  Organisms from microbes to humans engage in a variety of social behaviors,
which affect fitness in complex, often nonlinear ways. The question of how
these behaviors evolve has consequences ranging from antibiotic resistance to
human origins. However, evolution with nonlinear social interactions is
challenging to model mathematically, especially in combination with spatial,
group, and/or kin assortment. We derive a mathematical condition for natural
selection with synergistic interactions among any number of individuals. This
result applies to populations with arbitrary (but fixed) spatial or network
structure, group subdivision, and/or mating patterns. In this condition,
nonlinear fitness effects are ascribed to collectives, and weighted by a new
measure of collective relatedness. For weak selection, this condition can be
systematically evaluated by computing branch lengths of ancestral trees. We
apply this condition to pairwise games between diploid relatives, and to
dilemmas of collective help or harm among siblings and on spatial networks. Our
work provides a rigorous basis for extending the notion of ``actor", in the
study of social evolution, from individuals to collectives.
