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.
