Social learning and memory.

The adaptability of human populations to changing environments is often attributed to the human capacity for social learning, innovation, and culture. In rapidly changing environments, it has been shown that maintaining high levels of cultural variation is beneficial because it allows for efficient adaptation. However, in many theoretical models, a high level of cultural variation also implies that a large amount of useless and perhaps detrimental information must be maintained and used, leading to lower population fitness in general. Here, we begin to investigate this often conflicting relationship between adaptation and cultural variation. We explicitly allow for the interplay between social learning and environmental variability, alongside the capacity for "memory," i.e., the storage, retrieval, and forgetting of information. Here, memory allows individuals to retain unexpressed cultural variation, which does not directly impact adaptation. We show that this capacity for memory facilitates the evolution of social learning across a broader range of circumstances than previously thought. Results from this analysis may help to establish whether and when memory should be incorporated into cultural evolutionary models focused on questions of adaptation.

The interplay between age structure and cultural transmission.

Empirical work has shown that human cultural transmission can be heavily influenced by population age structure. We aim to explore the role of such age structure in shaping the cultural composition of a population when cultural transmission occurs in an unbiased way. In particular, we are interested in understanding the effect induced by the interplay between age structure and the cultural transmission process by allowing cultural transmission from individuals within a limited age range only. To this end we develop an age-structured cultural transmission model and find that age-structured and non age-structured populations evolving through unbiased transmission possess very similar cultural compositions (at a single point in time) at the population and sample level if the copy pool consists of a sufficiently large fraction of the population. If, however, an age constraint-a structural constraint restricting the pool of potential role models to individuals of a limited age range- exists, the cultural compositions of age-structured and non age-structured population show stark differences. This may have drastic consequences for our ability to correctly analyse cultural data sets. Rejections of tests of neutrality, blind to age structure and, importantly, the interaction between age structure and cultural transmission, are only indicative of biased transmission if it is known a priori that there are no or only weak age constraints acting on the pool of role models. As this knowledge is rarely available for specific empirical case studies we develop a generative inference approach based on our age-structured cultural transmission model and machine learning techniques. We show that in some circumstances it is possible to simultaneously infer the characteristics of the age structure, the nature of the transmission process, and the interplay between them from observed samples of cultural variants. Our results also point to hard limits on inference from population-level data at a single point in time, regardless of the approach used.

Effective population size for culturally evolving traits.

Population size has long been considered an important driver of cultural diversity and complexity. Results from population genetics, however, demonstrate that in populations with complex demographic structure or mode of inheritance, it is not the census population size, N, but the effective size of a population, Ne, that determines important evolutionary parameters. Here, we examine the concept of effective population size for traits that evolve culturally, through processes of innovation and social learning. We use mathematical and computational modeling approaches to investigate how cultural Ne and levels of diversity depend on (1) the way traits are learned, (2) population connectedness, and (3) social network structure. We show that one-to-many and frequency-dependent transmission can temporally or permanently lower effective population size compared to census numbers. We caution that migration and cultural exchange can have counter-intuitive effects on Ne. Network density in random networks leaves Ne unchanged, scale-free networks tend to decrease and small-world networks tend to increase Ne compared to census numbers. For one-to-many transmission and different network structures, larger effective sizes are closely associated with higher cultural diversity. For connectedness, however, even small amounts of migration and cultural exchange result in high diversity independently of Ne. Extending previous work, our results highlight the importance of carefully defining effective population size for cultural systems and show that inferring Ne requires detailed knowledge about underlying cultural and demographic processes.

Cultural diffusion dynamics depend on behavioural production rules.

Culture is an outcome of both the acquisition of knowledge about behaviour through social transmission, and its subsequent production by individuals. Acquisition and production are often discussed or modelled interchangeably, yet to date no study has explored the consequences of their interaction for cultural diffusions. We present a generative model that integrates the two, and ask how variation in production rules might influence diffusion dynamics. Agents make behavioural choices that change as they learn from their productions. Their repertoires may also change, and the acquisition of behaviour is conditioned on its frequency. We analyse the diffusion of a novel behaviour through social networks, yielding generalizable predictions of how individual-level behavioural production rules influence population-level diffusion dynamics. We then investigate how linking acquisition and production might affect the performance of two commonly used inferential models for social learning; network-based diffusion analysis, and experience-weighted attraction models. We find that the influence that production rules have on diffusion dynamics has consequences for how inferential methods are applied to empirical data. Our model illuminates the differences between social learning and social influence, demonstrates the overlooked role of reinforcement learning in cultural diffusions, and allows for clearer discussions about social learning strategies.

