@article{b1047e1bbbde4df7a1ca1b6d4c9c02cb,
title = "Derivation of replicator–mutator equations from a model in population genetics",
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.",
keywords = "Adaptive dynamics, Population genetic model, Scaling limits, replicator–mutator equation",
author = "Wakano, {Joe Yuichiro} and Tadahisa Funaki and Satoshi Yokoyama",
note = "Funding Information: T. Funaki is supported in part by the JSPS KAKENHI Grant Numbers (B) 26287014 and 26610019. Funding Information: J. Y. Wakano is supported in part by the JSPF KAKENHI Grant Number (C) 16K05283. Funding Information: S. Yokoyama is supported in part by the JSPS KAKENHI Grant Number (S) 24224004. Publisher Copyright: {\textcopyright} 2017, The JJIAM Publishing Committee and Springer Japan KK.",
year = "2017",
month = aug,
day = "1",
doi = "10.1007/s13160-017-0249-9",
language = "English",
volume = "34",
pages = "473--488",
journal = "Japan Journal of Industrial and Applied Mathematics",
issn = "0916-7005",
publisher = "Springer Japan",
number = "2",
}