Abstract: The social hierarchies observed in natural systems often show a high degree of transitivity. Transitive hierarchies do not only require rank differentiation within pairs of individuals but also a higher level ordering of relations within the group. Several authors have suggested that the formation of linear hierarchies at the group level is an emergent property of individual behavioural rules, referred to as winner and loser effects. Winner and loser effects occur if winners of previous conflicts are more likely to escalate the current conflict, whereas the losers of previous conflicts are less likely to do so. According to this idea, an individual's position in a hierarchy may not necessarily reflect its fighting ability, but may rather result from arbitrary historical asymmetries, in particular the history of victories and defeats. However, if this is the case, it is difficult to explain from an evolutionary perspective why a low ranking individual should accept its subordinate status. Here we present a game theoretical model to investigate whether winner and loser effects giving rise to transitive hierarchies can evolve and under which conditions they are evolutionarily stable. The main version of the model focuses on an extreme case in which there are no intrinsic differences in fighting ability between individuals. The only asymmetries that may arise between individuals are generated by the outcome of previous conflicts. We show that, at evolutionary equilibrium, these asymmetries can be utilized for conventional conflict resolution. Several evolutionarily stable strategies are based on winner and loser effects and these strategies give rise to transitive hierarchies.

Abstract: In recent years evidence has been accumulating that personalities are not only found in humans but also in a wide range of other animal species. Individuals differ consistently in their behavioural tendencies and the behaviour in one context is correlated with the behaviour in multiple other contexts. From an adaptive perspective, the evolution of animal personalities is still a mystery, because a more flexible structure of behaviour should provide a selective advantage. Accordingly, many researchers view personalities as resulting from constraints imposed by the architecture of behaviour (but see ref. 12). In contrast, we show here that animal personalities can be given an adaptive explanation. Our argument is based on the insight that the trade-off between current and future reproduction often results in polymorphic populations in which some individuals put more emphasis on future fitness returns than others. Life-history theory predicts that such differences in fitness expectations should result in systematic differences in risk-taking behaviour. Individuals with high future expectations (who have much to lose) should be more risk-averse than individuals with low expectations. This applies to all kinds of risky situations, so individuals should consistently differ in their behaviour. By means of an evolutionary model we demonstrate that this basic principle results in the evolution of animal personalities. It simultaneously explains the coexistence of behavioural types, the consistency of behaviour through time and the structure of behavioural correlations across contexts. Moreover, it explains the common finding that explorative behaviour and risk-related traits like boldness and aggressiveness are common characteristics of animal personalities.