TY - JOUR
T1 - Kingman's model with random mutation probabilities
T2 - Convergence and condensation i
AU - Yuan, Linglong
N1 - Funding Information:
The author acknowledges the support of the National Natural Science Foundation of China (Youth Programme, Grant 11801458). Competing Interests
Publisher Copyright:
© 2022 Cambridge University Press. All rights reserved.
PY - 2022/3/25
Y1 - 2022/3/25
N2 - 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.
AB - 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.
KW - Population dynamics
KW - distributional equation
KW - fitness distribution
KW - house of cards
KW - mutation-selection balance
KW - size-biased distribution
UR - http://www.scopus.com/inward/record.url?scp=85125597276&partnerID=8YFLogxK
U2 - 10.1017/apr.2021.33
DO - 10.1017/apr.2021.33
M3 - Article
AN - SCOPUS:85125597276
SN - 0001-8678
VL - 54
SP - 311
EP - 335
JO - Advances in Applied Probability
JF - Advances in Applied Probability
IS - 1
ER -