Speaker
Description
We consider a model of evolutionary game theory in group-structured populations, extending Luo and Mattingly’s multilevel selection framework to account for frequency dependent selection. In the limit of infinite group size and infinite number of groups, we derive a non-local PDE that describes the probability distribution of group compositions in the population. For special families of payoff matrices, we characterize the long-time behavior of solutions of our equation, with particular emphasis placed on understanding the most frequent group compositions at steady-state. We observe, regardless of how weak within-group selection is relative to between-group selection, that the most prevalent group composition will contain more defectors than the type of group which maximizes average group payoff if, and only if, maximum average payoff is not achieved by full cooperator groups. In such cases, the dynamics at the two levels cannot be decoupled, and we even observe cases in which cooperation cannot be sustained even when between-group competition favors perfect coexistence of cooperators and defectors.
