Limits to selection on standing variation in an asexual population

Nick Barton and Himani Sachdeva

Theoretical Population Biology, 2024, vol. 157, issue C, 129-137

Abstract: We consider how a population of N haploid individuals responds to directional selection on standing variation, with no new variation from recombination or mutation. Individuals have trait values z1,…,zN, which are drawn from a distribution ψ; the fitness of individual i is proportional to ezi. For illustration, we consider the Laplace and Gaussian distributions, which are parametrised only by the variance V0, and show that for large N, there is a scaling limit which depends on a single parameter NV0. When selection is weak relative to drift (NV0≪1), the variance decreases exponentially at rate 1/N, and the expected ultimate gain in log fitness (scaled by V0), is just NV0, which is the same as Robertson’s (1960) prediction for a sexual population. In contrast, when selection is strong relative to drift (NV0≫1), the ultimate gain can be found by approximating the establishment of alleles by a branching process in which each allele competes independently with the population mean and the fittest allele to establish is certain to fix. Then, if the probability of survival to time t∼1/V0 of an allele with value z is P(z), with mean P¯, the winning allele is the fittest of NP¯ survivors drawn from a distribution ψP/P¯. The expected ultimate change is ∼2log(1.15NV0) for a Gaussian distribution, and ∼−12log0.36NV0−log−log0.36NV0 for a Laplace distribution. This approach also predicts the variability of the process, and its dynamics; we show that in the strong selection regime, the expected genetic variance decreases as ∼t−3 at large times. We discuss how these results may be related to selection on standing variation that is spread along a linear chromosome.

Keywords: Adaptation; Standing variation; Asexual evolution; Genetic drift; Branching processes (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:157:y:2024:i:c:p:129-137

DOI: 10.1016/j.tpb.2024.04.001

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