Cooperation versus Dominance Hierarchies in Animal Groups

While some communities of animals living in groups may develop systems of cooperation or mutual altruism, many other animal societies are characterised by dominance hierarchies. This thesis is concerned with describing the development of cooperation and dominance hierarchies amongst animal groups. By using a game-theoretic framework, I develop and investigate simple models to describe social interactions amongst animals. In particular, I consider the situation in which the animals differ from each other by some asymmetry and I analyse the effect of such individual differences on the models. Unlike earlier work in this field, which tended to focus on cooperation or dominance hierarchies in isolation, I develop a model that allows both cooperation and dominance hierarchies to arise. Additionally, this work is novel in that it makes a connection between the Hawk–Dove model and the formation of a dominance hierarchy. I begin my analysis with a static analysis of the asymmetric Hawk–Dove game, using the concept of an evolutionary stable strategy. This is followed by the application of replicator dynamics to the problem. My analysis shows that neither of these standard approaches allow cooperation as an outcome, which motivates me to develop new but tractable dynamic models. The final model presented allows both cooperation and dominance relations in different circumstances, and I discuss how it can be used to model the formation of a dominance hierarchy. Finally, I investigate how much asymmetry is required in order to make qualitative differences in the relative frequencies of cooperation and dominance hierarchies.