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Kingman’s model with random mutation probabilities: convergence and condensation I
Published online by Cambridge University Press: 25 February 2022
Abstract
For a one-locus haploid infinite population with discrete generations, the celebrated model of Kingman describes the evolution of fitness distributions under the competition of selection and mutation, with a constant mutation probability. This paper generalises Kingman’s model by using independent and identically distributed random mutation probabilities, to reflect the influence of a random environment. The weak convergence of fitness distributions to the globally stable equilibrium is proved. Condensation occurs when almost surely a positive proportion of the population travels to and condenses at the largest fitness value. Condensation may occur when selection is favoured over mutation. A criterion for the occurrence of condensation is given.
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- © The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust
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