Cultural linkage: the influence of package transmission on cultural dynamics.

Many cultural traits are not transmitted independently, but together as a package. This can happen because, for example, media may store information together making it more likely to be transmitted together, or through cognitive mechanisms such as causal reasoning. Evolutionary biology suggests that physical linkage of genes (being on the same chromosome) allows neutral and maladaptive genes to spread by hitchhiking on adaptive genes, while the pairwise difference between neutral genes is unaffected. Whether packaging may lead to similar dynamics in cultural evolution is unclear. To understand the effect of cultural packages on cultural evolutionary dynamics, we built an agent-based simulation that allows links to form and break between cultural traits. During transmission, one trait and others that are directly or indirectly connected to it are transmitted together in a package. We compare variation in cultural traits between different rates of link formation and breakage and find that an intermediate frequency of links can lower cultural diversity, which can be misinterpreted as a signature of payoff bias or conformity. Further, cultural hitchhiking can occur when links are common.

A Game-Theoretical Winner and Loser Model of Dominance Hierarchy Formation.

Many animals spend large parts of their lives in groups. Within such groups, they need to find efficient ways of dividing available resources between them. This is often achieved by means of a dominance hierarchy, which in its most extreme linear form allocates a strict priority order to the individuals. Once a hierarchy is formed, it is often stable over long periods, but the formation of hierarchies among individuals with little or no knowledge of each other can involve aggressive contests. The outcome of such contests can have significant effects on later contests, with previous winners more likely to win (winner effects) and previous losers more likely to lose (loser effects). This scenario has been modelled by a number of authors, in particular by Dugatkin. In his model, individuals engage in aggressive contests if the assessment of their fighting ability relative to their opponent is above a threshold [Formula: see text]. Here we present a model where each individual can choose its own value [Formula: see text]. This enables us to address questions such as how aggressive should individuals be in order to take up one of the first places in the hierarchy? We find that a unique strategy evolves, as opposed to a mixture of strategies. Thus, in any scenario there exists a unique best level of aggression, and individuals should not switch between strategies. We find that for optimal strategy choice, the hierarchy forms quickly, after which there are no mutually aggressive contests.

Modelling Dominance Hierarchies Under Winner and Loser Effects.

Animals that live in groups commonly form themselves into dominance hierarchies which are used to allocate important resources such as access to mating opportunities and food. In this paper, we develop a model of dominance hierarchy formation based upon the concept of winner and loser effects using a simulation-based model and consider the linearity of our hierarchy using existing and new statistical measures. Two models are analysed: when each individual in a group does not know the real ability of their opponents to win a fight and when they can estimate their opponents' ability every time they fight. This estimation may be accurate or fall within an error bound. For both models, we investigate if we can achieve hierarchy linearity, and if so, when it is established. We are particularly interested in the question of how many fights are necessary to establish a dominance hierarchy.

Inference of Cultural Transmission Modes Based on Incomplete Information.

In this article we explore the theoretical limits of the inference of cultural transmission modes based on sparse population-level data. We approach this problem by investigating whether different transmission modes produce different temporal dynamics of cultural change. In particular, we explore whether different transmission modes result in sufficiently different distributions of the average time a variant stays the most common variant in the population, tmax, so that their inference can be guaranteed on the basis of an estimate of tmax. We assume time series data detailing the frequencies of different variants of a cultural trait in a population at different points in time and investigate the temporal resolution (i.e., the length of the time series and the distance between consecutive time points) that is needed to ensure distinguishability between transmission modes. We find that under complete information most transmission modes can be distinguished on the basis of the statistic tmax; however, we should not expect the same results if only infrequent information about the most common cultural variant in the population is available.

A non-equilibrium neutral model for analysing cultural change.

Neutral evolution is a frequently used model to analyse changes in frequencies of cultural variants over time. Variants are chosen to be copied according to their relative frequency and new variants are introduced by a process of random mutation. Here we present a non-equilibrium neutral model which accounts for temporally varying population sizes and mutation rates and makes it possible to analyse the cultural system under consideration at any point in time. This framework gives an indication whether observed changes in the frequency distributions of a set of cultural variants between two time points are consistent with the random copying hypothesis. We find that the likelihood of the existence of the observed assemblage at the end of the considered time period (expressed by the probability of the observed number of cultural variants present in the population during the whole period under neutral evolution) is a powerful indicator of departures from neutrality. Further, we study the effects of frequency-dependent selection on the evolutionary trajectories and present a case study of change in the decoration of pottery in early Neolithic Central Europe. Based on the framework developed we show that neutral evolution is not an adequate description of the observed changes in frequency.

