Group living is a widespread and ubiquitous phenomenon in the animal kingdom. Animals in groups are subjected to numerous costs and benefits. Of the benefits, increased protection from predators is the most theoretically and experimentally researched. Three ``principal'' effects explain the anti-predation benefits of grouping: collective vigilance, dilution of risk, and the confusion effect. In this thesis, new theoretical models are developed to study the behaviours that emerge from groups of prey. Using a mathematical approach, this research analyses how the principal anti-predation effects interact to influence the behaviours of grouping animals.
Through an analytical approach, the first part of this thesis examines the role of anti-predation effects on individuals with discrete behavioural choices. The outcomes of group interactions are classified by exact analytical conditions. Results are provided which show how factors relating to predation risk, such as group size, affect anti-predator behaviours.
Another component of this research uses field data to assess the theoretical results that are presented. The relative influence of each anti-predation effect, and how the anti-predation effect interact to influence individual behaviours within groups is assessed. Consideration of how predation risk and other factors of grouping affect behaviours is also analysed.
The final section of research considers highly flexible and continuous anti-predator behaviours. This shift in theory is relevant in groups of prey, for example in models of vigilance. Intuitive results are presented, and conditions are provided which determine qualitatively distinct behavioural dynamics when groups are characterised by continuous behaviours. Equivalences to the discrete behaviour analogue case are shown. It is also shown that individuals may choose neither of the discrete behavioural options. Conditions are derived which specify the occurrence of multiple distinct anti-predator behaviours emerging from a group initially composed of one behaviour, and when the reserve process occurs.
