Inclusive and personal fitness in synergistic evolutionary games on graphs

Abstract I study the evolution of a pair of competing behavioural alleles in a finite graph-structured population when there are non-additive or “synergistic” fitness effects. I begin with the Price equation and extend it to both a personal-fitness and an inclusive-fitness formulation. I thereby obtain an extension of “Hamilton's Rule” to synergistic effects and I calculate and interpret the generalized relatedness coefficients. I present an example of the analysis in a cycle graph with 4 nodes.