Phenotype adjustment promotes adaptive evolution in a game without conflict

Organisms may adjust their phenotypes in response to social and physical environments. Such phenotypic plasticity is known to help or retard adaptive evolution. Here, we study the evolutionary outcomes of adaptive phenotypic plasticity in an evolutionary game involving two players who have no conflicts of interest. A possible example is the growth and sex allocation of a lifelong pair of shrimps entrapped in the body of a sponge. We consider random pair formation, the limitation of total resources for growth, and the needs of male investment to fertilize eggs laid by the partner. We compare the following three different evolutionary dynamics: (1) No adjustment: each individual develops a phenotype specified by its own genotype; (2) One-player adjustment: the phenotype of the first player is specified by its own genotype, and the second player chooses the phenotype that maximizes its own fitness; (3) Two-player adjustment: the first player exhibits an initial phenotype specified by its own genotype, the second player chooses a phenotype given that of the first player, and finally, the first player readjusts its phenotype given that of the second player. We demonstrate that both one-player and two-player adjustments evolve to achieve maximum fitness. In contrast, the dynamics without adjustment fails in some cases to evolve outcomes with the highest fitness. For an intermediate range of male cost, the evolution of no adjustment realizes two hermaphrodites with equal size, whereas the one-player and two-player adjustments realize a small male and a large female.