Dynamics of Neutral and Selected Alleles When the Offspring Distribution Is Skewed
Ricky Der, Charles Epstein, Joshua B. Plotkin

Abstract

We analyze the dynamics of two alternative alleles in a simple model of a population that allows for large family sizes in the distribution of offspring number. This population model was first introduced by Eldon and Wakeley, who described the backward-time genealogical relationships among sampled individuals, assuming neutrality. We study the corresponding forward-time dynamics of allele frequencies, with or without selection. We derive a continuum approximation, analogous to Kimura’s diffusion approximation, and we describe three distinct regimes of behavior that correspond to distinct regimes in the coalescent processes of Eldon and Wakeley. We demonstrate that the effect of selection is strongly amplified in the Eldon–Wakeley model, compared to the Wright–Fisher model with the same variance effective population size. Remarkably, an advantageous allele can even be guaranteed to fix in the Eldon–Wakeley model, despite the presence of genetic drift. We compute the selection coefficient required for such behavior in populations of Pacific oysters, based on estimates of their family sizes. Our analysis underscores that populations with the same effective population size may nevertheless experience radically different forms of genetic drift, depending on the reproductive mechanism, with significant consequences for the resulting allele dynamics.

  • Received February 24, 2012.
  • Accepted May 28, 2012.
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