Spatial structure has been shown to promote altruistic behavior, however, it also increases the intensity of competition among relatives. Our purpose here is to develop a model in which this competition is minimized, more precisely a local increase in fecundity has a minimal competitive effect on the fitness of nearby individuals. We work with an island model in which sites are allowed to be empty, choosing our demographic rules so that in patches with higher fecundity, empty sites are filled at a higher rate. We also allow dispersal rates to evolve in response to the proportion of empty sites in the patch. Patches with different numbers of empty sites differ in frequency, in within-patch consanguinity, and in reproductive value. Using an inclusive fitness argument, we show that our model does promote altruism; indeed Hamilton's Rule is shown to hold. The only negative effect on an actor of a gift of fecundity to a patchmate turns out to be a slight decrease in reproductive value due to an increased probability of an empty site being occupied. We show that altruists are most favored in islands with an intermediate number of empty sites.

We study the evolution of a pair of competing behavioural alleles in a structured population when there are non-additive or ‘synergistic’ fitness effects. Under a form of weak selection and with a simple symmetry condition between a pair of competing alleles, Tarnita et al. provide a surprisingly simple condition for one allele to dominate the other. Their condition can be obtained from an analysis of a corresponding simpler model in which fitness effects are additive. Their result uses an average measure of selective advantage where the average is taken over the long-term—that is, over all possible allele frequencies—and this precludes consideration of any frequency dependence the allelic fitness might exhibit. However, in a considerable body of work with non-additive fitness effects—for example, hawk–dove and prisoner's dilemma games—frequency dependence plays an essential role in the establishment of conditions for a stable allele-frequency equilibrium. Here, we present a frequency-dependent generalization of their result that provides an expression for allelic fitness at any given allele frequency p. We use an inclusive fitness approach and provide two examples for an infinite structured population. We illustrate our results with an analysis of the hawk–dove game.

Studies of the evolution of a social trait often make ecological assumptions (of population structure, life history), and thus a trait can be studied many different times with different assumptions. Here, I consider a Moran model of continuous reproduction and use an inclusive fitness analysis to investigate the relationships between fecundity or survival selection and birth–death (BD) or death–birth (DB) demography on the evolution of a social trait. A simple symmetry obtains: fecundity (respectively survival) effects under BD behave the same as survival (respectively fecundity) effects under DB. When these results are specialized to a homogeneous population, greatly simplified conditions for a positive inclusive fitness effect are obtained in both a finite and an infinite population. The results are established using the elegant formalism of mathematical group theory and are illustrated with an example of a finite population arranged in a cycle with asymmetric offspring dispersal.