Non-monotonic effects of migration in subdivided populations

The influence of migration on the stochastic dynamics of subdivided populations is an intriguing but still open issue in a variety of evolutionary models. Inspired by methods of statistical physics, we analyze how migration affects relevantnon-equilibrium properties, such as the mean-fixation time (MFT) in a subdivided population, either fully connected or with a spatial structure. If evolution strongly favors coexistence of species (e.g., balancing selection), the MFT develops an unexpected minimum as a function of the migration rate. In a fully connected population, the observed behavior can be studied thanks to an emergent separation of time scales between local and global dynamics and therefore it carries over to other non-equilibrium processes in physics, biology, ecology, and social sciences.