## Electronic Journal of Probability

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

Jason Schweinsberg

#### Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1493258437

Digital Object Identifier
doi:10.1214/17-EJP58

Mathematical Reviews number (MathSciNet)
MR3646064

Zentralblatt MATH identifier
1362.92066

#### Citation

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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