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Absorption and fixation times for neutral and quasi-neutral populations with density dependence

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  • Parsons, Todd L.
  • Quince, Christopher
  • Plotkin, Joshua B.

Abstract

We study a generalisation of Moran’s population-genetic model that incorporates density dependence. Rather than assuming fixed population size, we allow the number of individuals to vary stochastically with the same events that change allele number, according to a logistic growth process with density dependent mortality. We analyse the expected time to absorption and fixation in the ‘quasi-neutral’ case: both types have the same carrying capacity, achieved through a trade-off of birth and death rates. Such types would be competitively neutral in a classical, fixed-population Wright–Fisher model. Nonetheless, we find that absorption times are skewed compared to the Wright–Fisher model. The absorption time is longer than the Wright–Fisher prediction when the initial proportion of the type with higher birth rate is large, and shorter when it is small. By contrast, demographic stochasticity has no effect on the fixation or absorption times of truly neutral alleles in a large population. Our calculations provide the first analytic results on hitting times in a two-allele model, when the population size varies stochastically.

Suggested Citation

  • Parsons, Todd L. & Quince, Christopher & Plotkin, Joshua B., 2008. "Absorption and fixation times for neutral and quasi-neutral populations with density dependence," Theoretical Population Biology, Elsevier, vol. 74(4), pages 302-310.
    • Handle: RePEc:eee:thpobi:v:74:y:2008:i:4:p:302-310
    DOI: 10.1016/j.tpb.2008.09.001
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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. González Casanova, Adrián & Miró Pina, Verónica & Pardo, Juan Carlos, 2020. "The Wright–Fisher model with efficiency," Theoretical Population Biology, Elsevier, vol. 132(C), pages 33-46.
    3. González Casanova, Adrián & Kurt, Noemi & Wakolbinger, Anton & Yuan, Linglong, 2016. "An individual-based model for the Lenski experiment, and the deceleration of the relative fitness," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2211-2252.

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