1

Evolutionary theories of cultural change

Tom Wenseleers1 , Siegfried Dewitte2 and Andreas De Block3

1. Department of Biology, Zoological Institute, Catholic University of Leuven, Naamsestraat

59, 3000 Leuven, Belgium

2. Research Group Marketing, Faculty of Economics and Business, Catholic University of

Leuven, Naamsestraat 69, 3000 Leuven, Belgium

3. Institute of Philosophy, Centre for Logic and Analytical Philosophy, Catholic University of

Leuven, Dekenstraat 2, 3000 Leuven, Belgium

Corresponding author: Tom Wenseleers (tom.wenseleers@bio.kuleuven.be)

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Evolutionary theories of cultural change

Tom Wenseleers, Siegfried Dewitte and Andreas De Block

Over the last decades, many scholars have hinted at the possibility of a grand

evolutionary synthesis, which would revolutionize the social sciences by bringing genetic

and cultural evolution under a common umbrella. Yet, the many perceived

idiosyncrasies of cultural evolution have long posed an obstacle for such an

interdisciplinary synthesis. New discoveries in biology as well as recent developments in

theoretical evolutionary biology, however, show that the alleged differences between

genetic and cultural evolution may be smaller than previously suspected. In addition,

important applications of cultural evolution theory have started to appear in diverse

fields within the social sciences. A general evolutionary theory of cultural change,

therefore, finally seems to be within reach.

The idea that evolution is not limited to the biological realm, but also applies to culture has a

long history, and goes back at least to Darwin [1-3]. Darwin saw clear analogies, for example,

between the way in which languages and species evolve, noting that "proofs that both have

been developed through a gradual process are curiously parallel" [1]. Likewise, Darwin

referred to the diffusion of successful technological innovations to underscore the point that

adaptive variants should spread in the population [1]. Since Darwin, the analogy between

cultural and biological evolution has often been reiterated [2-3], for example in Richard

Dawkins’ The Selfish Gene [4], in which the term ‘meme’ was coined to refer to cultural bits

of information that spread from mind to mind via imitation, learning or imposition. The lack

of a formal framework and certain conceptual issues, however, resulted in memetics

struggling somewhat to establish itself as a science [5], and a mathematically rigorous

approach to cultural evolution only took off in the 1980ies, when two highly influential books

were published by Cavalli-Sforza and Feldman [6] and Boyd and Richerson [7], addressing

such topics such as how cultural traits get transmitted and spread in populations [6-7], how

cultural evolution interacts with genetic evolution [7] and under what conditions cultural

learning might be adaptive [7]. Later, cladistic analysis and the comparative method also

started to be increasingly used to reconstruct cultural phylogenies and test comparative

hypotheses about human bio-cultural evolution [8].

Only recently have these evolutionary approaches to cultural change started to gain

widespread attention within the social sciences, with several new book-length treatments

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advocating their use in a diverse set of fields, including archaeology [9-10], anthropology [9-

10], economics [11-12], historical linguistics [13-16] and textual criticism [15, 17]. However,

despite these signs of increasing acceptance, there is still great resistance to these theories in

some quarters [18-20]. One of the main reasons for these reservations are the many perceived

differences between genetic and cultural inheritance [18-26], in which cultural evolution is

usually considered "more complex" than biological evolution [26-27]. Nevertheless, as we

will argue here, many of the alleged peculiarities of cultural inheritance in fact do have

analogues in biological evolution. In addition, we will review recent work showing that both

at the microevolutionary and macroevolutionary scales, cultural change can be successfully

analysed using evolutionary methods. The tremendous potential of these methods will be

illustrated with some recent applications of cultural evolution theory to the study of human

cooperation and the analysis of the historical relationship among cultural lineages. We

conclude that a Darwinian synthesis of bio-cultural evolution is coming closer than ever

before and may be well on its way to become one of the cornerstones of the modern social

sciences.

