero. 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