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.
ISSN 0001-8678, 1475-6064
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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: | 4901 Applied Mathematics, 49 Mathematical Sciences, 4905 Statistics |
| Divisions: | Faculty of Science and Engineering > School of Physical Sciences |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 03 Mar 2022 08:53 |
| Last Modified: | 06 Dec 2024 19:57 |
| DOI: | 10.1017/apr.2021.33 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3149992 |
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