Tradeoffs between the strength of conformity and number of conformists in variable environments.

Organisms often respond to environmental change phenotypically, through learning strategies that enhance fitness in variable and changing conditions. But which strategies should we expect in population exposed to those conditions? We address this question by developing a mathematical model that specifies the consequences of different mixtures of individual and social learning strategies on the frequencies of different cultural variants in temporally and spatially changing environments. Assuming that alternative cultural variants are differently well-adapted to diverse environmental conditions, we are able to evaluate which mixture of learning strategies maximises the mean fitness of the population. We find that, even in rapidly changing environments, a high proportion of the population will always engage in social learning. In those environments, the highest adaptation levels are achieved through relatively high fractions of individual learning and a strong conformist bias. We establish a negative relationship between the proportion of the population learning socially and the strength of conformity operating in a population: strong conformity requires fewer conformists (i.e. larger proportion of individual learning), while many conformists can only be found when conformist transmission is weak. Investigations of cultural diversity show that in frequently changing environments high levels of adaptation require high level of cultural diversity. Finally, we demonstrate how the developed mathematical framework can be applied to time series of usage or occurrence data of cultural traits. Using Approximate Bayesian Computation we are able to infer information about the underlying learning processes that could have produced observed patterns of variation in the dataset.

Beyond collective intelligence: Collective adaptation.

We develop a conceptual framework for studying collective adaptation in complex socio-cognitive systems, driven by dynamic interactions of social integration strategies, social environments and problem structures. Going beyond searching for 'intelligent' collectives, we integrate research from different disciplines and outline modelling approaches that can be used to begin answering questions such as why collectives sometimes fail to reach seemingly obvious solutions, how they change their strategies and network structures in response to different problems and how we can anticipate and perhaps change future harmful societal trajectories. We discuss the importance of considering path dependence, lack of optimization and collective myopia to understand the sometimes counterintuitive outcomes of collective adaptation. We call for a transdisciplinary, quantitative and societally useful social science that can help us to understand our rapidly changing and ever more complex societies, avoid collective disasters and reach the full potential of our ability to organize in adaptive collectives.

The fundamentals of cultural adaptation: implications for human adaptation.

The process of human adaptation to novel environments is a uniquely complex interplay between cultural and genetic changes. However, mechanistically, we understand little about these processes. To begin to untangle these threads of human adaptation we use mathematical models to describe and investigate cultural selective sweeps. We show that cultural sweeps differ in important ways from the genetic equivalents. The models show that the dynamics of cultural selective sweeps and, consequently, their differences from genetic sweeps depend critically on cultural transmission mechanisms. Further, we consider the effect of processes unique to culture such as foresight and innovations in response to an environmental change on adaptation. Finally we show that a 'cultural evolutionary rescue', or the survival of an endangered population by means of cultural adaptation, is possible. We suggest that culture might make a true, genetic, evolutionary rescue plausible for human populations.

An investigation of the relationship between innovation and cultural diversity.

In this paper we apply reaction-diffusion models to explore the relationship between the rate of behavioural innovation and the level of cultural diversity. We investigate how both independent invention and the modification and refinement of established innovations impact on cultural dynamics and diversity. Further, we analyse these relationships in the presence of biases in cultural learning and find that the introduction of new variants typically increases cultural diversity substantially in the short term, but may decrease long-term diversity. Independent invention generally supports higher levels of cultural diversity than refinement. Repeated patterns of innovation through refinement generate characteristic oscillating trends in diversity, with increasing trends towards greater average diversity observed for medium but not low innovation rates. Conformity weakens the relationship between innovation and diversity. The level of cultural diversity, and pattern of temporal dynamics, potentially provide clues as to the underlying process, which can be used to interpret empirical data.

Demography and language competition.

Attempts to describe language competition and extinction in a mathematical way have enjoyed increased popularity recently. In this paper I review recent modeling approaches and, based on these findings, propose a model of reaction-diffusion type. I analyze the dynamics of interactions of a population with two monolingual groups and a group that is bilingual in these two languages. The results show that demographic factors, such as population growth or population dispersal, play an important role in the competition dynamic. Furthermore, I consider the impact of two strategies for language maintenance: adjusting the status of the endangered language and adjusting the availability of monolingual and bilingual educational resources.

Generative inference for cultural evolution.

