FST and genetic diversity in an island model with background selection

Background selection, by which selection on deleterious alleles reduces diversity at linked neutral sites, influences patterns of total neutral diversity, πT, and genetic differentiation, FST, in structured populations. The theory of background selection may be split into two regimes: the background selection regime, where selection pressures are strong and mutation rates are sufficiently low such that deleterious alleles are at a deterministic mutation-selection balance, and the interference selection regime, where selection pressures are weak and mutation rates are sufficiently high that deleterious alleles accumulate and interfere with another, leading to selective interference. Previous work has quantified the effects of background selection on πT and FST only for deleterious alleles in the background selection regime. Furthermore, there is evidence to suggest that migration reduces the effects of background selection on FST, but this has not been fully explained. Here, we derive novel theory to predict the effects of migration on background selection experienced by a subpopulation and extend previous theory from the interference selection regime to make predictions in an island model. Using simulations, we show that this theory best predicts FST and πT. Moreover, we demonstrate that background selection may generate minimal increases in FST under sufficiently high migration rates, because migration reduces correlated effects on fitness over generations within subpopulations. However, we show that background selection may still cause substantial reductions in πT, particularly for metapopulations with a larger effective population size. Our work further extends the theory of background selection into structured populations, and suggests that background selection will minimally confound locus-to-locus FST scans.