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

Joe Yuichiro Wakano, Tadahisa Funaki, Satoshi Yokoyama

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    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
    Volume34
    Issue number2
    DOIs
    Publication statusPublished - 2017 Aug 1

    Fingerprint

    Genetic Drift
    Mathematical Biology
    Individual-based Model
    Adaptive Dynamics
    Markov Chain Model
    Population Genetics
    Scaling Limit
    Population Size
    Mutation
    Game
    Fluctuations
    Converge
    Formulation
    Dependent
    Interaction
    Markov processes
    Model

    Keywords

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

    ASJC Scopus subject areas

    • Engineering(all)
    • Applied Mathematics

    Cite this

    Derivation of replicator–mutator equations from a model in population genetics. / Wakano, Joe Yuichiro; Funaki, Tadahisa; Yokoyama, Satoshi.

    In: Japan Journal of Industrial and Applied Mathematics, Vol. 34, No. 2, 01.08.2017, p. 473-488.

    Research output: Contribution to journalArticle

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