# The evolution of social traits in network structured populations

# The evolution of social traits in network structured populations

Over many decades theoretical biologists have grappled with the question of how to measure the relative selective advantage of different behavioral strategies. The various approaches to this question have fallen into one of the following categories: fixation probability of a mutant allele in a wild type population, some measures of gene frequency and gene frequency change, and a formulation of a different type of fitness called the inclusive fitness. Countless theoretical studies have examined the relationship between these approaches, and it has generally been thought that, under standard simplifying assumptions, they yield equivalent results. Most of this theoretical work, however, has assumed internal symmetry (homogeneity) of the population interaction structure -- i.e., that all individuals are equivalent. I will explore the question of selective advantage in a general (heterogeneous) population and provide a mathematical framework within which the relationship between these measures of fitness becomes clear. I will show that, although appropriate measures of fixation probability and gene frequency change are equivalent, they are not in general equivalent to the inclusive fitness effect. In the process I will discuss recent results in evolutionary game theory and the evolution of cooperation.