When the costs and benefits of engaging in cooperative behaviors depend on the size of the cooperative group, group size and level of cooperation should not be expected to evolve independently. Nevertheless, past work often examined the evolution of group size and the evolution of helping behavior separately. Further, Allee effects within-groups (positive density dependence in small groups) often arise from prosocial behaviors between group members and are, by definition, a group-size effect. Thus, Allee effects have the potential to link the evolution of cooperation with the evolution of group size. But again, these ecological factors are typically neglected when considering the evolution of cooperation. Interestingly, social mammals (in particular carnivorans) often live in more weakly-related groups than those typically studied for the evolution of cooperation and are especially prone to group-level Allee effects. In this study, we build a theoretical model of a group subject to Allee effects, with a particular focus on social carnivorans. We equip individuals in our models with a trait controlling preferred group size and a trait controlling the degree of cooperation. We introduce mutant phenotypes in a resident population to determine how cooperation and group size evolve in tandem.
Results/Conclusions
We find that group size evolution can promote the evolution of cooperation in our models. In particular, resident populations with a preference for small groups are invasible to increased cooperation, but not decreased cooperation. Conversely, resident populations with a preference for large groups are not invasible to increased cooperation, but rather decreased cooperation. Notably, these results hold even if groups are entirely unrelated; that is, inclusive fitness is not considered. Our results show that Allee effects are important to the evolution of cooperation, as well as the evolution of group size. Further, they show that the evolution of group size is intimately linked to the evolution of cooperation. Thus, studies attempting to understand these two traits should consider that they evolve dependently.