Eco-evolutionary metapopulation dynamics of Batesian mimicry: Conditions for mimics without models

Batesian mimicry is adopted by palatable prey species (mimics) to avoid predator attack by resembling unpalatable species (models). Despite numerous studies on this phenomenon, several aspects of its evolution remain unclear. One of the key questions is whether mimics can exist allopatrically from their models. Classical theory suggests that mimics should typically exist sympatrically with their models because the protection afforded to mimics relies on predators learning to associate the model's phenotype with unpalatability. However, several studies have reported mimics that live outside the distribution range of their models. This phenomenon is called "mimics without models". Although various hypotheses have been proposed to explain mimics without models, these hypotheses have been independently developed based on either ecological or evolutionary perspectives. In this study, we adopted eco-evolutionary dynamics, a framework that simultaneously addresses both ecological and evolutionary processes, aiming for an integrated understanding of these hypotheses. We identified that mimics without models occurred when specific conditions are satisfied by the six parameters, including carrying capacities, migration rate of mimics, migration rate of predators, and the evolution rate of mimic phenotype. As an important finding, the migration of predators should be restricted under eco-evolutionary feedback, which differed from previous predictions that considered population and evolutionary dynamics independently.