Imitation or innovation? Unselective mixed strategies can provide a better solution

Current theory about the evolution of social learning in a changing environment predicts the emergence of mixed strategies that rely on some selective combination of social and asocial learning. However, the results of a recent tournament of social learning strategies [Rendell et al. Science 328(5975):208?C213, 2010] suggest that the success relies almost entirely on copying to learn behavior. Those authors conclude that mixed strategies are vulnerable to invasion by individuals using social learning strategies alone. Here we perform a competition using unselective strategies that differ only in the degree of social versus asocial learning. We show that, under the same conditions of the aforementioned tournament, a pure social learning strategy can be invaded by an unselectively mixed strategy and attain an equilibrium where the latter is majority. Although existing theory suggests that copying other individuals unselectively is not adaptive, we show that, at this equilibrium, the average individual fitness of the population is higher than for a population of pure asocial learners, overcoming Rogers?? paradox in finite populations.     

Evolution of social versus individual learning in an infinite island model

We model the evolution of learning in a population composed of infinitely many, finite-sized islands connected by migration. We assume that there are two discrete strategies, social and individual learning, and that the environment is spatially homogeneous but varies temporally in a periodic or stochastic manner. Using a population-genetic approximation technique, we derive a mathematical condition for the two strategies to coexist stably and the equilibrium frequency of social learners under stable coexistence. Analytical and numerical results both reveal that social learners are favored when island size is large or migration rate between islands is high, suggesting that spatial subdivision disfavors social learners. We also show that the average fecundity of the population under stable coexistence of the two strategies is in general lower than that in the absence of social learners and is minimized at an intermediate migration rate.     

Strategic social learning and the population dynamics of human behavior: the game of Go

Human culture is widely believed to undergo evolution, via mechanisms rooted in the nature of human cognition. A number of theories predict the kinds of human learning strategies, as well as the population dynamics that result from their action. There is little work, however, that quantitatively examines the evidence for these strategies and resulting cultural evolution within human populations. One of the obstacles is the lack of individual-level data with which to link transmission events to larger cultural dynamics. Here, we address this problem with a rich quantitative database from the East Asian board game known as Go. We draw from a large archive of Go games spanning the last six decades of professional play, and find evidence that the evolutionary dynamics of particular cultural variants are driven by a mix of individual and social learning processes. Particular players vary dramatically in their sensitivity to population knowledge, which also varies by age and nationality. The dynamic patterns of opening Go moves are consistent with an ancient, ongoing arms race within the game itself.     

An experimental comparison of human social learning strategies: payoff-biased social learning is adaptive but underused

Analytical models have identified a set of social learning strategies that are predicted to be adaptive relative to individual (asocial) learning. In the present study, human participants engaged in an ecologically valid artifact-design task with the opportunity to engage in a range of social learning strategies: payoff bias, conformity, averaging and random copying. The artifact (an arrowhead) was composed of multiple continuous and discrete attributes which jointly generated a complex multimodal adaptive landscape that likely reflects actual cultural fitness environments. Participants exhibited a mix of individual learning and payoff-biased social learning, with negligible frequencies of the other social learning strategies. This preference for payoff-biased social learning was evident from the initial trials, suggesting that participants came into the study with an intrinsic preference for this strategy. There was also a small but significant increase in the frequency of payoff-biased social learning over sessions, suggesting that strategy choice may itself be subject to learning. Frequency of payoff-biased social learning predicted both absolute and relative success in the task, especially in a multimodal (rather than unimodal) fitness environment. This effect was driven by a minority of hardcore social learners who copied the best group member on more than half of trials. These hardcore social learners were also above-average individual learners, suggesting a link between individual and social learning ability. The lower-than-expected frequency of social learning may reflect the existence of information producer–scrounger dynamics in human populations.     

