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Abstract:
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.
