Haploids, polymorphisms and fluctuating selection

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I analyze the joint impact of directional and fluctuating selection with reversible mutation in finite bi-allelic haploid populations using diffusion approximations of the Moran and chemostat models. Results differ dramatically from those of the classic Wright–Fisher diffusion. There, a strong dispersive effect attributable to fluctuating selection dissipates nascent polymorphisms promoted by a relatively weak emergent frequency dependent selective effect. The dispersive effect in the Moran diffusion with fluctuations every birth–death event is trivial. The same frequency dependent selective effect now dominates and polymorphism is promoted. The dispersive effect in the chemostat diffusion with fluctuations every generation is identical to that in the Wright–Fisher diffusion. Nevertheless, polymorphism is again promoted because the emergent frequency dependent effect is doubled, an effect attributable to geometric reproduction within generations. Fluctuating selection in the Moran and chemostat diffusions can also promote bi-allelic polymorphisms when one allele confers a net benefit. Rapid fluctuations within generations are highly effective at promoting polymorphism in large populations. The bi-allelic distribution is approximately Gaussian but becomes uniform and then U-shaped as the frequency of environmental fluctuations decreases to once a generation and then once every multiple generations. Trade-offs (negative correlations in fitness) help promote polymorphisms but are not essential. In all three models the frequency dependent effect raises the probability of ultimate fixation of new alleles, but less effectively in the Wright–Fisher diffusion. Individual-based forward simulations confirm the calculations.

Original languageEnglish (US)
Pages (from-to)16-30
Number of pages15
JournalTheoretical Population Biology
StatePublished - Dec 2018

Bibliographical note

Funding Information:
I thank Brian Golding for constructive and insightful comments. I also wish to thank John Wakeley and two anonymous reviewers for their gentle yet thorough critiques that allowed me to greatly improve the manuscript.

Publisher Copyright:
© 2018 Elsevier Inc.


  • Diffusion approximation
  • Fluctuating selection
  • Genic selection
  • Haploid/clonal polymorphism


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