Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#243545] of Richard T. Durrett

Papers Published

  1. Schweinsberg, J; Durrett, R, Random partitions approximating the coalescence of lineages during a selective sweep, Annals of Applied Probability, vol. 15 no. 3 (2005), pp. 1591-1651, ISSN 1050-5164 [MR2152239 (2006c:92012)], [doi]
    (last updated on 2017/12/16)

    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. © Institute of Mathematical Statistics. 2005.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320