Approximating Genetic Hitchhiking by Coalescents with Multiple Collisions
Rick Durrett and Jason Schweinsberg
Abstract. The fixation of advantageous mutations in a population has the effect of reducing variation in the DNA sequence near that mutation. Kaplan, Hudson, and Langley (1989) used a three-phase simulation model to study the effect of selective sweeps on genealogies. However, most subsequent work has simplified their approach by assuming that the number of individuals with the advantageous allele follows the logistic differential equation. We show that the impact of a selective sweep can be accurately approximated by a random partition created by a stick-breaking process. Our simulation results show that ignoring the randomness when the number of individuals with the advantageous allele is small can lead to substantial errors.
There are two papers on this topic:
Following up on this work we have investigated the effect of recurrent selective sweeps:
A coalescent model for the effect of advantageous mutations on the genealogy of a population
Abstract When an advantageous mutation occurs in a population, the favorable
allele may spread to the entire population in a short time, an
event known as a selective sweep. As a
result, when we sample $n$ individuals from a population and trace their
ancestral lines backwards in time, many lineages may coalesce almost
instantaneously at the time of a selective sweep. We show that
as the population size goes to infinity, this process converges to a
coalescent process called a coalescent with multiple collisions.
A better approximation for finite populations can be obtained using
a coalescent with simultaneous multiple collisions. We also show how
these coalescent approximations can be used to get insight into
how beneficial mutations affect the behavior of statistics that
have been used to detect departures from the usual Kingman's coalescent.
Preprint as PDF. Stochastic Processes and their Applications, to appear
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