Dynamics of Neutral and Selected Alleles When the Offspring Distribution Is Skewed

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 WrightFisher 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. W HEREAS natural selection undoubtedly plays an important role in adaptation, genetic drift is recognized as an equally or even more important force in shaping the patterns of heritable variation in a population. At a qualitative level, genetic drift implies that variation will tend to be lost from a population over time, even in the absence of selection, and that, in the presence of selection, the fitter type in a population is not guaranteed to fix. Our understanding of genetic drift and its interplay with natural selection has been shaped primarily by the population models introduced by Wright and Fisher (Wright 1931;Fisher 1958) and Moran (Moran 1958). Most work in population genetics rests implicitly on the Wright-Fisher framework, including Kimura's work on fixation probabilities (Kimura 1955), Ewens' sampling formula (Ewens 1972;Lessard 2007), Kingman's coalescent (Kingman 1982), tests of neutrality (Hudson et al. 1987;Tajima 1989;McDonald and Kreitman 1991;Fu and Li 1992;Fay and Wu 2000), and techniques for inferring mutation rates and selection pressures (Sawyer and Hartl 1992;Yang and Bielawski 2000;Bustamante et al. 2001;Desai and Plotkin 2008).The behavior of the Wright-Fisher model is remarkably robust to modifications of the model's underlying assumptions. Indeed, many other population genetic models, including the Moran process (Moran 1958), and a number of Karlin-Taylor and Cannings processes (Karlin and McGregor 1964;Cannings 1974;Ewens 2004), share the same diffusion limit as the Wright-Fisher model (Möhle 2001) and therefore have very similar behavior in sufficiently large populations. Likewise, the Kingman coalescent-that is, the backwardtime d...

A High Load of Non-neutral Amino-Acid Polymorphisms Explains High Protein Diversity Despite Moderate Effective Population Size in a Marine Bivalve With Sweepstakes Reproduction

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“…Although high fecundity per se need not result in high fecundity variance (Nunney 1996), ‘sweepstakes’ effects and sexual selection that diminish the number of successfully breeding adults may be important in a variety of taxa, from plants to both terrestrial and aquatic invertebrates (Frankham 1995b; Pray et al 1996; Boudry et al 2002; Hedrick 2005); high reproductive skew changes expectations about how genetic drift works in relation to population size (Eldon & Wakeley 2006; Der et al 2012). Genetic draft will further exacerbate small N e /N ratios for abundant species (Gillespie 2001).…”

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