One of the major challenges in cultural evolution is to understand why and how various forms of social learning are used in human populations, both now and in the past. To date, much of the theoretical work on social learning has been done in isolation of data, and consequently many insights focus on revealing the learning processes or the distributions of cultural variants that are expected to have evolved in human populations. In population genetics, recent methodological advances have allowed a greater understanding of the explicit demographic and/or selection mechanisms that underlie observed allele frequency distributions across the globe, and their change through time. In particular, generative frameworks-often using coalescent-based simulation coupled with approximate Bayesian computation (ABC)-have provided robust inferences on the human past, with no reliance on a priori assumptions of equilibrium. Here, we demonstrate the applicability and utility of generative inference approaches to the field of cultural evolution. The framework advocated here uses observed population-level frequency data directly to establish the likely presence or absence of particular hypothesized learning strategies. In this context, we discuss the problem of equifinality and argue that, in the light of sparse cultural data and the multiplicity of possible social learning processes, the exclusion of those processes inconsistent with the observed data might be the most instructive outcome. Finally, we summarize the findings of generative inference approaches applied to a number of case studies.This article is part of the theme issue 'Bridging cultural gaps: interdisciplinary studies in human cultural evolution'.

Inferring processes of cultural transmission: the critical role of rare variants in distinguishing neutrality from novelty biases.

Neutral evolution assumes that there are no selective forces distinguishing different variants in a population. Despite this striking assumption, many recent studies have sought to assess whether neutrality can provide a good description of different episodes of cultural change. One approach has been to test whether neutral predictions are consistent with observed progeny distributions, recording the number of variants that have produced a given number of new instances within a specified time interval: a classic example is the distribution of baby names. Using an overlapping generations model, we show that these distributions consist of two phases: a power-law phase with a constant exponent of [Formula: see text], followed by an exponential cut-off for variants with very large numbers of progeny. Maximum-likelihood estimations of the model parameters provide a direct way to establish whether observed empirical patterns are consistent with neutral evolution. We apply our approach to a complete dataset of baby names from Australia. Crucially, we show that analyses based on only the most popular variants, as is often the case in studies of cultural evolution, can provide misleading evidence for underlying transmission hypotheses. While neutrality provides a plausible description of progeny distributions of abundant variants, rare variants deviate from neutrality. Further, we develop a simulation framework that allows the detection of alternative cultural transmission processes. We show that anti-novelty bias is able to replicate the complete progeny distribution of the Australian dataset.This article is part of the themed issue 'Process and pattern in innovations from cells to societies'.

Inferring individual-level processes from population-level patterns in cultural evolution.

Our species is characterized by a great degree of cultural variation, both within and between populations. Understanding how group-level patterns of culture emerge from individual-level behaviour is a long-standing question in the biological and social sciences. We develop a simulation model capturing demographic and cultural dynamics relevant to human cultural evolution, focusing on the interface between population-level patterns and individual-level processes. The model tracks the distribution of variants of cultural traits across individuals in a population over time, conditioned on different pathways for the transmission of information between individuals. From these data, we obtain theoretical expectations for a range of statistics commonly used to capture population-level characteristics (e.g. the degree of cultural diversity). Consistent with previous theoretical work, our results show that the patterns observed at the level of groups are rooted in the interplay between the transmission pathways and the age structure of the population. We also explore whether, and under what conditions, the different pathways can be distinguished based on their group-level signatures, in an effort to establish theoretical limits to inference. Our results show that the temporal dynamic of cultural change over time retains a stronger signature than the cultural composition of the population at a specific point in time. Overall, the results suggest a shift in focus from identifying the one individual-level process that likely produced the observed data to excluding those that likely did not. We conclude by discussing the implications for empirical studies of human cultural evolution.

Evolutionary dynamics of the cryptocurrency market.

The cryptocurrency market surpassed the barrier of $100 billion market capitalization in June 2017, after months of steady growth. Despite its increasing relevance in the financial world, a comprehensive analysis of the whole system is still lacking, as most studies have focused exclusively on the behaviour of one (Bitcoin) or few cryptocurrencies. Here, we consider the history of the entire market and analyse the behaviour of 1469 cryptocurrencies introduced between April 2013 and May 2017. We reveal that, while new cryptocurrencies appear and disappear continuously and their market capitalization is increasing (super-)exponentially, several statistical properties of the market have been stable for years. These include the number of active cryptocurrencies, market share distribution and the turnover of cryptocurrencies. Adopting an ecological perspective, we show that the so-called neutral model of evolution is able to reproduce a number of key empirical observations, despite its simplicity and the assumption of no selective advantage of one cryptocurrency over another. Our results shed light on the properties of the cryptocurrency market and establish a first formal link between ecological modelling and the study of this growing system. We anticipate they will spark further research in this direction.