Open Access
Translator Disclaimer
August 2005 Random partitions approximating the coalescence of lineages during a selective sweep
Jason Schweinsberg, Rick Durrett
Ann. Appl. Probab. 15(3): 1591-1651 (August 2005). DOI: 10.1214/105051605000000430


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.


Download Citation

Jason Schweinsberg. Rick Durrett. "Random partitions approximating the coalescence of lineages during a selective sweep." Ann. Appl. Probab. 15 (3) 1591 - 1651, August 2005.


Published: August 2005
First available in Project Euclid: 15 July 2005

zbMATH: 1073.92029
MathSciNet: MR2152239
Digital Object Identifier: 10.1214/105051605000000430

Primary: 92D10
Secondary: 05A18 , 60J85 , 92D15

Keywords: Coalescence , hitchhiking , mutation , random partition , selective sweep

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.15 • No. 3 • August 2005
Back to Top