Two success-biased social learning strategies

I compare the evolutionary dynamics of two success-biased social learning strategies, which, by definition, use the success of others to inform one’s social learning decisions. The first, “Compare Means”, causes a learner to adopt cultural variants with highest mean payoff in her sample. The second, “Imitate the Best”, causes a learner to imitate the single most successful individual in her sample. I summarize conditions under which each strategy performs well or poorly, and investigate their evolution via a gene-culture coevolutionary model. Despite the adaptive appeal of these strategies, both encounter conditions under which they systematically perform worse than simply imitating at random. Compare Means performs worst when the optimal cultural variant is usually at high frequency, while Imitate the Best performs worst when suboptimal variants sometimes produce high payoffs. The extent to which it is optimal to use success-biased social learning depends strongly on the payoff distributions and environmental conditions that human social learners face.     

Coexistence of individual and social learners during range expansion

Individual learning and social learning are two primary abilities supporting cultural evolution. Conditions for their evolution have mostly been studied by investigating gene frequency dynamics, which essentially implies constant population size. Predictions from such “static” models may only be of partial relevance to the evolution of advanced individual learning in modern humans, because modern humans have experienced rapid population growth and range expansion during “out-of-Africa.” Here we model the spatial population dynamics of individual and social learners by a reaction–diffusion system. One feature of our model is the inclusion of the possibility that social learners may fail to find an exemplar to copy in regions where the population density is low. Due to this attenuation effect, the invasion speed of social learners is diminished, and various kinds of invasion dynamics are observed. Our primary findings are: (1) individual learners can persist indefinitely when invading environmentally homogeneous infinite space; (2) the occurrence of individual learners at the front may inhibit the spread of social learners. These results suggest that “out-of-Africa” may have driven the evolution of advanced individual learning ability in modern humans.     

SOCIAL LEARNERS REQUIRE PROCESS INFORMATION TO OUTPERFORM INDIVIDUAL LEARNERS

Humans exhibit a rich and complex material culture with no equivalent in animals. Also, social learning, a crucial requirement for culture, is particularly developed in humans and provides a means to accumulate knowledge over time and to develop advanced technologies. However, the type of social learning required for the evolution of this complex material culture is still debated. Here, using a complex and opaque virtual task, the efficiency of individual learning and two types of social learning (product‐copying and process‐copying) were compared. We found that (1) individuals from process‐copying groups outperformed individuals from product‐copying groups or individual learners, whereas access to product information was not a sufficient condition for providing an advantage to social learners compared to individual learners; (2) social learning did not seem to affect the exploration of the fitness landscape; (3) social learning led to strong within‐group convergence and also to between‐group convergence, and (4) individuals used widely variable social learning strategies. The implications of these results for cumulative culture evolution are discussed.     

A mixed strategy model for the emergence and intensification of social learning in a periodically changing natural environment

Based on a population genetic model of mixed strategies determined by alleles of small effect, we derive conditions for the evolution of social learning in an infinite-state environment that changes periodically over time. Each mixed strategy is defined by the probabilities that an organism will commit itself to individual learning, social learning, or innate behavior. We identify the convergent stable strategies (CSS) by a numerical adaptive dynamics method and then check the evolutionary stability (ESS) of these strategies. A strategy that is simultaneously a CSS and an ESS is called an attractive ESS (AESS). For certain parameter sets, a bifurcation diagram shows that the pure individual learning strategy is the unique AESS for short periods of environmental change, a mixed learning strategy is the unique AESS for intermediate periods, and a mixed learning strategy (with a relatively large social learning component) and the pure innate strategy are both AESS's for long periods. This result entails that, once social learning emerges during a transient era of intermediate environmental periodicity, a subsequent elongation of the period may result in the intensification of social learning, rather than a return to innate behavior.     

A mixed strategy model for the emergence and intensification of social learning in a periodically changing natural environment

Based on a population genetic model of mixed strategies determined by alleles of small effect, we derive conditions for the evolution of social learning in an infinite-state environment that changes periodically over time. Each mixed strategy is defined by the probabilities that an organism will commit itself to individual learning, social learning, or innate behavior. We identify the convergent stable strategies (CSS) by a numerical adaptive dynamics method and then check the evolutionary stability (ESS) of these strategies. A strategy that is simultaneously a CSS and an ESS is called an attractive ESS (AESS). For certain parameter sets, a bifurcation diagram shows that the pure individual learning strategy is the unique AESS for short periods of environmental change, a mixed learning strategy is the unique AESS for intermediate periods, and a mixed learning strategy (with a relatively large social learning component) and the pure innate strategy are both AESS's for long periods. This result entails that, once social learning emerges during a transient era of intermediate environmental periodicity, a subsequent elongation of the period may result in the intensification of social learning, rather than a return to innate behavior.     

