Adaptive Fixation in Two-Locus Models of Stabilizing Selection and Genetic Drift
Andreas Wollstein, Wolfgang Stephan


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 about 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 pre-adapted 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 more than 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.

  • Received March 31, 2014.
  • Accepted July 20, 2014.