Cultural versus biological inheritance

The isomorphism between biological and cultural evolution is obvious: both depend on

variation, heredity, and differential trait replication [3], and both tend to favour adaptive

complexity [7]. That this is more than just a loose analogy has been successfully shown by a

swathe of models that have analysed the spread of cultural traits in populations using methods

drawn from classical population genetics [6-7, 28-29]. These models have shown, among

others, that cumulative cultural evolution can occur even if cultural replication is relatively

inaccurate [30], if cultural variants are continuous rather than discrete [23, 30], and if traits

combine via blending as opposed to stochastic, particulate inheritance [6-7, 23]. But what

about some of the other alleged differences between cultural and biological evolution? Even

just in terms of inheritance, the differences are many. Transcription and biological

reproduction are the main mechanisms of biological inheritance; different forms of social

learning, such as imprinting, conditioning, direct instruction, observation and selective

imitation, underlie cultural inheritance [26]. Other peculiarities of cultural inheritance include

the fact that (1) inheritance paths are very plastic [26] and show a greater incidence of

horizontal transmission [6], which may result in reticulate, non tree-like, evolution [19, 31],

(2) cultural inheritance usually involves active individual choice [20], and tends to be guided

by certain transmission biases [7] (see Glossary), (3) cultural inheritance may involve many

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successive learning or unlearning opportunities throughout one's life [27], (4) cultural variants

may be acquired by observing and blending the traits of a large number of "cultural parents"

[6-7, 21, 25], (5) cultural change often involves directed, adaptive changes that are guided by

intelligence and foresight [32-33] and (6) cultural evolution may have Lamarckian properties

[33].

In recent years, however, several authors have argued that many of these peculiarities

can also be found in biological systems [20-21, 31, 34]. In bacteria, for example, horizontal

gene transfer (HGT) is quite common and a major mechanism for acquiring certain traits such

as antibiotic resistance [35]. Naturally competent bacteria [36], for instance, are able to

actively acquire DNA from the environment via transformation (potentially at several stages

throughout their life, and from multiple parent cells), and usually do so contingent on

particular environmental conditions and in a selective way, allowing only DNA similar to

their own to enter the cell [36]. In the jargon of cultural evolution theory, such individual

choice would be referred to as a "model-based similarity bias" [7]. In other cases, the agency

for HGT in bacteria instead lies with the donor cell – somewhat more akin to indoctrination or

imposition in cultural evolution – as in virus-mediated transduction or plasmid-mediated

conjugation [35]. And occasionally, genes appear to make such big jumps that the once so

orderly "tree of life" is now thought to be more akin to a "web of life" [35].

Similar reticulate forms of evolution can be seen in various species of plants, insects

and fish which following interspecific hybridization may form entirely new species [37],

among strains of viruses which can recombine when they co-infect the same host [38], and –

at the intraspecific level – in the form of gene flow, caused by migration and sexual

reproduction [39]. In addition, directed, adaptive change can be seen in various forms of

phenotypic plasticity, such as in algae, bacteria and yeast which can adaptively increase their

mutation rate under adverse conditions to increase the chance of producing surviving daughter

mutants [40], or in water fleas, which can grow defensive spines on their heads when exposed

to fish predators [41]. In the case of water fleas, this epigenetic phenotypic modification has

even been shown to be heritable, making it an example of Lamarckian evolution [41], and

other similar cases of heritable acquired characteristics have now been documented in over

100 species of animals, plants and microorganisms [34]. Finally, the way in which epigenetic

modifications may be acquired or lost throughout an organism's life depending on certain

environmental feedbacks has also been specifically likened to the process of individual

learning [42].

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Towards a generalized theory of evolutionary change

The above remarks show that, whilst genuine differences between cultural and biological

evolution certainly do exist, there are also many deep similarities. In fact, many authors have

shown that the similarities go beyond the purely verbal level, and have demonstrated that a

population genetic theorem known as the Price equation [43-45] can serve as a unified basis

to successfully analyze both [30, 43-54]. This is possible thanks to the fact that the Price

equation can work with any inheritance system, e.g. based on either genetic or cultural

descent [52], blending or particulate inheritance [16] and involving any number of parents

[43], and that it can model phenotypic change across any time scale [55], and irrespective of

how phenotypes are determined at a mechanistic level [55]. Importantly, the Price equation in

itself also unifies many other fundamental equations used in genetics and evolutionary

biology, such as the replicator equation [56] and the breeder equation from quantitative

genetics [45, 57].

Recently, Kerr & Godfrey-Smith [52] further generalized the original Price equation by

allowing plasticity in the inheritance system (Box 1). The result was an intuitive version of

Price's theorem, showing that a trait will spread in a population when (1) carriers leave a more

than average number of (genetic or cultural) descendants (Fig. 1a,b), (2) the trait shows

directed change across inheritance paths (Fig. 1c,d) or (3) it is inherited from a fewer than

average number of parents (Fig. 1e). The latter captures the well known fact in biology that

asexual mutants usually beat sexually reproducing individuals, owing to the fact that they can

transmit their genetic material undiluted to future generations [52]. In cultural evolution, the

equivalent would be the spread of trait variants that can be acquired from fewer models [52],

e.g. by being easier to learn. Additionally distinguishing between the transmission of traits to

biological descendants and nonrelatives [6], and allowing for directed trait changes within an

individual's lifetime [55], the result is a formal scheme that can accommodate all of the

aforementioned peculiarities of either cultural or biological evolution (Fig. 1, Box 1).

