Coevolutionary dynamics in structured populations ofthree species

Inspired by the experiments with the three strains of E. coli bacteria as well as the three morphs of Uta stansburiana lizards, a model of cyclic dominance was proposed to investigate the mechanisms facilitating the maintenance of biodiversity in spatially structured populations. Subsequent studies enriched the original model with various biologically motivated extension repeating the proposed mathematical analysis and computer simulations. The research presented in this thesis unifies and generalises these models by combining the birth, selection-removal, selection-replacement and mutation processes as well as two forms of mobility into a generic metapopulation model. Instead of the standard mathematical treatment, more controlled analysis with inverse system size and multiscale asymptotic expansions is presented to derive an approximation of the system dynamics in terms of a well-known pattern forming equation. The novel analysis, capable of increased accuracy, is evaluated with improved numerical experiments performed with bespoke software developed for simulating the stochastic and deterministic descriptions of the generic metapopulation model. The emergence of spiral waves facilitating the long term biodiversity is confirmed in the computer simulations as predicted by the theory. The derived conditions on the stability of spiral patterns for different values of the biological parameters are studied resulting in discoveries of interesting phenomena such as spiral annihilation or instabilities caused by nonlinear diffusive terms.