Kimmo Eriksson

Why copy others? Insights from the social learning strategies tournament.

It Pays to Be a Copy Cat Does it pay to copy what others do? Rendell et al. (p. 208) elected to copy Robert Axelrods 1979 tournament in which strategies for playing the iterated prisoners dilemma game were pitted against each other until an overall winner emerged—the tit-for-tat strategy. In the 2008 tournament, 100 social learning strategies designed to cope with a changing environment competed against each other; the winning strategy involved sampling the behaviors of other players periodically, rather than exploring the environment alone. Learning from what others do is more efficient than learning all on one’s own. Social learning (learning through observation or interaction with other individuals) is widespread in nature and is central to the remarkable success of humanity, yet it remains unclear why copying is profitable and how to copy most effectively. To address these questions, we organized a computer tournament in which entrants submitted strategies specifying how to use social learning and its asocial alternative (for example, trial-and-error learning) to acquire adaptive behavior in a complex environment. Most current theory predicts the emergence of mixed strategies that rely on some combination of the two types of learning. In the tournament, however, strategies that relied heavily on social learning were found to be remarkably successful, even when asocial information was no more costly than social information. Social learning proved advantageous because individuals frequently demonstrated the highest-payoff behavior in their repertoire, inadvertently filtering information for copiers. The winning strategy (discountmachine) relied nearly exclusively on social learning and weighted information according to the time since acquisition.

Lecture Hall Partitions

AbstractWe prove a finite version of the well-known theorem that says that the number of partitions of an integer N into distinct parts is equal to the number of partitions of N into odd parts. Our version says that the number of “lecture hall partitions of length n ” of N equals the number of partitions of N into small odd parts: 1,3,5, ldots, 2n-1 . We give two proofs: one via Botts formula for the Poincaré series of the affine Coxeter group

Critical points in current theory of conformist social learning

\tilde C_n

Modelling the evolution and diversity of cumulative culture

, and one direct proof.

Accumulation of independent cultural traits.

Sorting a permutation by block moves is a task that every bridge player has to solve every time she picks up a new hand of cards. It is also a problem for the computational biologist, for block moves are a fundamental type of mutation that can explain why genes common to two species do not occur in the same order in the chromosome, It is not known whether there exists an optimal sorting procedure running in polynomial time. Bafna and Pevzner gave a polynomial time algorithm that sorts any permutation of length n in at most 3n/4 moves. Our new algorithm improves this to [(2n - 2)/3] for n greater than or equal to 9. For the reverse permutation, we give an exact expression for the number of moves needed, namely [(n + 1)/2]. Computations of Bafha and Pevzner up to n = 10 seemed to suggest that this is the worst case; but as it turns out, a first counterexample occurs for n = 13, i.e. the bridge players case. Professional card players never sort by rank, only by suit. For this case, we give a complete answer to the optimal sorting problem.

Stable matching in a common generalization of the marriage and assignment models

Abstract Existing mathematical models suggest that gene-culture coevolution favours a conformist bias in social learning, that is, a psychological mechanism to preferentially acquire the most common cultural variants. Here we show that this conclusion relies on specific assumptions that seem unrealistic, such as that all cultural variants are known to every individual. We present two models that remove these assumptions, showing that: 1) the rate of cultural evolution and the adaptive value of culture are higher in a population in which individuals pick cultural variants at random (Random strategy) rather than picking the most common one (Conform strategy); 2) in genetic evolution the Random strategy out-competes the Conform strategy, unless cultural evolution is very slow, in which case Conform and Random usually coexist; 3) the individuals’ ability to evaluate cultural variants is a more important determinant of the adaptive value of culture than frequency-based choice strategies. We also review existin...

Lecture Hall Partitions II

The ability to acquire knowledge and skills from others is widespread in animals and is commonly thought to be responsible for the behavioural traditions observed in many species. However, in spite of the extensive literature on theoretical analyses and empirical studies of social learning, little attention has been given to whether individuals acquire knowledge from a single individual or multiple models. Researchers commonly refer to instances of sons learning from fathers, or daughters from mothers, while theoreticians have constructed models of uniparental transmission, with little consideration of whether such restricted modes of transmission are actually feasible. We used mathematical models to demonstrate that the conditions under which learning from a single cultural parent can lead to stable culture are surprisingly restricted (the same reasoning applies to a single social-learning event). Conversely, we demonstrate how learning from more than one cultural parent can establish culture, and find that cultural traits will reach a nonzero equilibrium in the population provided the product of the fidelity of social learning and the number of cultural parents exceeds 1. We discuss the implications of the analysis for interpreting various findings in the animal social-learning literature, as well as the unique features of human culture.

ARE PEOPLE REALLY CONFORMIST-BIASED? AN EMPIRICAL TEST AND A NEW MATHEMATICAL MODEL

Previous work on mathematical models of cultural evolution has mainly focused on the diffusion of simple cultural elements. However, a characteristic feature of human cultural evolution is the seemingly limitless appearance of new and increasingly complex cultural elements. Here, we develop a general modelling framework to study such cumulative processes, in which we assume that the appearance and disappearance of cultural elements are stochastic events that depend on the current state of culture. Five scenarios are explored: evolution of independent cultural elements, stepwise modification of elements, differentiation or combination of elements and systems of cultural elements. As one application of our framework, we study the evolution of cultural diversity (in time as well as between groups).