  Relatedness and synergy affect the selection pressure on cooperation and
altruism. Although early work investigated the effect of these factors
independently of each other, recent efforts 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 fitness approach of inclusive fitness 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 different synergies of kind (arising from differential fitness
effects on individuals expressing or not expressing helping) and can be
subjected to different synergies of scale (arising from economies or
diseconomies of scale). We find 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 effects of relatedness (or spatial structure) on the evolution of
helping.
