Rigorous results for a population model with selection I: evolution of the fitness distribution

2015/07/01 by Jason Schweinsberg, Schweinsberg, Jason · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Social Sciences · #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Mathematical and Theoretical Epidemiology and Ecology Models #math.PR #msc:60J27 #msc:60J75 #msc:60J80 #msc:92D15 #msc:92D25

paper · pdf · doi:10.48550/arxiv.1507.00393

99 pages

arxiv created 2015/07/01 · arxiv updated 2015/07/03

Abstract

We consider a model of a population of fixed size N undergoing selection. Each individual acquires beneficial mutations at rate μ_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 μ_N and s_N, we obtain rigorous results for the rate at which mutations accumulate in the population and the distribution of the fitnesses of individuals in the population at a given time. Our results confirm predictions of Desai and Fisher (2007).

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