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This study investigates how periodic migration, rather than constant gene flow, influences selection dynamics in a two-deme population with spatially heterogeneous selection. By analyzing a Moran model with a mutant advantageous in one habitat and disadvantageous in the other, the research quantifies the impact of migration period, phase, and asymmetry on steady-state mutant frequencies. The key finding is that periodic migration generally drives the population towards neutrality, reducing mutant frequency when advantageous on average and increasing it when deleterious, with the strongest effects observed for out-of-phase and directionally asymmetric migration.
Periodic migration can push populations towards neutrality, altering evolutionary trajectories even with identical average gene flow rates.
Migration and selection jointly shape evolutionary outcomes in spatially structured populations. Migration can vary over time as ecological shifts, such as changes in sea level, alter habitat connectivity. Here, we study the impact of periodic migration on selection within a geographically subdivided population. Using a two-deme Moran model with spatially heterogeneous selection, we analyze a scenario in which a mutant genotype is advantageous in one habitat and disadvantageous in the other. Keeping the time-averaged migration rate fixed, we vary the period, relative phase, and directional asymmetry of migration and examine the resulting steady-state mutant frequency. We find that migration periodicity generally drives the population toward neutrality: relative to constant migration, it decreases the mutant frequency when mutants are advantageous on average and increases it when they are deleterious, without reversing the direction of selection in the parameter regimes examined. This effect is strongest for out-of-phase migration, which models seasonal migration, and is further enhanced by directional asymmetry. The response to the migration period is generally non-monotonic, with an intermediate characteristic period producing the largest deviation from constant-migration behavior under in-phase migration. These results arise from the coupling between migration and local selection in Moran process: temporal modulation of migration changes not only the exchange of individuals between habitats but also the local population composition on which selection acts. Our results show that populations with identical mean migration rates can show different evolutionary outcomes depending on the temporal organization of gene flow.