Inclusive Fitness on Evolutionary Graphs

Abstract

The evolution of cooperative behaviours has received a large amount of attention in the literature. A recurrent result is that a spatial population structure often aids the evolution of cooperation. One such possible structure is a graph. Members of the population reside on vertices and interact with those connected by edges. The population changes over time via births and deaths and these changes are manifest in changing gene frequencies.

I am interested in the change in frequency of a cooperative allele and one way to calculate this is with the inclusive fitness effect. The inclusive fitness effect is the sum of the effects of a behaviour on the members of a population, each effect weighted by a measure of genetic relatedness.

In this thesis, I derive inclusive fitness theory in the context of evolutionary graphs.

I provide new ways of calculating components of the inclusive fitness effect and high-light remaining challenges posed by graph-structured population models.