Weak genetic draft and the Lewotin's paradox

Abstract

Recurrent selective sweeps reduce diversity at linked neutral loci, a regime known as genetic draft. Most theoretical work has focused on the tight draft regime, where the selected and neutral loci are closely linked, leading to Multiple Merger Coalescents and a diversity largely insensitive to population size. Here, we investigate the neglected regime of loose genetic draft, where sweeps at a distant linked locus have individually negligible effects but collectively drive diversity. To explore this regime systematically, we make extensive use of the RIF model (Random Initial and Final conditions), a semi-deterministic approximation of selective sweeps that is 103 times faster than standard Wright-Fisher simulations and equally accurate. Using this framework, we derive novel analytical approximations for the coalescence probability under a single sweep, valid for a wide range of recombination-to-selection ratios A = c/s, and show that they outperform several previous approximations from the literature, which are only accurate for small A. Under recurrent loose draft (0.1 < A < 0.5), the effective population size scales as a power law of census size, Ne {propto} N 2A, which could contribute to the observed non-linear dependence of diversity on population size. Crucially, despite this strong reduction in diversity, the genealogy converges to a Kingman coalescent, making loose draft patterns indistinguishable from neutrality by standard tests.