Abstract
The rapid fixation of an advantageous allele leads to a reduction in linked neutral variation around the target of selection. The genealogy at a neutral locus in such a selective sweep can be simulated by first generating a random path of the advantageous allele's frequency and then a structured coalescent in this background. Usually the frequency path is approximated by a logistic growth curve. We discuss an alternative method that approximates the genealogy by a random binary splitting tree, a so-called Yule tree that does not require first constructing a frequency path. Compared to the coalescent in a logistic background, this method gives a slightly better approximation for identity by descent during the selective phase and a much better approximation for the number of lineages that stem from the founder of the selective sweep. In applications such as the approximation of the distribution of Tajima's D, the two approximation methods perform equally well. For relevant parameter ranges, the Yule approximation is faster.
Highlights
THE model of genetic hitchhiking, introduced in Maynard Smith and Haigh (1974), has become an increasingly important tool for detecting loci under strong positive directional selection in a genome (Nurminsky 2005)
During the fixation of a beneficial allele, neutral variation around the target of selection is partially eliminated. This leads to the reduction of sequence diversity at neutral loci linked to a site under strong positive selection, a phenomenon known as a selective sweep
Initiated by the ‘‘revisiting’’ of the hitchhiking effect by Kaplan et al (1989), coalescent theory has helped to understand diversity patterns formed by selective sweeps: the ancestry of a sample at a neutral locus that is linked to the selected one is modeled as a structured coalescent; its background is the frequency curve of the selectively advantageous allele that increases from 0 to 1 during the sweep
Summary
Consider a population of N haploid individuals and two linked loci, a selected one and a neutral one. In the Yule process approximation, two individuals in the sample (two leaves of the tree) are identical by descent at the neutral locus from the beginning of the sweep if and only if they are not separated by a recombination event along their lineages This simple scheme of generating a genealogy under a selective sweep is based on the time transformation dt 1⁄4 (1 À Xt)dt (see Figure 1). The Yule approximation allows us to simulate the random partition of a sample (with respect to identity by descent at the neutral locus) in two stages: first, generate the sample genealogy by the coalescence mechanism (7), and generate recombination events along the sample lineages with probabilities (8) Note that this method does not require any explicit simulation of the frequency curve X or that of the full Yule tree. For the special case of n 1⁄4 2 in a Moran model, simulation studies by Schweinsberg and Durrett (2005) already showed that the Yule approximation outperforms the logistic one
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