Electronic Journal of Probability

Rigorous results for a population model with selection II: genealogy of the population

Jason Schweinsberg

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We consider a model of a population of fixed size $N$ undergoing selection. Each individual acquires beneficial mutations at rate $\mu _N$, and each beneficial mutation increases the individual’s fitness by $s_N$. Each individual dies at rate one, and when a death occurs, an individual is chosen with probability proportional to the individual’s fitness to give birth. Under certain conditions on the parameters $\mu _N$ and $s_N$, we show that the genealogy of the population can be described by the Bolthausen-Sznitman coalescent. This result confirms predictions of Desai, Walczak, and Fisher (2013), and Neher and Hallatschek (2013).

Article information

Electron. J. Probab., Volume 22 (2017), paper no. 38, 54 pp.

Received: 28 January 2017
Accepted: 18 April 2017
First available in Project Euclid: 27 April 2017

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Zentralblatt MATH identifier

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J75: Jump processes 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 92D15: Problems related to evolution 92D25: Population dynamics (general)

population model selection Bolthausen-Sznitman coalescent

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Schweinsberg, Jason. Rigorous results for a population model with selection II: genealogy of the population. Electron. J. Probab. 22 (2017), paper no. 38, 54 pp. doi:10.1214/17-EJP58. https://projecteuclid.org/euclid.ejp/1493258437

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