Continuous models for genetic evolution in large populatons

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Abstract

We consider a recently proposed generalisation of the Kimura equation,a Fokker-Planck type equation describing the evolution of p . x; t/ , the probabil-ity of finding a fraction x of mutants at time t in a population evolving accordingto standard models in evolutionary biology. We present a detailed description ofthe solution, and we show that it naturally divides in two different time scales: thefirst determined by the drift (the natural selection), the second by the diffusion (thegenetic drift).
Original languageEnglish
Title of host publicationDynamics, Games and Science
EditorsM.M. Peixoto, D. Rand, A. A. Pinto
Place of PublicationHeidelberg
PublisherSpringer
Pages239-242
Volume1
ISBN (Electronic)978-3-642-11456-4
ISBN (Print)978-3-642-11455-7
DOIs
Publication statusPublished - 2011

Publication series

NameSpringer Proceedings in Mathematics
PublisherSpringer
Volume1
ISSN (Print)2190-5614

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Chalub, F. A. D. C. C., & Souza, M. O. (2011). Continuous models for genetic evolution in large populatons. In M. M. Peixoto, D. Rand, & A. A. Pinto (Eds.), Dynamics, Games and Science (Vol. 1, pp. 239-242). (Springer Proceedings in Mathematics; Vol. 1). Heidelberg: Springer. https://doi.org/10.1007/978-3-642-11456-4_15