An accurate model for genetic hitch-hiking

We suggest a simple deterministic approximation for the growth of the favoured-allele frequency during a selective sweep. Using this approximation we introduce an accurate model for genetic hitch-hiking. Only when Ns < 10 (N is the population size and s denotes the selection coefficient), are discrepancies between our approximation and direct numerical simulations of a Moran model noticeable. Our model describes the gene genealogies of a contiguous segment of neutral loci close to the selected one, and it does not assume that the selective sweep happens instantaneously. This enables us to compute SNP distributions on the neutral segment without bias.

💡 Research Summary

The paper presents a novel deterministic approximation for the trajectory of a favored allele during a selective sweep and integrates this approximation into a comprehensive model of genetic hitch‑hiking. Traditional hitch‑hiking models often assume that a sweep is instantaneous, treating the selected allele as if it jumps from its initial frequency to fixation in a single step. This assumption simplifies the mathematics but fails to capture the continuous interplay between selection and recombination that shapes the genealogies of nearby neutral loci.

To address this limitation, the authors first derive a simple ordinary differential equation for the mean frequency p(t) of the advantageous allele in a Moran population: dp/dt = s p (1 – p), where s is the selection coefficient. Solving this equation yields a logistic growth curve, p(t) = 1 /