Random partitions approximating the coalescence of lineages during a selective

• 成果类型: Article
• 署名作者: Schweinsberg, J; Durrett, R
• 署名单位: University of California System; University of California San Diego; Cornell University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000430
• 发表日期: 2005
• 页码: 1591-1651
• 关键词: yule process; hitchhiking; polymorphism; population

摘要

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.