Electronic Journal of Probability
- Electron. J. Probab.
- Volume 22 (2017), paper no. 38, 54 pp.
Rigorous results for a population model with selection II: genealogy of the population
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).
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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)
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