Effects of population- and seed bank noise 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 noise 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 present noise depending on seed production and the state of the seed bank. We investigate if this noise 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 noise in above-ground and seed bank compartments. Time scale analysis and dimension reduction methods allow us to reduce the corresponding Fokker-Planck equation to a one-dimensional diffusive Moran model. We first show that if the above-ground noise classically affects the rate of genetic drift, below-ground noise reduces 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 seed bank noise, 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.