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

TL;DR

This paper investigates how growth-merging-dilution dynamics in deme-structured populations can promote cooperation, providing analytical conditions and simulations that highlight the importance of hard selection for cooperation to emerge and persist.

Contribution

It offers the first analytical framework for cooperation in deme-structured populations under growth-merging cycles, emphasizing the role of hard selection.

Findings

Analytical conditions for increased cooperator fraction during logistic growth.

Higher fixation probability of cooperators under weak selection.

Stochastic growth further enhances cooperation.

Abstract

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. 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. 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. Furthermore, we analytically express the fixation probability of cooperators under weak selection, yielding a criterion for cooperative mutants to have a higher fixation probability than neutral ones. Finally, numerical simulations show that stochastic growth further promotes cooperation. Overall, hard selection is essential for cooperation to be promoted in deme-structured populations.