Academic journal article Genetics

Adaptive Fixation in Two-Locus Models of Stabilizing Selection and Genetic Drift

Academic journal article Genetics

Adaptive Fixation in Two-Locus Models of Stabilizing Selection and Genetic Drift

Article excerpt

ABSTRACT The relationship between quantitative genetics and population genetics has been studied for nearly a century, almost since the existence of these two disciplines. Here we ask to what extent quantitative genetic models in which selection is assumed to operate on a polygenic trait predict adaptive fixations that may lead to footprints in the genome (selective sweeps). We study two-locus models of stabilizing selection (with and without genetic drift) by simulations and analytically. For symmetric viability selection we find that ~16% of the trajectories may lead to fixation if the initial allele frequencies are sampled from the neutral site-frequency spectrum and the effect sizes are uniformly distributed. However, if the population is preadapted when it undergoes an environmental change (i.e., sits in one of the equilibria of the model), the fixation probability decreases dramatically. In other two-locus models with general viabilities or an optimum shift, the proportion of adaptive fixations may increase to >24%. Similarly, genetic drift leads to a higher probability of fixation. The predictions of alternative quantitative genetics models, initial conditions, and effect-size distributions are also discussed.

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QUANTITATIVE genetics assumes that selection on an adaptive character involves simultaneous selection at multiple loci controlling the trait. This may cause small to moderate allele-frequency shifts at these loci, in particular when traits are highly polygenic (Barton and Keightley 2002). Therefore, adaptation does not require new muta- tions in the short term. Instead, selection uses alleles found in the standing variation of a population. Genome-wide polymorphism data and association studies suggest that this quantitative genetic view is relevant (Pritchard and Di Rien- zo 2010; Pritchard et al. 2010; Mackay et al. 2012).

Different types of selection on a trait, such as directional, stabilizing, or disruptive selection, modify the genetic composition of a population and favor either extreme or intermediate genotypic values of the trait. In this study we focus on stabilizing selection, which drives a trait toward a phenotypic optimum. Many models of this common form of selection have been analyzed. The central question in all these studies has been whether stabilizing selection can explain the maintenance of genetic variation. This is considered an important question, as it has been known for long that stabilizing selection exhausts genetic variation (Fisher 1930; Robertson 1956), yet quantitative traits ex- hibit relatively high levels of genetic variation in nature (Endler 1986; Falconer and Mackay 1996; Lynch and Walsh 1998).

Here we ask a different question, namely how much adaptive evolution is predicted by quantitative genetic models of stabilizing selection? In contrast to quantitative genetics, in population genetics and genomics our under- standing of the genetics of adaptation has revolved in recent years around the role of selective sweeps, i.e., signatures of positive directional selection in the genome. The model un- derlying this population genetic view of adaptation is that of the hitchhiking effect developed for sexual species by Maynard Smith and Haigh (1974). The hitchhiking process describes how the fixation of a beneficial allele (starting from very low frequency) affects neutral or weakly selected variation linked to the selected site. For single and recurrent advantageous alleles appearing in a population, the model has been further developed by Kaplan et al. (1989), Stephan et al. (1992), Stephan (1995), and Barton (1998). Later this model was generalized to sweeps from standing variation or soft sweeps taking into account that sweeps may also occur if the initial frequency of the beneficial allele is not very low (Innan and Kim 2004; Hermisson and Pennings 2005).

Yet, despite its simplicity, the use of the hitchhiking model was quite successful in recent years in detecting evidence for positive directional selection in the genomes of plant and animal species. …

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