Kingman’s model with random mutation probabilities: convergence and condensation I

Yuan, Linglong ORCID: 0000-0002-7851-1631 (2022) Kingman’s model with random mutation probabilities: convergence and condensation I. Advances in Applied Probability, 54 (1). pp. 311-335.

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Official URL: http://dx.doi.org/10.1017/apr.2021.33

Abstract

<jats:title>Abstract</jats:title><jats:p>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.</jats:p>

Item Type:	Article
Uncontrolled Keywords:	Stem Cell Research, Stem Cell Research - Nonembryonic - Non-Human
Divisions:	Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	03 Mar 2022 08:53
Last Modified:	15 Mar 2024 13:27
DOI:	10.1017/apr.2021.33
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3149992