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Abstract

This thesis investigates the evolution of structured populations involving multiplayer evolutionary games, with a particular focus on realistic, coordinated movement behaviours. Building on recent advancements in evolutionary graph theory, most notably the Broom-Rycht´aˆr framework, which extends the classical evolutionary models to incorporate more realistic features such as multiplayer interactions, this thesis addresses a gap in the existing mathematical literature concerning the modelling of coordinated movement within evolutionary settings. Existing models have primarily focused on independent movement, and more recently, history-dependent movement. Although the theory underlying the framework has been explored in various directions, several movement mechanisms have been developed that characterise coordinated movement, for example, herding and dispersal. By extending existing parameters within the framework, this thesis develops a general methodology for embedding a wide range of considered movement processes into evolutionary settings on arbitrary network structures. We demonstrate that certain levels of aggregation and dispersal can benefit specific types of individuals depending on the considered game, for example, public goods. Throughout this thesis, we consider key evolutionary measures, including fixation probabilities, predictors such as mean group size and temperature and aggregation metrics, and show that their influence is determined by the nature of both the movement process and game.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Department of Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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