Code from: Evolution of phenotypic plasticity owing to migration

Phenotypic plasticity enables organisms to produce better-suited phenotypes when the environment changes, enhancing fitness under adverse conditions. Yet responding to environmental cues may provide little use in a constant environment, where organisms already express optimal phenotypes. The forces that sustain plasticity and account for its widespread presence, thus, remain unclear, as plasticity must remain advantageous to persist. Although typically associated with changing environments, maintenance of plasticity requires generational turnover such that parents and offspring regularly encounter different conditions. Here, we demonstrate that even low number of migrants between locally adapted populations, in constant environments, can promote the emergence and persistence of phenotypic plasticity even when plasticity is costly, never associated with the fittest genotype, and independent of its genetic architecture. We support this conclusion by exploring the parameter space of a two-locus, two-deme model using stochastic simulations and analytical approximations. We derive analytical conditions under which plasticity is adaptively maintained as a function of selection strength, migration, and fitness trade-offs. These findings reshape our understanding of the evolutionary origins of plasticity and offer insight into how maladaptive traits can invade adapted populations in stable environments.