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

Jason Schweinsberg

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arXiv · 1507.00394

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

Jason Schweinsberg

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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).

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Jason Schweinsberg. 2015-07-01. Rigorous results for a population model with selection II: genealogy of the population. https://arxiv.org/abs/1507.00394

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