Evolution of Cooperation on Stochastic Dynamical Networks

Cooperative behavior that increases the fitness of others at a cost to oneself can be promoted by natural selection only in the presence of an additional mechanism. One such mechanism is based on population structure, which can lead to clustering of cooperating agents. Recently, the focus has turned to complex dynamical population structures such as social networks, where the nodes represent individuals and links represent social relationships. We investigate how the dynamics of a social network can change the level of cooperation in the network. Individuals either update their strategies by imitating their partners or adjust their social ties. For the dynamics of the network structure, a random link is selected and breaks with a probability determined by the adjacent individuals. Once it is broken, a new one is established. This linking dynamics can be conveniently characterized by a Markov chain in the configuration space of an ever-changing network of interacting agents. Our model can be analytically solved provided the dynamics of links proceeds much faster than the dynamics of strategies. This leads to a simple rule for the evolution of cooperation: The more fragile links between cooperating players and non-cooperating players are (or the more robust links between cooperators are), the more likely cooperation prevails. Our approach may pave the way for analytically investigating coevolution of strategy and structure.     

ROGERS' PARADOX RECAST AND RESOLVED: POPULATION STRUCTURE AND THE EVOLUTION OF SOCIAL LEARNING STRATEGIES

We explore the evolution of reliance on social and asocial learning using a spatially explicit stochastic model. Our analysis considers the relative merits of four evolved strategies, two pure strategies (asocial and social learning) and two conditional strategies (the "critical social learner," which learns asocially only when copying fails, and the "conditional social learner," which copies only when asocial learning fails). We find that spatial structure generates outcomes that do not always conform to the finding of earlier theoretical analyses that social learning does not enhance average individual fitness at equilibrium (Rogers' paradox). Although we describe circumstances under which the strategy of pure social learning increases the average fitness of individuals, we find that spatial structure introduces a new paradox, which is that social learning can spread even when it decreases the average fitness of individuals below that of asocial learners. We also show that the critical social learner and conditional social learner both provide solutions to the aforementioned paradoxes, although we find some conditions in which pure (random) social learning out-competes both conditional strategies. Finally, we consider the relative merits of critical and conditional social learning under various conditions.     

Oscillatory dynamics in evolutionary games are suppressed by heterogeneous adaptation rates of players

Game dynamics in which three or more strategies are cyclically competitive, as represented by the rock-scissors-paper game, have attracted practical and theoretical interests. In evolutionary dynamics, cyclic competition results in oscillatory dynamics of densities of individual strategists. In finite-size populations, it is known that oscillations blow up until all but one strategies are eradicated if without mutation. In the present paper, we formalize replicator dynamics with players who have different adaptation rates. We show analytically and numerically that the heterogeneous adaptation rate suppresses the oscillation amplitude. In social dilemma games with cyclically competing strategies and homogeneous adaptation rates, altruistic strategies are often relatively weak and cannot survive in finite-size populations. In such situations, heterogeneous adaptation rates save coexistence of different strategies and hence promote altruism. When one strategy dominates the others without cyclic competition, fast adaptors earn more than slow adaptors. When not, mixture of fast and slow adaptors stabilizes population dynamics, and slow adaptation does not imply inefficiency for a player.     

On the number of independent cultural traits carried by individuals and populations

In species subject to individual and social learning, each individual is likely to express a certain number of different cultural traits acquired during its lifetime. If the process of trait innovation and transmission reaches a steady state in the population, the number of different cultural traits carried by an individual converges to some stationary distribution. We call this the trait-number distribution. In this paper, we derive the trait-number distributions for both individuals and populations when cultural traits are independent of each other. Our results suggest that as the number of cultural traits becomes large, the trait-number distributions approach Poisson distributions so that their means characterize cultural diversity in the population. We then analyse how the mean trait number varies at both the individual and population levels as a function of various demographic features, such as population size and subdivision, and social learning rules, such as conformism and anti-conformism. Diversity at the individual and population levels, as well as at the level of cultural homogeneity within groups, depends critically on the details of population demography and the individual and social learning rules.     

