Migration pulsedness alters patterns of allele fixation and local adaptation in a mainland-island model

Geneflow across populations is a critical determinant of population genetic structure, divergence and local adaptation. While evolutionary theory typically envisions geneflow as a continuous connection among populations, many processes make it fluctuating and intermittent. We analyze a mainland-island model in which migration occurs as recurrent "pulses". We derive mathematical predictions regarding how the level of migration pulsedness affects the effective migration rate, for neutral and selected mainland alleles. We find that migration pulsedness can either decrease or increase geneflow, depending on the selection regime. Migration increases gene-flow for sufficiently (counter)selected alleles (s < s1), but reduces it otherwise. We provide a mathematical approximation of the threshold selection s1, which is verified in stochastic simulations. Migration pulsedness thus affects the fixation rate at different loci in opposite ways, in a way that cannot be described as a change in effective population size. We show that migration pulsedness would generally reduce the level of local adaptation, and introduce an additional genetic load: the "pulsedness load". Our results indicate that migration pulsedness can be detrimental to the adaptation and persistence of small peripheral populations, with implications in management and conservation. Our results highlight temporally variable migration as an important process for evolutionary and population genetics.