Phenotype affinity mediated interactions can facilitate the evolution of cooperation

We study the coevolutionary dynamics of the diversity of phenotype and the evolution of cooperation in the Prisoner's Dilemma. Rather than pre-assigning zero-or-one interaction rate, we diversify the rate of interaction by associating it with phenotypes. Individuals each carry a set of potentially expressible traits and expresses a number of such traits at a cost proportional to the number. The set of traits expressed constitutes phenotype. Phenotypes and thus the rate of interaction are evolvable over time. Our results show that nonnegligible cost of expressing traits restrains phenotype diversity, and the evolutionary race mainly proceeds on between cooperative strains and defective strains who express a very few traits. It pays for cooperative strains to express a very few traits. Though such a low level of expression weakens reciprocity between cooperative strains, it decelerates the rate of interaction between cooperative strains and defective strains to a larger degree, leading to the predominance of cooperative strains over defective strains. We also find that evolved diversity of phenotype can occasionally destabilize due to the invasion of defective mutants, implying that cooperation and diversity of phenotype can mutually reinforce each other. Our results may help better understand the coevolution of cooperation and the diversity of phenotype.