Promotion of cooperation in deme-structured populations with growth-merging dynamics

The spatial structure of populations may promote the emergence and maintenance of cooperation. Cooperation in the prisoner's dilemma is favored under specific update rules in evolutionary graph theory models with one individual per node of a graph, but this effect vanishes in models with well-mixed demes connected by migrations under soft selection (each deme contributing independently of its productivity). In contrast, experiments and models involving cycles of growth, merging and dilution have shown that spatial structure can favor cooperation. Here, we reconcile these findings by studying deme-structured populations under growth-merging-dilution dynamics, corresponding to a clique (fully connected graph) under hard selection (each deme contributing in proportion to its productivity). We obtain analytical conditions for the cooperator fraction to increase during deterministic logistic growth, and to increase on average under dilution-growth-merging cycles, in the weak selection regime, where fitness differences between genotypes are small. Furthermore, we analytically express the fixation probability of cooperators under weak selection, yielding a criterion for cooperators to have a higher fixation probability than neutral mutants. Finally, numerical simulations show that stochastic growth further promotes cooperation. Overall, hard selection is essential for cooperation to be promoted in deme-structured populations.