Further expansion of the terms in the Price equation can sometimes give additional

insight. For example, the selection components can be rewritten as the product of a selection

differential, a phenotypic variance and a heritability [45, 57] (Box 1). This makes it clear why

a low transmission fidelity of traits is not a problem in cultural evolution: despite reducing the

heritability and reducing the efficacy of selection, it increases the phenotypic variance that

selection can act on, thus countering the variance-reducing effect of blending inheritance [7].

(Besides, studies have shown that the cultural heritability of some traits, such as religious

affiliation, can be very high [58].) A long-standing problem with the Price equation, that of

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dynamic sufficiency, i.e. that the equation cannot easily be reapplied over multiple time steps,

has recently also been solved using special methods [59], and a first application to gene-

culture coevolutionary analysis already appeared [54]. Such coevolutionary analyses

specifically keep track of the joint dynamics of genetic and cultural traits [28, 60], i.e. of

phenogenotype frequencies. This can be important, because cultural learning rules may be

partly genetically determined [24, 28, 60], cultural traits may sometimes hitchhike with genes

if they are nonrandomly associated [23, 28, 59-60], and the spread of certain cultural traits can

exert strong genetic selection, as in the cultural practice of cattle farming which in Northern

Europe selected for lactose tolerance [28, 60]. For complex problems, arriving at an analytical

solution is not always easy, and simulations can be used instead [29, 53], although even then,

the constituent terms of the Price equation can still be calculated numerically to get a better

insight into the evolutionary dynamics [53].

The puzzle of human altruism

That the Price equation provides a very useful basis for modelling cultural change is

illustrated by several recent applications in diverse fields such as linguistics [16],

anthropology [47] and evolutionary economics [48]. One area, however, in which the

framework has proven particularly fruitful is in the study of human cooperation [45, 49-50,

54, 61]. Countless economic experiments have shown that humans frequently cooperate with

others, even at a cost to themselves and despite the fact that these other individuals may not

be genetically related [12, 62]. From a genetic perspective, such altruistic behaviour is

difficult to account for [46, 63]. But what if altruism is culturally determined? Models have

shown that this may offer a way out of the conundrum [29, 49, 54, 64-65]. This is because

relative to genetic inheritance, cultural transmission has a much greater potential to decrease

the variance within groups whilst augmenting the variance between groups [29, 49]. This is

true particularly if cultural traits follow a "one-to-many" transmission pattern [6, 54]. E.g., if

altruism is propagated by a single leader or teacher [6], groups will end up varying in their

mean level of altruism. Provided that more altruistic groups as a whole do better than more

selfish ones, this would enable altruism to spread – a process known as "cultural group

selection" [12, 29, 49]. Looked at from another perspective, individuals within each group are

under this transmission scheme "cultural relatives" [54, 64-65], and this drives the evolution

of altruism via the cultural analogue of kin selection [64-65]. For example, if everybody in a

group copies a single individual in the group with a probability p and someone else with a

probability 1-p, then the cultural relatedness between individuals has been calculated to be

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approximately p2 [6, 54]. If p is high enough, this allows altruism to be selected for when

under genetic selection it would not be [54, 64-65]. These two interpretations – of cultural

group or kin selection – in fact turn out to be mathematically equivalent [46, 63], and can

easily be derived – once again – from the Price equation [46, 54, 63]. At an empirical level,

cultural group and kin selection have been invoked to provide explanations for such

phenomena as religious prosociality [29, 66] and ingroup favouritism [29, 62, 66-67] – the

tendency for people to be more cooperative towards groupmates or cultural relatives.

