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

2015/07/01 by Jason Schweinsberg, Schweinsberg, Jason · 1 citation
Biochemistry, Genetics and Molecular Biology · Social Sciences · Medicine · #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.1507.00393

Abstract

We consider a model of a population of fixed size N undergoing selection.\nEach individual acquires beneficial mutations at rate \μ_N, and each\nbeneficial mutation increases the individual's fitness by s_N. Each\nindividual dies at rate one, and when a death occurs, an individual is chosen\nwith probability proportional to the individual's fitness to give birth. Under\ncertain conditions on the parameters \μ_N and s_N, we obtain rigorous\nresults for the rate at which mutations accumulate in the population and the\ndistribution of the fitnesses of individuals in the population at a given time.\nOur results confirm predictions of Desai and Fisher (2007).\n

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