ASSORTATIVE SOCIAL LEARNING AND ITS IMPLICATIONS FOR HUMAN (AND ANIMAL?) SOCIETIES

Choosing from whom to learn is an important element of social learning. It affects learner success and the profile of behaviors in the population. Because individuals often differ in their traits and capabilities, their benefits from different behaviors may also vary. Homophily, or assortment, the tendency of individuals to interact with other individuals with similar traits, is known to affect the spread of behaviors in humans. We introduce models to study the evolution of assortative social learning (ASL), where assorting on a trait acts as an individual‐specific mechanism for filtering relevant models from which to learn when that trait varies. We show that when the trait is polymorphic, ASL may maintain a stable behavioral polymorphism within a population (independently of coexistence with individual learning in a population). We explore the evolution of ASL when assortment is based on a nonheritable or partially heritable trait, and when ASL competes with different non‐ASL strategies: oblique (learning from the parental generation) and vertical (learning from the parent). We suggest that the tendency to assort may be advantageous in the context of social learning, and that ASL might be an important concept for the evolutionary theory of social learning.     

The evolution of conformist social learning can cause population collapse in realistically variable environments

Why do societies collapse? We use an individual-based evolutionary model to show that, in environmental conditions dominated by low-frequency variation (“red noise”), extirpation may be an outcome of the evolution of cultural capacity. Previous analytical models predicted an equilibrium between individual learners and social learners, or a contingent strategy in which individuals learn socially or individually depending on the circumstances. However, in red noise environments, whose main signature is that variation is concentrated in relatively large, relatively rare excursions, individual learning may be selected from the population. If the social learning system comes to lack sufficient individual learning or cognitively costly adaptive biases, behavior ceases tracking environmental variation. Then, when the environment does change, fitness declines and the population may collapse or even be extirpated. The modeled scenario broadly fits some human population collapses and might also explain nonhuman extirpations. Varying model parameters showed that the fixation of social learning is less likely when individual learning is less costly, when the environment is less red or more variable, with larger population sizes, and when learning is not conformist or is from parents rather than from the general population. Once social learning is fixed, extirpation is likely except when social learning is biased towards successful models. Thus, the risk of population collapse may be reduced by promoting individual learning and innovation over cultural conformity, or by preferential selection of relatively fit individuals as models for social learning.     

How does competition affect the transmission of information?

The use of social information is a prerequisite to the evolution of culture. In humans, social learning allows individuals to aggregate adaptive information and increase the complexity of technology at a level unparalleled in the animal kingdom. However, the potential to use social information is related to the availability of this type of information. Although most cultural evolution experiments assume that social learners are free to use social information, there are many examples of information withholding, particularly in ethnographic studies. In this experiment, we used a computer-based cultural game in which players were faced with a complex task and had the possibility to trade a specific part of their knowledge within their groups. The dynamics of information transmission were studied when competition was within- or exclusively between-groups. Our results show that between-group competition improved the transmission of information, increasing the amount and the quality of information. Further, informational access costs did not prevent social learners from performing better than individual learners, even when between-group competition was absent. Interestingly, between-group competition did not entirely eliminate access costs and did not improve the performance of players as compared with within-group competition. These results suggest that the field of cultural evolution would benefit from a better understanding of the factors that underlie the production and the sharing of information.     

Sex ratio evolution under probabilistic sex determination

Sex allocation theory has been remarkably successful at explaining the prevalence of even sex ratios in natural populations and at identifying specific conditions that can result in biased sex ratios. Much of this theory focuses on parental sex determination (SD) strategies. Here, we consider instead the evolutionary causes and consequences of mixed offspring SD strategies, in which the genotype of an individual determines not its sex, but the probability of developing one of multiple sexes. We find that alleles specifying mixed offspring SD strategies can generally outcompete alleles that specify pure strategies, but generate constraints that may prevent a population from reaching an even sex ratio. We use our model to analyze sex ratios in natural populations of Tetrahymena thermophila, a ciliate with seven sexes determined by mixed SD alleles. We show that probabilistic SD is sufficient to account for the occurrence of skewed sex ratios in natural populations of T. thermophila, provided that their effective population sizes are small. Our results highlight the importance of genetic drift in sex ratio evolution and suggest that mixed offspring SD strategies should be more common than currently thought.     

