The Annals of Applied Probability

Random partitions approximating the coalescence of lineages during a selective sweep

Jason Schweinsberg and Rick Durrett

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When a beneficial mutation occurs in a population, the new, favored allele may spread to the entire population. This process is known as a selective sweep. Suppose we sample n individuals at the end of a selective sweep. If we focus on a site on the chromosome that is close to the location of the beneficial mutation, then many of the lineages will likely be descended from the individual that had the beneficial mutation, while others will be descended from a different individual because of recombination between the two sites. We introduce two approximations for the effect of a selective sweep. The first one is simple but not very accurate: flip n independent coins with probability p of heads and say that the lineages whose coins come up heads are those that are descended from the individual with the beneficial mutation. A second approximation, which is related to Kingman’s paintbox construction, replaces the coin flips by integer-valued random variables and leads to very accurate results.

Article information

Ann. Appl. Probab., Volume 15, Number 3 (2005), 1591-1651.

First available in Project Euclid: 15 July 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 92D10: Genetics {For genetic algebras, see 17D92}
Secondary: 60J85: Applications of branching processes [See also 92Dxx] 92D15: Problems related to evolution 05A18: Partitions of sets

Coalescence random partition selective sweep mutation hitchhiking


Schweinsberg, Jason; Durrett, Rick. Random partitions approximating the coalescence of lineages during a selective sweep. Ann. Appl. Probab. 15 (2005), no. 3, 1591--1651. doi:10.1214/105051605000000430.

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