Cooperation and punishment in community-structured populations with migration

•For weak local selection, conflict between groups leading to full group extinction can sustain cooperation for very large group sizes.•Migration proportional to fitness is methodologically simpler than migration between groups of variable size.•Fitness-based migration as a model of individual competition shows evolutionary outcomes similar to explicit group conflict.

The stable presence of punishing strategies in various cooperative species is a persistent puzzle in the study of the evolution of cooperation. To investigate the effect of group competition, we study the evolutionary dynamics of the Public Goods Game with punishment in a metapopulation that consists of separate communities. In addition to (a) well-mixed non-interacting communities, we model three distinct types of interaction between communities, (b) Migration independent of fitness; (c) Competition between whole communities, where entire communities replace each other depending on average fitness; (d) Migration where the probability of an offspring replacing an individual in another community depends on fitness. We use stochastic simulations to study the long-run frequencies of strategies with these interactions, subject to high mutation and migration rates. In cases (a) and (b), the transition between cooperation/punishment and defection regimes occurs for similar parameter values; with migration (b), the transitions are steeper due to higher total mixing. Fitness-based migration (d) by contrast can help support cooperation, changing the locations of transitions, but while group selection (c) does stabilise cooperation over much of the parameter space, fitness-based migration (d) acts as a proxy for group selection only in a smaller region.