Evolutionary Game Dynamics Driven By Mutations Under Frequency Dependent Selection
Evolutionary game theory and theoretical population genetics are two different fields sharing many common properties. In both fields, theoretical models are built to explore evolutionary dynamics; various evolutionary forces, such as selection, mutation, and random genetic drift, are involved in the modeling. However, in terms of concrete models, evolutionary game theory is often considered to deal with phenotypes, while theoretical population genetics describes genotypes. Is it possible and worth to combine approaches from both fields? We address this question by analyzing the evolutionary dynamics driven by random mutations in the framework of evolutionary game theory. Mutations provide a continuous input of new variability into a population, which is exposed to natural selection. In evolutionary game theory, mutations are often assumed to occur among predefined types. This assumption initially made in the study of behavioral phenotypes (i.e. human behaviors), might be less reasonable in studies at the level of genes or genotypes. An alternative assumption is made in the infinite allele model in theoretical population genetics, where every mutation brings a new allele to the population. However, the resulting evolutionary dynamics based on the infinite allele model has only been studied in the context of neutral and constant selection. In this thesis, we propose an evolutionary game theoretic model, which combines the assumption of infinite alleles and frequency dependent fitness. We investigate the evolutionary dynamics in finite and infinite populations based on this model. The fixation probability of a single mutant, the diversity of a population, and the changes of the average population fitness are strikingly different under constant selection and frequency dependent selection scenarios. These results imply that connecting evolutionary game theory and theoretical population genetics approaches can bring a different and insightful view in understanding evolutionary dynamics.