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

Parsons, Todd L., Quince, Christopher and Plotkin, Joshua B. (2008) Absorption and fixation times for neutral and quasi-neutral populations with density dependence. Theoretical Population Biology, 74 (4). pp. 302-310. ISSN 0040-5809

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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.

Item Type: Article
Additional Information: Funding Information: The authors thank Sergey Kryazhimskiy and three anonymous reviewers for comments that greatly improved the final manuscript; we are particularly grateful to the latter for bringing the studies ( Antal and Scheuring, 2006; Taylor et al., 2006 ) to our attention. Christopher Quince was supported by the University of Glasgow. Todd L. Parsons and Joshua B. Plotkin were supported by a grant from the Burroughs Wellcome Fund. Joshua B. Plotkin also acknowledges support from the James S. McDonnell Foundation.
Uncontrolled Keywords: absorption,allele,asymptotic,competition,density-dependent,drift,fixation,logistic,moran,neutral,stochastic,wright-fisher,ecology, evolution, behavior and systematics ,/dk/atira/pure/subjectarea/asjc/1100/1105
Faculty \ School: Faculty of Science > School of Biological Sciences
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Depositing User: LivePure Connector
Date Deposited: 12 Sep 2022 11:30
Last Modified: 23 Sep 2022 02:53
URI: https://ueaeprints.uea.ac.uk/id/eprint/88130
DOI: 10.1016/j.tpb.2008.09.001

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