On the other hand, cultural group or kin selection are no universal panacea, and whether

or not they actually favour cooperation heavily depends on what cultural transmission pattern

is in place [50, 54, 68]. For example, success or "payoff-biased" cultural transmission [7, 49],

whereby individuals tend to copy the most successful individuals in the population, can make

it very hard for cooperation to evolve [50, 68]. The reason is that under payoff-biased

transmission, helping a neighbour will result in a lower individual payoff, and this in turn will

make it less likely that the helping individual will be imitated in the future [50, 68]. Likewise,

a conformist bias, whereby individuals tend to copy the most common variant in the group [7,

49], will in itself not select for cooperation, unless cooperation is already common to begin

with [54]. Furthermore, cultural relatedness has been shown to decline very rapidly as the

number of cultural parents increase [65]. Again, this puts significant constraints on the

cultural evolution of cooperation. Finally, models have shown that it can be hard for a genetic

learning rule to copy traits from a single "leader" to become established in a population [54],

and that due to selective learning [69], individuals may only end up copying altruistic traits

when they can acquire other fitness-enhancing traits with them [70].

What about some other forms of human biological self sacrifice, such as religious

celibacy? Boyd and Richerson [7] developed a simple model showing that the persistence of

such traits can also be explained on the basis of cultural evolution theory if individuals, by

having fewer children, can gain more social influence. This applies to celibacy, where priests,

by remaining childless, can spend more time spreading the faith [4, 7, 71-72]. Cultural traits

such as these, which spread at the expense of an individual's biological fitness, have been

referred to as "selfish memes" [4, 7, 71-72] and have been likened to some horizontally

transmitted pathogens or certain classes of "ultraselfish genes" [73], which rely on similar

strategies to spread.

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Cultural phylogenies

As we have shown, cultural microevolution can be analysed with exactly the same tools as the

ones which have been used to study genetic evolution, such as population genetic, kin and

group selection models. Does this mean that one should also be able to use phylogenetic

methods to dissect the broader patterns of cultural macroevolution? The issue has long been

contentious, since culture is thought to rarely evolve in a strictly tree-like fashion, owing to

the widespread incidence of horizontal transmission and borrowing [2, 19, 29] (but see

Collard et al. [9] for a corrolary). More than half of all the words in the English language, for

example, have been borrowed from French following the Norman conquest [2]. In recent

years, however, following the discovery that biological systems may be characterised by

similar reticulate forms of evolution [35, 37-39], phylogenetic methods have been developed

that are able to reconstruct reticulate phylogenetic networks rather than strictly bifurcating

trees [39, 74-79]. These methods now offer great potential for addressing the issue of

borrowing in cultural macroevolution.

Phylogenetic network methods encompass two major approaches [39, 74-76]. In

implicit phylogenetic network approaches, such as the split decomposition (SplitsTree) [75] or

Neighbor-Net methods [75], conflicting phylogenetic signal in a dataset is represented using

"split graphs", which allows one to assess graphically how tree-like a given phylogeny is (Fig.

2a,b) [39, 74]. In explicit phylogenetic network methods, by contrast, the aim is to obtain an

explicit phylogenetic network [39, 74]. Such networks can e.g. be based on overall statistical

parsimony ("maximum parsimony networks") [39, 74] or on the conflation of a set of

conflicting input trees [75-76]. Finally, there are also explicit network methods which produce

reticulograms [39, 74, 77-79], in which case a base tree is first constructed using a standard

phylogenetic method, which is then improved upon by adding unidirectional or bidirectional

reticulation events. Such methods can be either character-based, employing criteria such as

maximum parsimony [77] or maximum compatibility [78], or distance-based, as in the T-Rex

method [79].

Even though phylogenetic network approaches have only been developed relatively

recently, successful applications to cultural evolution have already appeared in diverse fields,

including historical linguistics [8, 15, 31], textual criticism [15, 17, 80-82], cultural

anthropology [9-10, 22], archaeology [9-10] and palaeontology [10]. In historical linguistics,

for example, Nakhleh et al. [78], developed a method known as “perfect phylogenetic

networks” to produce reticulograms of various Indo-European languages, enabling them to

infer historical contact among certain distinct lingeages (for a review on the use of

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phylogenetic methods in historical linguistics, see Refs. [15, 83]). Similarly, the Neighbor-Net

method has been used to identify the hybrid origin of some Creole languages [31], such as

Sranan (Fig. 2a), as well as to demonstrate some less extreme cases of borrowing among

Indo-European and Bantu languages [8, 15]. Others instead focused on certain classes of more

slowly evolving words, such as the Swadesh word list of basic vocabulary items, to overcome

the problem of borrowing [2, 83-84]. This approach was for example taken by Gray and

Atkinson [84], who, using a Bayesian model, succeeded in accurately dating the Indo-

European language tree (for other studies on the dating of language trees using phylogenetic

methods see Refs. [9, 13, 15]).

