Derivation of replicator–mutator equations from a model in population genetics

Joe Yuichiro Wakano*, Tadahisa Funaki, Satoshi Yokoyama

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We introduce a Markov chain model to study evolution of a continuous trait based on population genetics. It corresponds to individual-based model which includes frequency dependent selection caused by m-player game interactions and stochastic fluctuations due to random genetic drift and mutation. We prove that under a proper scaling limit as the population size increases the system converges to the solution of replicator–mutator equations. Our result establishes an affirmative mathematical base to the adaptive dynamics formulation employed in the theory of the mathematical biology.

Original languageEnglish
Pages (from-to)473-488
Number of pages16
JournalJapan Journal of Industrial and Applied Mathematics
Issue number2
Publication statusPublished - 2017 Aug 1


  • Adaptive dynamics
  • Population genetic model
  • Scaling limits
  • replicator–mutator equation

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics


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