Evolutionary Graph Theory of Biased Sexual Reproduction

Abstract

Evolutionary dynamics research has traditionally focused on asexual reproduction, where reproduction consists of an individual putting a clone of itself into the population. However, many real organisms reproduce sexually, where two individuals mate and each contribute genetic material to the child. Additionally, genetic elements called gene drives can bias the sexual reproduction process and thus cause their inheritance probability to be greater than half. In this thesis, we propose several evolutionary graph theory models of biased sexual reproduction. We use a combination of mathematical tools and computational simulations to analyze the behavior of these models with a variety of different graphs and parameter values. We hope this research could be used to help design gene drives and plan their release strategy, and to help understand the evolutionary dynamics of sexual reproduction more generally.