Electronic Journal of Probability
- Electron. J. Probab.
- Volume 17 (2012), paper no. 31, 36 pp.
Fixation probability for competing selective sweeps
We consider a biological population in which a beneficial mutation is undergoing a selective sweep when a second beneficial mutation arises at a linked locus. We investigate the probability that both mutations will eventually fix in the population. Previous work has dealt with the case where the second mutation to arise confers a smaller benefit than the first. In that case population size plays almost no rôle. Here we consider the opposite case and observe that, by contrast, the probability of both mutations fixing can be heavily dependent on population size. Indeed the key parameter is $rN$, the product of the population size and the recombination rate between the two selected loci. If $rN$ is small, the probability that both mutations fix can be reduced through interference to almost zero while for large $rN$ the mutations barely influence one another. The main rigorous result is a method for calculating the fixation probability of a double mutant in the large population limit.
Electron. J. Probab., Volume 17 (2012), paper no. 31, 36 pp.
Accepted: 23 April 2012
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 92D15: Problems related to evolution
This work is licensed under aCreative Commons Attribution 3.0 License.
Cuthbertson, Charles; Etheridge, Alison; Yu, Feng. Fixation probability for competing selective sweeps. Electron. J. Probab. 17 (2012), paper no. 31, 36 pp. doi:10.1214/EJP.v17-1954. https://projecteuclid.org/euclid.ejp/1465062353