Another nice application of phylogenetic network approaches was provided by

Barbrook et al. [80], who used the SplitsTree method to reconstruct the history of manual

copying by scribes of different versions of The Canterbury Tales, and demonstrated that it can

correctly identify all the manuscript groups that had been recognized based on traditional

stemmatic analysis [80] (Fig. 2b). In some cases, phylogenetic analysis of different parts of

the manuscripts also provided clear evidence for copyists switching from source manuscript

during transcription [85], and the incidence of such exemplar change could be statistically

demonstrated using methods originally developed to detect recombination among DNA

sequences [15]. In the study of the phylogeny of the Canterbury Tales, such "contaminated"

manuscript versions of hybrid origin were excluded [80, 85], resulting in a very tree-like

overall reconstruction, although multifurcations were evident in some places, presumably due

to copying from the same source manuscript [80, 85] (Fig. 2b). To assess the accuracy of

different phylogenetic methods, artificial textual traditions have been used [86-87]. Finally, a

fascinating application of phylogenetic network methods to technological change was

provided by Temkin & Eldredge [22], who used T-Rex to reconstruct a phylogeny of cornets,

resulting in a clear depiction of technological advances in design and borrowing of

manufacturing technology among makers (Fig. 2c).

Conclusion

The parallels between biological and cultural evolution have led to the establishment of

general evolutionary approaches for the study of cultural change, including gene-culture

coevolution models [7], which can provide a micro-evolutionary dissection of biocultural

change, as well as phylogenetic approaches [8-10, 13-17, 31, 83], which can help to

reconstruct the historical relationship and contact events among cultural lineages, but also

allow nonindependence in cross-cultural analyses to be taken into account – an issue known

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as Galton's problem [8-10, 31]. Many researchers believe that these evolutionary theories of

cultural change provide an ideal framework for the unification of the behavioural and social

sciences [11, 20, 88-89]. Gene-culture coevolution provides a nice middle ground between

evolutionary psychology and human behavioural ecology, with their emphasis on our evolved

human nature, and the autonomy of the cultural realm, that many scholars in the social

sciences subscribe to [20]. If cultural transmission is assumed to be payoff-biased, gene-

culture coevolution could also be argued to encompass economic evolutionary game theory as

a special case [11, 24]. Phylogenetic approaches, in turn, have clearly shown great promise in

providing a formal quantitative basis for the historical analysis of the relationships among

languages [2, 13, 15, 83-84], texts [17, 80-82, 85-86] and cultural artefacts [8-10, 22]. Hence,

it is clear that a huge number of areas in the social sciences could potentially benefit from an

evolutionary approach to culture. Conversely, evolutionary approaches to cultural change

could also certainly benefit from traditional social science methods and the findings they have

generated, for example to get a better micro-level understanding of the cultural transmission

process [15, 31, 83] and inheritance structures [90], or to constrain phylogenetic trees based

on known historical evidence [84].

Evidently, there are also still many outstanding questions and challenges within the area

of the evolutionary study of cultural change (Box 2). One of the biggest challenges is the lack

of sufficiently general methods to quantify cultural inheritance [91], e.g. allowing vertical

cultural transmission to be disentangled from genetic inheritance [92]. Methods such as

extended twin studies in behavioural genetics [93], phylogenetic approaches [9], correlational

analysis of cultural inheritance [58], social network analysis [91, 94] and social psychological

experimentation [90-91] might all be of some use, but each of these methods still faces

significant problems [91]. E.g., the latter four methods do not control for genetic effects, and

behavioural genetics methods only work over the timespan of one generation, which is not

ideal for fast evolving cultural traits such as certain fads or fashions. However, a recently

developed method to detect cultural learning whilst simultaneously controling for genetic and

environmental effects [91], might hold some promise, as well as a method to measure

heritabilities based on the regression of phenotypic similarity on (genetic, or by extension,

cultural) relatedness [95]. Nevertheless, it is clear that even in the absence of solutions for

such outstanding problems, evolutionary theory has already resulted in a much deeper

understanding of the complexities involved in cultural transmission and change, and we can

only look forward to the many exciting discoveries that undoubtedly still lie ahead.

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Acknowledgements

We are grateful to Robert Boyd, Peter Godfrey-Smith, Benjamin Kerr and Laurent Lehmann

for constructive comments and discussion and apologize to all those whose work we could not

mention within the limited space of this paper. This study was supported by a postdoctoral

fellowship from the Research Foundation Flanders to T.W.

