The Fisher-Wright model with deterministic seed bank and selection

Seed banks are a common characteristics to many plant species, 1 which allow storage of genetic diversity in the soil as dormant seeds for various 2 periods of time. We investigate an above-ground population following a Fisher3 Wright model with selection coupled with a deterministic seed bank assuming 4 the length of the seed bank is kept constant and the number of seeds is large. 5 To assess the combined impact of seed banks and selection on genetic diversity, 6 we derive a general diffusion model. We compute the equilibrium solution of 7 the site-frequency spectrum and derive the times to fixation of an allele with 8 and without selection. Finally, it is demonstrated that seed banks enhance the 9 effect of selection onto the site-frequency spectrum while slowing down the 10 time until the mutation-selection equilibrium is reached. 11