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Fisher–Wright model with deterministic seed bank and selection

Author

Listed:
  • Koopmann, Bendix
  • Müller, Johannes
  • Tellier, Aurélien
  • Živković, Daniel

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.

Suggested Citation

  • Koopmann, Bendix & Müller, Johannes & Tellier, Aurélien & Živković, Daniel, 2017. "Fisher–Wright model with deterministic seed bank and selection," Theoretical Population Biology, Elsevier, vol. 114(C), pages 29-39.
    • Handle: RePEc:eee:thpobi:v:114:y:2017:i:c:p:29-39
    DOI: 10.1016/j.tpb.2016.11.005
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    Citations

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    Cited by:

    1. Heinrich, Lukas & Müller, Johannes & Tellier, Aurélien & Živković, Daniel, 2018. "Effects of population- and seed bank size fluctuations on neutral evolution and efficacy of natural selection," Theoretical Population Biology, Elsevier, vol. 123(C), pages 45-69.
    2. Blath, Jochen & Tóbiás, András, 2020. "Invasion and fixation of microbial dormancy traits under competitive pressure," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7363-7395.
    3. Usman Sanusi & Sona John & Johannes Mueller & Aurélien Tellier, 2022. "Quiescence Generates Moving Average in a Stochastic Epidemiological Model with One Host and Two Parasites," Mathematics, MDPI, vol. 10(13), pages 1-22, June.
    4. Jain, Kavita & Kaushik, Sachin, 2022. "Joint effect of changing selection and demography on the site frequency spectrum," Theoretical Population Biology, Elsevier, vol. 146(C), pages 46-60.
    5. Blath, Jochen & Buzzoni, Eugenio & Koskela, Jere & Wilke Berenguer, Maite, 2020. "Statistical tools for seed bank detection," Theoretical Population Biology, Elsevier, vol. 132(C), pages 1-15.

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