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Glossary

altruism: a behavior that increases the fitness of another individual but decreases the fitness of the actor. culture: information or behavior shared by a population or subpopulation that is acquired from conspecifics through some mix of imitation, imposition and learning. cultural fitness: the relative rate of increase of a cultural variant, taking into account possible nonrandom associations with other cultural or genetic traits with which the variant can hitchhike. cultural relatedness: measure of the tendency that a pair of interacting individuals is more likely to carry identical cultural variants than is a pair of individuals sampled at random from the population [65]. cultural selection: a process by which certain cultural variants increase or decrease in frequency due to being adopted by other individuals at different rates [6]. cultural kin selection: the process whereby a cultural variant coding for altruistic behaviour spreads in the population because it increases the fitness of culturally related individuals [65]. cultural group selection: a process whereby a cultural variant spreads in the population because it increases the success of the group as a whole, despite possible negative effects of the trait on the relative success of individuals within each group [49]. cultural transmission: non-genetic transmission of information or of a trait from one individual to another in a population. genetic relatedness: measure of the tendency that a pair of interacting individuals is more likely to carry identical genetic variants (alleles) than is a pair of individuals sampled at random from the population [63]. guided variation: a process within the individual that produces directed, adaptive change [7]. maximum compatibility: phylogenetic method that aims to find a tree whereby a maximum number of characters evolve without homoplasy (convergent evolution to the same character state). maximum parsimony: phylogenetic method that aims to find the tree requiring the least number of character changes. phenogenotype: the joint combination of one's biological genotype and cultural phenotype, which are often non-randomly associated (i.e. occurring in linkage disequilibrium) [28]. reticulate evolution: an evolutionary process following a non-tree like pattern. split decomposition: phylogenetic method whereby conflicting phylogenetic signal in a given dataset is represented using parallelograms or "split graphs". transmission biases: different trait transmission biases which may occur in cultural evolution and by which cultural variants are selected [7]; direct (or content) biases are genetically or culturally determined biases to adopt one trait over another (e.g. a preference to eat sugary food); frequency-dependent biases are preferences to adopt one trait over another based on its frequency in the local group and can be either conformist or, more rarely, nonconformist; model-based biases are preferences to take particular individuals as a model, e.g. based on prestige, skill, success, age, sex or similarity to oneself.

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Box 1: The Price equation: a general theory of evolutionary change

Suppose we are interested in calculating the average change zΔ in the value of some trait z

between an "ancestor" population and a "descendant" population over a certain time step. To

start, let us connect all an ancestor individuals to all dn descendant-population individuals

according to the way in which either genes or cultural traits are inherited, and let us also

connect identical individuals in the ancestor and descendant population for those that happen

to survive [52]. For any possible connection between ancestor i and descendant j, we define ijC to be 1 if inheritance occurs (or if they refer to the same individual), and 0 otherwise (for

simplicity we use dichotomous connections, but continuous weights could also be assigned).

The total number of connections leading from an ancestor a or to a descendant d are denoted

as aC* and *dC ; the overall total number of connections is designated *

*C . Extending original

work by Price [43-44, 46], Kerr & Godfrey-Smith [52] showed that with this setup zΔ is

given by

)~,cov()ave()~,cov( ddad

aa Pzz)(Dzz −Δ+=Δ (eqn. 1)

where )~,cov( aa Dz and )~,cov( dd Pz are the (population) covariances between the phenotypes

az of ancestors a and their relative number of descendants )//(~ ***

aaa nCCD = and between

the phenotypes dz of descendants d and their relative number of parents )//(~ **

*ddd nCCP = ;

)ave( adz)(Δ is the mean change in phenotype across inheritance paths. Eqn. 1 shows that

variants will tend to spread when they cause individuals to have more than an average number

of descendants (first term), they show biased transmission (second term) or they can be copied

from a fewer than average number of parents (or cultural models) (third term) [52].

