Measures of relative fitness of social behaviors in finite structured population models

How should we measure the relative selective advantage of different behavioral strategies? The various approaches to this question have fallen into one of the following categories: the fixation probability of a mutant allele in a wild type population, some measures of gene frequency and gene frequency change, and a formulation of the inclusive fitness effect. 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 homogeneity of the population interaction structure— that is, that all individuals are equivalent. We explore the question of selective advantage in a general (heterogeneous) population and 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. The latter does not reflect effects of selection acting via mutation, which can arise on heterogeneous structures, even for low mutation. Our theoretical framework provides a transparent analysis of the different biological factors at work in the comparison of these fitness measures and suggests that their theoretical and empirical use needs to be revised and carefully grounded in a more general theory.