Cooperation and punishment in community-structured populations with migration.

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.

Nonequivalence of updating rules in evolutionary games under high mutation rates.

Moran processes are often used to model selection in evolutionary simulations. The updating rule in Moran processes is a birth-death process, i. e., selection according to fitness of an individual to give birth, followed by the death of a random individual. For well-mixed populations with only two strategies this updating rule is known to be equivalent to selecting unfit individuals for death and then selecting randomly for procreation (biased death-birth process). It is, however, known that this equivalence does not hold when considering structured populations. Here we study whether changing the updating rule can also have an effect in well-mixed populations in the presence of more than two strategies and high mutation rates. We find, using three models from different areas of evolutionary simulation, that the choice of updating rule can change model results. We show, e. g., that going from the birth-death process to the death-birth process can change a public goods game with punishment from containing mostly defectors to having a majority of cooperative strategies. From the examples given we derive guidelines indicating when the choice of the updating rule can be expected to have an impact on the results of the model.