Effects of population- and seed bank size fluctuations on neutral evolution and efficacy of natural selection.

Population genetics models typically consider a fixed population size and a unique selection coefficient. However, population dynamics inherently generate fluctuations in numbers of individuals and selection acts on various components of the individuals' fitness. In plant species with seed banks, the size of both the above- and below-ground compartments induce fluctuations depending on seed production and the state of the seed bank. We investigate if this fluctuation has consequences on (1) the rate of genetic drift, and (2) the efficacy of selection. We consider four variants of two-allele Moran-type models defined by combinations of presence and absence of fluctuations in the population size in above-ground and seed bank compartments. Time scale analysis and dimension reduction methods allow us to reduce the corresponding Fokker-Planck equations to one-dimensional diffusion approximations of a Moran model. We first show that if the fluctuations of above-ground population size classically affect the rate of genetic drift, fluctuations of below-ground population size reduce the diversity storage effect of the seed bank. Second, we consider that selection can act on four different components of the plant fitness: plant or seed death rate, seed production or seed germination. Our striking result is that the efficacy of selection for seed death rate or germination rate is reduced by fluctuations in the seed bank size, whereas selection occurring on plant death rate or seed production is not affected. We derive the expected site-frequency spectrum reflecting this heterogeneity in selection efficacy between genes underpinning different plant fitness components. Our results highlight the importance to consider the effect of ecological noise to predict the impact of seed banks on neutral and selective evolution.