The effect of a reduction in population size on mean fitness and inbreeding depression

A sudden reduction in population size increases the rate of genetic drift, reducing variability and increasing the mean level of homozygosity. The resulting increase in exposure of strongly deleterious, recessive or partially recessive alleles to selection against homozygotes may lead to their being purged from the population, potentially allowing mean fitness to increase after an initial decline, and accelerating the decline in inbreeding depression associated with reduced variability. However, detailed population genetic theory on the effects of population bottlenecks on mean fitness and inbreeding depression remains limited. We develop a theoretical framework for small, randomly mating populations founded from a large population at mutation-selection-drift equilibrium, using both simulations and approximate analytical results. These provide quantitative predictions for the dynamics of the population's mean fitness and level of inbreeding depression following a bottleneck. In particular, we derive an approximate expression for the time needed for mean fitness to recover after an initial decline; such a recovery requires selection to be sufficiently strong relative to drift, and mutations to be sufficiently recessive. In contrast, weakly deleterious mutations cause reductions in mean fitness and inbreeding depression that are similar in size to those predicted from increases in homozygosity for neutral alleles, over the relatively short timescales considered here.