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Evolutionary Game Theory and the Prisoner's Dilemma (PD) Game in particular have been used to study the evolution of cooperation. We consider a population of asexually reproducing, age-structured individuals in a two-dimensional square lattice structure. The individuals employ fixed cooperative or defecting strategies towards their neighbors in repeating interactions to accumulate reproductive fitness. We focus on the effects of the persistence of past interactions and interactive neighborhood size on the evolution of cooperation. We show that larger neighborhood sizes are generally detrimental to cooperation and that the persistence of fitness effects decreases the likelihood of the evolution of cooperation in small neighborhoods. However, for larger neighborhood sizes the persistence effect is reversed. Thus, our study corroborates earlier studies that population structure increases the evolutionary potential for cooperative behavior in a PD paradigm. This finding may explain the heterogeneity of previous results on the effect of neighborhood size and cautions that the persistence of fitness outcomes needs to be considered in analyses of the evolution of cooperative behavior. The persistence of fitness outcomes of pairwise interactions may vary dramatically in biological and social systems and could have profound effects on the evolution of cooperation in various contexts.

The evolution of cooperation is affected by the persistence of fitness effects, the neighborhood size and their interaction