Fisher-Wright model with deterministic seed bank and selection

TL;DR

This paper models the impact of deterministic seed banks on genetic diversity in plant populations using a Fisher-Wright framework with selection, deriving a diffusion approximation to analyze allele fixation times and the site-frequency spectrum.

Contribution

It introduces a diffusion model incorporating seed banks and selection, providing new insights into their combined effects on genetic variation and evolutionary dynamics.

Findings

Seed banks increase the effect of selection on genetic variation.

Seed banks slow down the approach to mutation-selection equilibrium.

The model quantifies how seed banks influence fixation times and site-frequency spectrum.

Abstract

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.