Continuous models for genetic evolution in large populatons

Fábio Augusto da Costa Carvalho Chalub; Max O. Souza

doi:10.1007/978-3-642-11456-4_15

Continuous models for genetic evolution in large populatons

Fábio Augusto da Costa Carvalho Chalub, Max O. Souza

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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 language	English
Title of host publication	Dynamics, Games and Science
Editors	M.M. Peixoto, D. Rand, A. A. Pinto
Place of Publication	Heidelberg
Publisher	Springer
Pages	239-242
Volume	1
ISBN (Electronic)	978-3-642-11456-4
ISBN (Print)	978-3-642-11455-7
DOIs	https://doi.org/10.1007/978-3-642-11456-4_15
Publication status	Published - 2011

Publication series

Name	Springer Proceedings in Mathematics
Publisher	Springer
Volume	1
ISSN (Print)	2190-5614

Access to Document

10.1007/978-3-642-11456-4_15Licence: Unspecified

Cite this

@inbook{b11fe0950c9e4e58b9459d1b13d322c6,

title = "Continuous models for genetic evolution in large populatons",

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).",

author = "Chalub, {F{\'a}bio Augusto da Costa Carvalho} and Souza, {Max O.}",

note = "Sem PDF conforme Despacho.",

year = "2011",

doi = "10.1007/978-3-642-11456-4_15",

language = "English",

isbn = "978-3-642-11455-7",

volume = "1",

series = "Springer Proceedings in Mathematics",

publisher = "Springer",

pages = "239--242",

editor = "M.M. Peixoto and D. Rand and Pinto, {A. A.}",

booktitle = "Dynamics, Games and Science",

address = "Netherlands",

}

TY - CHAP

T1 - Continuous models for genetic evolution in large populatons

AU - Chalub, Fábio Augusto da Costa Carvalho

AU - Souza, Max O.

N1 - Sem PDF conforme Despacho.

PY - 2011

Y1 - 2011

N2 - 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).

AB - 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).

U2 - 10.1007/978-3-642-11456-4_15

DO - 10.1007/978-3-642-11456-4_15

M3 - Chapter

SN - 978-3-642-11455-7

VL - 1

T3 - Springer Proceedings in Mathematics

SP - 239

EP - 242

BT - Dynamics, Games and Science

A2 - Peixoto, M.M.

A2 - Rand, D.

A2 - Pinto, A. A.

PB - Springer

CY - Heidelberg

ER -