Kingman's model with random mutation probabilities: Convergence and condensation i

Linglong Yuan

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)311-335
Number of pages25
JournalAdvances in Applied Probability
Issue number1
Publication statusPublished - 25 Mar 2022


  • Population dynamics
  • distributional equation
  • fitness distribution
  • house of cards
  • mutation-selection balance
  • size-biased distribution


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