Evolutionary games and population dynamics: from theory to applications

Evolutionary game theory (EGT) was developed to model biological populations, and the early models had great success in explaining apparently paradoxical biological behaviour. Animal and human populations are complex, however, involving important factors such as social relationships, space and time. Thus whilst EGT is a great tool to conceptualize and understand real-world biological interactions, standard EGT is often too simplistic and therefore insufficient to describe the interactions at hand with a sufficient level of realism. There has thus been a lot of work in developing more realistic models of populations, including by participants in this project, and this is a rapidly growing area. There is a great shortage of, and need for, highly trained and versatile researchers comfortable with the mixture of mathematical modeling, biological knowledge and expertise in computing and the analysis of data. It is rare for undergraduates to be taught all of these skills, and so a significant training focus is needed at PhD level. The development of a strong group of such researchers is at the centre of this proposal, and we have developed a training plan to give them the required expertise in the relevant areas, and their combination. We will pursue 4 research themes, 2 developing methodology and 2 focused on applications. The first concerns the modelling of structured populations, incorporating more realistic spatial and social interactions. The second considers important out of equilibrium dynamical concepts, often neglected in favour of equilibria. The third focuses on the mathematical modelling of cancer and its treatment. Here the two above concepts are especially important. The fourth considers ecological and epidemiological modelling where the focus is on structural complexity relating to the interplay of different timescales and the management and analysis of epidemiological data. Whilst specialising, all ESRs will gain knowledge of all of these important themes.