Group size effects in social evolution

How the size of social groups affects the evolution of cooperative behaviors is a classic question in evolutionary biology. Here we investigate group size effects in the evolutionary dynamics of games in which individuals choose whether to cooperate or defect and payoffs do not depend directly on the size of the group. We find that increasing the group size decreases the proportion of cooperators at both stable and unstable rest points of the replicator dynamics. This implies that larger group sizes can have negative effects (by reducing the amount of cooperation at stable polymorphisms) and positive effects (by enlarging the basin of attraction of more cooperative outcomes) on the evolution of cooperation. These two effects can be simultaneously present in games whose evolutionary dynamics feature both stable and unstable rest points, such as public goods games with participation thresholds. Our theory recovers and generalizes previous results and is applicable to a broad variety of social interactions that have been studied in the literature.