title: Fisher-Wright model with deterministic seed bank and selection.
abstract: Seed banks are 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. 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.
authors.affiliation: Center for Mathematics, Technische Universität München, 85748 Garching, Germany.
authors.forename: Bendix
authors.initials: B
authors.lastname: Koopmann
authors.affiliation: Center for Mathematics, Technische Universität München, 85748 Garching, Germany; Institute for Computational Biology, Helmholtz Center Munich, 85764 Neuherberg, Germany. Electronic address: johannes.mueller@mytum.de.
authors.forename: Johannes
authors.initials: J
authors.lastname: Müller
authors.affiliation: Section of Population Genetics, Center of Life and Food Sciences Weihenstephan, Technische Universität München, 85354 Freising, Germany.
authors.forename: Aurélien
authors.initials: A
authors.lastname: Tellier
authors.affiliation: Section of Population Genetics, Center of Life and Food Sciences Weihenstephan, Technische Universität München, 85354 Freising, Germany.
authors.forename: Daniel
authors.initials: D
authors.lastname: Živković
mesh_terms: D044822:Biodiversity; D014644:Genetic Variation; D010944:Plants; D000068098:Seed Bank; D012639:Seeds / Q000502:physiology*; D012987:Soil; D013045:Species Specificity
chemical_list: D012987:Soil
keywords: Diffusion; Fisher–Wright model; Seed bank; Selection; Site-frequency spectrum; Times to fixation