Importantly, eqn. 1 does not assume faithful transmission of traits. This was shown by Okasha

[57], who noted that ))ave(()~,cov()ave()~,cov( daaaa

daa zDzz)(Dz Δ+=Δ+ [57], where

)~,cov( daa Dz is the covariance between the mean phenotypes azd of the descendants of

ancestors a and the ancestors' relative number of descendants aD~ and ))ave(( azΔ is the mean

change in phenotype between ancestors a and their connected descendants. Furthermore, we

can regress descendant phenotypes on ancestor phenotypes [57], 111d . ε++= aa zhaz and

222 . ε++= da

d zhaz (where daz is the mean phenotype of the ancestors of a given

descendant d), so that after substitution we get 1d ).~,cov()~,cov( hDzDz aaaa = and

2).~,cov()~,cov( hPzPz dda

dd = (assuming that the number of descendants of ancestors or

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number of parents of descendants do not covary with the residuals ε ). Further writing

covariances as the product of a regression and a variance [57], we obtain

2~1~ ).var())ave(().var( hzzhzz da

zPaa

zD da

daa ββ −Δ+=Δ (eqn. 2)

where aa zD~β and

da

d zP~β are the regressions of the relative number of descendants of ancestors

on the phenotypes of ancestors and of the relative number of parents of descendants on the

mean phenotype of the ancestors of these descendants, )var( az and )var( daz are the

variances in these phenotypes and the h coefficients are known as narrow-sense heritabilities

in case phenotypic change is measured over one generation. Eqn. 2 shows that evolutionary

change can be partitioned into two selection components, each composed of the product of a

selection differential (β , caused by the effect of the trait on the number of descendants or the

inheritance system), a phenotypic variance, and a heritability (h) (first and third term), plus a

transmission bias from ancestors to connected descendants (second term). Note that in both

genetic and cultural evolution "descendants" may entail the individual itself (if, with relative

probability S~ , it had survived to the next time step), direct biological descendants ( B~ ) (in

case of vertical transmission[6]) and nonrelatives ( N~ ) (in case of horizontal or oblique

transmission[6]), so that aaaaa zNzBzSzD ~~~~ ββββ ++= . Similarly, ))ave(( azΔ may both refer to a

change in phenotype within an individual's lifetime (individual transformation, e.g. due to

individual learning in cultural evolution) [55] or to biased trait transmission to other

individuals (Fig. 1). It is worth noting that all these evolution factors can also be subject to

stochasticity, and be a cause of drift. Okasha [57] shows how the contribution of drift can be

separated out by writing aD~ , dP~ or az)(Δ as the sum of an expected value and a random

deviation.

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Box 2: Outstanding Questions

Could a general theory of selection be further extended and applied to cultural evolution? E.g. could class or age structure and individual attributes be incorporated by differentially weighing individuals or inheritance paths [45-46]?

Could cultural evolution theory be integrated more closely with other fields, such as social network analysis [94], or the diffusion of innovations and epidemiological literature [94]?

How can cultural inheritance patterns be accurately quantified empirically [58, 92]? How can cumulative cultural evolution occur despite a fast mutation rate and are there

upper limits on the mutation rate, as there are in biological evolution [96]? Is there adaptive adjustment of the mutation rate in cultural evolution [40]? Are there tradeoffs between the speed and the fidelity with which traits can be transmitted [96]?

Are there parallells between the evolutionary causes of cultural inheritance and certain forms of horizontal gene transfer, such as natural competence in bacteria [36], or between the dynamics of individual learning and the feedback mechanisms involved in epigenetic phenotypic modification [34]?

Could cultural diversity arise in an analogous way as sympatric speciation, and be modelled using methods from adaptive dynamics [56], or is cultural diversity merely the result of cultural drift [6]?

How do cultural and genetic evolution interact [7], and under what conditions is either cultural or genetic evolution expected to be ahead in models of antagonistic coevolution?

Under what conditions does cultural evolution promote or hinder the evolution of cooperation, and how do the conditions compare to those under genetic inheritance [24, 46]?

What are the cultural, cognitive and genetic constraints that maintain stable clusters of culturally transmitted traits?

How domain-general or domain-specific are different modes and mechanisms of cultural transmission?

Could phylogenetic network methods [39, 74-76] be further extended, e.g. to distinguish between borrowing, convergent evolution and noise in the data, or to provide better quantitative and statistical support for reticulation events?

Could standard or network cultural phylogenies be constructed based on an explicit maximum likelihood or Bayesian evolutionary model [31], e.g. in the context of the evolution of language incorporating models of phonological change [83]?

Could ancestral state reconstruction [8, 31] be used to reconstruct extinct protolanguages or produce reconstructions of lost manuscripts or cultural artefacts?

How should phylogenetic non-independence [8, 31] be accounted for in comparative analyses if phylogenies are reticulate and the phylogenies of the traits to be compared are not identical [19]?

