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Rigorous results for a population model with selection

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If you have a question about this talk, please contact Mustapha Amrani .

Random Geometry

We consider a model of a population of fixed size $N$ in which each individual acquires beneficial mutations at rate $mu$. 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. We obtain rigorous results for the rate at which mutations accumulate in the population, the distribution of the fitnesses of individuals in the population at a given time, and the genealogy of the population. Our results confirm predictions of Desai and Fisher (2007), Desai, Walczak, and Fisher (2013), and Neher and Hallatschek (2013).

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