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Abstract

Relatedness and synergy aect the selection pressure on cooperation and altruism. Although early work investigated the eect of these factors independently of each other, recent eorts have been aimed at exploring their interplay. Here, we contribute to this ongoing synthesis in two distinct but complementary ways. First, we integrate models of n-player matrix games into the direct tness approach of inclusive tness theory, hence providing a framework to consider synergistic social interactions between relatives in family and spatially structured populations. Second, we illustrate the usefulness of this framework by delineating three distinct types of helping traits (\whole-group", \nonexpresser-only" and \expresser-only"), which are characterized by dierent synergies of kind (arising from dierential tness eects on individuals expressing or not expressing helping) and can be subjected to dierent synergies of scale (arising from economies or diseconomies of scale). We nd that relatedness and synergies of kind and scale can interact to generate nontrivial evolutionary dynamics, such as cases of bistable coexistence featuring both a stable equilibrium with a positive level of helping and an unstable helping threshold. This broadens the qualitative eects of relatedness (or spatial structure) on the evolution of helping.