Evolution of social learning: a mathematical analysis

Social learning is an important ability seen in a wide range of animals including humans. It has been argued that individual learning, social learning, and innate determination of behavior are favored by natural selection when environmental changes occur at short, intermediate, and long intervals, respectively. Only recently, however, has the hypothesis been examined by means of mathematical models. In this paper, we construct a simple model in which each organism uses one of three genetically determined strategies--it is an individual learner, a social learner or an "innate"--and the three types of organisms are in direct competition with each other. A reduced model, involving only the individual learners and innates, is effectively linear, and we show that by solving the eigenvalue problem of this reduced system we arrive at a good approximation to the global dynamics of the full model. We also study the effect of stochastic environmental changes and reversible mutations among the three strategies. Our results are consistent with the predictions of previous studies. In addition, we identify a critical level of environmental constancy below which only individual and social learners are present.     

Individual acquisition of “stick pounding” behavior by naïve chimpanzees

Many studies investigating culture in nonhuman animals tend to focus on the inferred need of social learning mechanisms that transmit the form of a behavior to explain the population differences observed in wild animal behavioral repertoires. This research focus often results in studies overlooking the possibility of individuals being able to develop behavioral forms without requiring social learning. The disregard of individual learning abilities is most clearly observed in the nonhuman great ape literature, where there is a persistent claim that chimpanzee behaviors, in particular, require various forms of social learning mechanisms. These special social learning abilities have been argued to explain the acquisition of the relatively large behavioral repertoires observed across chimpanzee populations. However, current evidence suggests that although low‐fidelity social learning plays a role in harmonizing and stabilizing the frequency of behaviors within chimpanzee populations, some (if not all) of the forms that chimpanzee behaviors take may develop independently of social learning. If so, they would be latent solutions—behavioral forms that can (re‐)emerge even in the absence of observational opportunities, via individual (re)innovations. Through a combination of individual and low‐fidelity social learning, the population‐wide patterns of behaviors observed in great ape species are then established and stably maintained. This is the Zone of Latent Solutions (ZLS) hypothesis. The current study experimentally tested the ZLS hypothesis for pestle pounding, a wild chimpanzee behavior. We tested the reinnovation of this behavior in semi‐wild chimpanzees at Chimfunshi Wildlife Orphanage in Zambia, Africa, (N = 90, tested in four social groups). Crucially, all subjects were naïve to stick pounding before testing. Three out of the four tested groups reinnovated stick pounding—clearly demonstrating that this behavioral form does not require social learning. These findings provide support for the ZLS hypothesis alongside further evidence for the individual learning abilities of chimpanzees.     

The impact of imitation on vaccination behavior in social contact networks

Previous game-theoretic studies of vaccination behavior typically have often assumed that populations are homogeneously mixed and that individuals are fully rational. In reality, there is heterogeneity in the number of contacts per individual, and individuals tend to imitate others who appear to have adopted successful strategies. Here, we use network-based mathematical models to study the effects of both imitation behavior and contact heterogeneity on vaccination coverage and disease dynamics. We integrate contact network epidemiological models with a framework for decision-making, within which individuals make their decisions either based purely on payoff maximization or by imitating the vaccination behavior of a social contact. Simulations suggest that when the cost of vaccination is high imitation behavior may decrease vaccination coverage. However, when the cost of vaccination is small relative to that of infection, imitation behavior increases vaccination coverage, but, surprisingly, also increases the magnitude of epidemics through the clustering of non-vaccinators within the network. Thus, imitation behavior may impede the eradication of infectious diseases. Calculations that ignore behavioral clustering caused by imitation may significantly underestimate the levels of vaccination coverage required to attain herd immunity.