My main research interest is the application of game theory to the mathematical modelling of biology, especially using the concept of the Evolutionarily Stable Strategy (ESS). My work has generally been theoretical, considering both purely mathematical work on the theory of games in an evolutionary context and more specific problems when a particular animal behaviour or trait is concerned. I have published and continue to publish work in the three main areas listed below.
Mathematical models of evolution This area involves the development of the general mathematical theory of evolution, rather than any specific application. Early work considered Patterns of Evolutionarily Stable Strategies; a theoretical investigation into the coexistence of different ESSs in the important game class matrix games. A key theme has been multi-player game theory. Most evolutionary game theory concerns two-player games only; this work includes an extension of the theory to many players. A significant branch of this work on multi-player games involves modelling dominance hierarchy formation and maintenance. I have also been involved in the development of other aspects of mathematical evolutionary theory. The most important recent work in this area involves the modelling of evolution on graphs, where populations can possess a complex non-homogeneous structure.
Models of parasitism I have modelled two major types of parasitic behaviour on birds. The first of these involves the modelling of kleptoparasitism, where animals acquire food by stealing from others. This work began with the development of a general modelling framework for kleptoparasitism and considers the circumstances under which it is best to steal food (or not) for different scenarios and varying biological and mathematical assumptions. The second area is the modelling of brood parasitism. Raising young can be costly, and some birds lay their eggs in the nests of other birds to avoid this cost. Various models of both conspecific and interspecific parasitism are considered.
Evolutionary responses to predators and group living A key priority for many animals is the avoidance of predators. Many such prey animals choose to live in groups, and these two features are often strongly related. I have considered two major types of interactions between prey and predators, the first of these being antipredator vigilance in animal groups. This an extension of a well established theory involving trade-offs in time spent watching for predators and foraging, into dynamic changes in group structure and in spatial and positioning factors. The second is the co-evolution of defence and signalling. Many animals possess high levels of toxins to make them unpalatable to potential predators. Such defences are invisible, so they are often also brightly coloured to signal these defences, and success depends upon a sufficient number of conspecifics with these traits for predators to learn to avoid them.
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