Cooperation, involuntary defection, and Polymorphic Evolutionary Games.

The subject of involuntary defection in the context of cycles of interaction approach to direct reciprocal cooperation was introduced some time ago (J. Theor. Biol., 242: 873-879). Current work is motivated by the subsequent accumulation of empirical evidence and the advances in the methodology of evolutionary games. In recent decades it become clear that individuals in many animal species vary consistently in their behavioral responses to specific challenges-animal personality. Moreover, these differences have a hereditary component. Finally, investigations into the effects of neuropeptides on behavior suggest that the variations in animal personalities involve polymorphisms based on non-Mendelian heritability within the neuropeptide signaling systems. The last observation suggests that animal personalities can be productively analyzed via Polymorphic Evolutionary Games, which allow us to add genetic model(s) to standard (phenotypic) evolutionary games. Such an analysis of reciprocal cooperation is the subject of the current paper. The results indicate that there is a marked difference between models that assume Mendelian vs. non-Mendelian inheritance of the pertinent traits. Monomorphic and polymorphic-Mendelian models predict pure-strategy (single phenotype) ESS, whereas the non-Mendelian genetic model predicts a mixed strategy ESS exhibiting all three phenotypes.