  Seed banks are a common characteristics to many plant species, which allow
storage of genetic diversity in the soil as dormant seeds for various periods
of time. We investigate an above-ground population following a Fisher-Wright
model with selection coupled with a deterministic seed bank assuming the length
of the seed bank is kept constant and the number of seeds is large. To assess
the combined impact of seed banks and selection on genetic diversity, we derive
a general diffusion model. The applied techniques outline a path of
approximating a stochastic delay differential equation by an appropriately
rescaled stochastic differential equation, which is a common issue in
statistical physics. We compute the equilibrium solution of the site-frequency
spectrum and derive the times to fixation of an allele with and without
selection. Finally, it is demonstrated that seed banks enhance the effect of
selection onto the site-frequency spectrum while slowing down the time until
the mutation-selection equilibrium is reached.
