Asymptotics of steady states of a selection-mutation equation for small mutation rate

Àngel Calsina; Sílvia Cuadrado; Laurent Desvillettes; Gaël Raoul

doi:10.1017/S0308210510001629

Asymptotics of steady states of a selection-mutation equation for small mutation rate

Àngel Calsina, Sílvia Cuadrado, Laurent Desvillettes, Gaël Raoul

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

15 Citations (Scopus)

Abstract

We consider a selection-mutation equation for the density of individuals with respect to a continuous phenotypic evolutionary trait. We assume that the competition term for an individual with a given trait depends on the traits of all the other individuals, therefore giving an infinite-dimensional nonlinearity. Mutations are modelled by means of an integral operator. We prove existence of steady states and show that, when the mutation rate goes to zero, the asymptotic profile of the population is a Cauchy distribution. © Royal Society of Edinburgh 2013.

Original language	English
Pages (from-to)	1123-1146
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume	143
Issue number	6
DOIs	https://doi.org/10.1017/S0308210510001629
Publication status	Published - 1 Jan 2013

Access to Document

10.1017/S0308210510001629

Fingerprint Dive into the research topics of 'Asymptotics of steady states of a selection-mutation equation for small mutation rate'. Together they form a unique fingerprint.

Cite this

@article{2b7359439e764f61a7a081a12016953e,

title = "Asymptotics of steady states of a selection-mutation equation for small mutation rate",

abstract = "We consider a selection-mutation equation for the density of individuals with respect to a continuous phenotypic evolutionary trait. We assume that the competition term for an individual with a given trait depends on the traits of all the other individuals, therefore giving an infinite-dimensional nonlinearity. Mutations are modelled by means of an integral operator. We prove existence of steady states and show that, when the mutation rate goes to zero, the asymptotic profile of the population is a Cauchy distribution. {\textcopyright} Royal Society of Edinburgh 2013.",

author = "{\`A}ngel Calsina and S{\'i}lvia Cuadrado and Laurent Desvillettes and Ga{\"e}l Raoul",

year = "2013",

month = jan,

day = "1",

doi = "10.1017/S0308210510001629",

language = "English",

volume = "143",

pages = "1123--1146",

journal = "Proceedings of the Royal Society of Edinburgh Section A: Mathematics",

issn = "0308-2105",

number = "6",

}

TY - JOUR

T1 - Asymptotics of steady states of a selection-mutation equation for small mutation rate

AU - Calsina, Àngel

AU - Cuadrado, Sílvia

AU - Desvillettes, Laurent

AU - Raoul, Gaël

PY - 2013/1/1

Y1 - 2013/1/1

N2 - We consider a selection-mutation equation for the density of individuals with respect to a continuous phenotypic evolutionary trait. We assume that the competition term for an individual with a given trait depends on the traits of all the other individuals, therefore giving an infinite-dimensional nonlinearity. Mutations are modelled by means of an integral operator. We prove existence of steady states and show that, when the mutation rate goes to zero, the asymptotic profile of the population is a Cauchy distribution. © Royal Society of Edinburgh 2013.

AB - We consider a selection-mutation equation for the density of individuals with respect to a continuous phenotypic evolutionary trait. We assume that the competition term for an individual with a given trait depends on the traits of all the other individuals, therefore giving an infinite-dimensional nonlinearity. Mutations are modelled by means of an integral operator. We prove existence of steady states and show that, when the mutation rate goes to zero, the asymptotic profile of the population is a Cauchy distribution. © Royal Society of Edinburgh 2013.

U2 - 10.1017/S0308210510001629

DO - 10.1017/S0308210510001629

M3 - Article

VL - 143

SP - 1123

EP - 1146

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 6

ER -