Random partitions approximating the coalescence of lineages during a selective sweep. (English) Zbl 1073.92029
Summary: 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 coinss come up heads are those that are descended from the individual with the beneficial mutation. A second approximation, which is related to J. F. C. Kingman’s paintbox construction [J. Lond. Math. Soc., II Ser. 18, 374–380 (1978; Zbl 0415.92009)], replaces the coin flips by integer-valued random variables and leads to very accurate results.
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 coinss come up heads are those that are descended from the individual with the beneficial mutation. A second approximation, which is related to J. F. C. Kingman’s paintbox construction [J. Lond. Math. Soc., II Ser. 18, 374–380 (1978; Zbl 0415.92009)], replaces the coin flips by integer-valued random variables and leads to very accurate results.
MSC:
| 92D10 | Genetics and epigenetics |
| 60J85 | Applications of branching processes |
| 05A18 | Partitions of sets |
| 92D15 | Problems related to evolution |
Citations:
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