16

B B B B S SB B B B B B

S B S B S SB N N B N N

B N B N S SS B N B N S

a

b

c

e

self (S) and biological descendants (B)

S N S B B BN S N S N B

d

Evolution due to Variant spreads if Interpretation in biological evolution Interpretation in cultural evolution

effect on # of descendants(vertical transmission)

carriers survive better or leave a more than average# of biological descendants

natural selection(viability or fecundity selection)

cultural selection via an effect on biological fitness (through viability or fecundity selection)

effect on # of descendants(horizontal or oblique

transmission)

it is copied to or is taken up by a more than average # of unrelated individuals

horizontal gene transfer(in bacteria due to transformation, transduction or conjugation)(similarity bias if genes are preferentially acquired from members of the same species)

cultural selection via greater oblique or horizontal cultural transmission (due to imitation or social learning) (potentially driven by certain transmission biases)

directed individual transformation

there is directed individual change(Lamarckian if changes are heritable)

phenotypic plasticity, epigenetic changes (may be heritable)

individual learning(may be culturally heritable)

directed mutation there is directed change across inheritance paths

biased mutation, meiotic drive (guided variation if bias is towards adaptive variant, e.g. in presence of adaptive mutation)

directed change to due intelligence or foresight(guided variation)

effect on inheritance system it descends from a fewer than average # of parents

spread of asexually (uniparentally) inherited variants ("cost of sex")

spread of variants that can be learned or imitated from or can be imposed by fewer individuals

0).var(0))((ave

0).var(

2~

1~

=

=Δ

≠

hzz

hz

da

zP

a

azD

da

d

aa

β

β

biological descendants (B) or nonrelatives (N)

biological descendants (B) or nonrelatives (N)

nonrelatives (N)

self(S)

0).var(0))((ave

0).var(

2~

1~

=

=Δ

≠

hzz

hz

da

zP

a

azD

da

d

aa

β

β

0).var(0))((ave

0).var(

2~

1~

=

≠Δ

=

hzz

hz

da

zP

a

azD

da

d

aa

β

β

0).var(0))((ave

0).var(

2~

1~

=

≠Δ

=

hzz

hz

da

zP

a

azD

da

d

aa

β

β

0).var(0))((ave

0).var(

2~

1~

≠

=Δ

=

hzz

hz

da

zP

a

azD

da

d

aa

β

β

Fig. 1

17

Fig. 1. Basic factors of evolution in a generalized model of evolutionary change based on the Price equation (Box 1, eqn. 2), and how it applies to

genetic and cultural evolution (modified from ref. [52]). All individuals in the population are matched up with all individuals alive at a next point

in time and connected according to the way in which traits are transmitted, i.e. following genetic descent in biological evolution or cultural descent

in the case of cultural evolution. In both cases, traits may be transmitted either to biological descendants (B) (under vertical transmission) or to

nonrelatives (N) (under horizontal or oblique transmission). Individuals in the descendant population that are survivors from the ancestral

population are also connected with themselves through time (S). For simplicity we consider a closed population (no immigration or emigration). A

given trait variant (black) will increase in frequency when a) carriers have greater personal survival or an above-average number of biological

descendants, b) carriers leave an above-average number of copies in nonrelatives, c) there is increased expression of the trait within an individual's

lifetime, d) there is biased transmission to biological descendants or nonrelatives or e) it can be copied from fewer parents (or cultural models)

(parental phenotypes can combine either via stochastic particulate inheritance or blending inheritance). Each of these basic factors of evolution can

be caused by a variety of mechanisms, and can arise naturally in both biological and cultural evolution. They can also all be subject to

stochastisticity, and be a cause of genetic or cultural drift [57].

18

a

b

c

Fig. 2

19

Fig. 2: Applications of implicit and explicit phylogenetic network methods to cultural

evolution: (a) a Neighbor-Net analysis of basic vocabulary data showing conflicting signal in

a set of Germanic languages; the bold lines represent the signal grouping English with the

creole Sranan, while the dotted lines represent the signal grouping Sranan with Dutch and

other Western Germanic languages [31], (b) a SplitsTree analysis of 43 manuscript versions

of the Prologue to the Wife of Bath’s Tales [80, 85]; in the C/D group the tree shows clear

examples of multifurcations, presumably due to copying from the same source manuscript and

(c) an evolutionary tree of cornets obtained using T-Rex showing technological advances in

design and borrowing of manufacturing technology among makers (curved lines) [22].

Adapted with permission from Ref. [31], the Konrad Lorenz Institute for Evolution and

Cognition Research, Ref. [80], Nature Publishing Group and Ref. [22], Wenner-Gren

Foundation for Anthropological Research.

20

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