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

17 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)	-
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	143
Issue number	6
DOIs	https://doi.org/10.1017/S0308210510001629
Publication status	Published - 1 Jan 2013

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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.",

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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.

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

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