The stochastic modelling of social and territorial behaviour
This thesis considers mathematical models of the interaction between social and territorial behaviour in animals, mainly by probabilistic methods. Chapter 1 introduces the Resource Dispersion Hypothesis, which suggests that territorial behaviour plus dispersed food resources can explain the existence of social groups, and describes an existing model of the process, due to Carr and Macdonald. In Chapter 2 the model of Carr and Macdonald is analysed, and in Chapter 3 an improved model is suggested and its main properties derived, primarily using renewal theory. Chapters 4 and 5 consider various spatial models for territory formation, and the effect, of spatial factors on social behaviour, using analytic and simulation-based methods. Chapter 6 considers the evolution of social behaviour using both discrete-time deterministic models and branching processes to investigate the viability of different strategies of social behaviour in the presence of dispersed resources.