A coalescent model for the effect of advantageous mutations on the genealogy of a population

• Published in: Stochastic processes and their applications Vol. 115; no. 10; pp. 1628 - 1657
• Main Authors: Durrett, Rick, Schweinsberg, Jason
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.10.2005; Elsevier Science; Elsevier
• Series: Stochastic Processes and their Applications
• Subjects: Applications; Biology, psychology, social sciences; Coalescence; Coalescence Selective sweep Genealogy Tajima's D-statistic; Exact sciences and technology; Genealogy; Markov processes; Mathematics; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Selective sweep; Statistics; Stochastic processes; Tajima's D-statistic; secondary 90D10; Genealogy; Tajima's D-statistic; 60J27; Selective sweep; 90D15; Coalescence; Statistical method; primary 60J27; 90D15 Coalescence; Population size; Finite population; Stochastic process; Tajima D statistics
• ISSN: 0304-4149; 1879-209X
• DOI: 10.1016/j.spa.2005.04.009

When an advantageous mutation occurs in a population, the favorable allele may spread to the entire population in a short time, an event known as a selective sweep. As a result, when we sample n individuals from a population and trace their ancestral lines backwards in time, many lineages may coalesce almost instantaneously at the time of a selective sweep. We show that as the population size goes to infinity, this process converges to a coalescent process called a coalescent with multiple collisions. A better approximation for finite populations can be obtained using a coalescent with simultaneous multiple collisions. We also show how these coalescent approximations can be used to get insight into how beneficial mutations affect the behavior of statistics that have been used to detect departures from the usual Kingman's coalescent.