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

Handle URI:
http://hdl.handle.net/10754/597628
Title:
Asymptotics of steady states of a selection–mutation equation for small mutation rate
Authors:
Calsina, Àngel; Cuadrado, Sílvia; Desvillettes, Laurent; Raoul, Gaël
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.
Citation:
Calsina À, Cuadrado S, Desvillettes L, Raoul G (2013) Asymptotics of steady states of a selection–mutation equation for small mutation rate. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 143: 1123–1146. Available: http://dx.doi.org/10.1017/S0308210510001629.
Publisher:
Cambridge University Press (CUP)
Journal:
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
Dec-2013
DOI:
10.1017/S0308210510001629
Type:
Article
ISSN:
0308-2105; 1473-7124
Sponsors:
A.C. and S. C. were partly supported by Grant nos MTM2008-06349-C03-03, 2009-SGR-345 and MTM2011-27739-C04-02. L. D. and G. R. were partly supported by Project CBDif-Fr ANR-08-BLAN-0333-01. G. R. was partly supported by Award no. KUK-I1-007-43 of Peter A. Markowich, made by the King Abdullah University of Science and Technology (KAUST). Finally, all authors were partly supported by the bilateral PICASSO project POLYCELL, Grant no. 22978WA.
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Full metadata record

DC FieldValue Language
dc.contributor.authorCalsina, Àngelen
dc.contributor.authorCuadrado, Sílviaen
dc.contributor.authorDesvillettes, Laurenten
dc.contributor.authorRaoul, Gaëlen
dc.date.accessioned2016-02-25T12:43:20Zen
dc.date.available2016-02-25T12:43:20Zen
dc.date.issued2013-12en
dc.identifier.citationCalsina À, Cuadrado S, Desvillettes L, Raoul G (2013) Asymptotics of steady states of a selection–mutation equation for small mutation rate. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 143: 1123–1146. Available: http://dx.doi.org/10.1017/S0308210510001629.en
dc.identifier.issn0308-2105en
dc.identifier.issn1473-7124en
dc.identifier.doi10.1017/S0308210510001629en
dc.identifier.urihttp://hdl.handle.net/10754/597628en
dc.description.abstractWe 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.en
dc.description.sponsorshipA.C. and S. C. were partly supported by Grant nos MTM2008-06349-C03-03, 2009-SGR-345 and MTM2011-27739-C04-02. L. D. and G. R. were partly supported by Project CBDif-Fr ANR-08-BLAN-0333-01. G. R. was partly supported by Award no. KUK-I1-007-43 of Peter A. Markowich, made by the King Abdullah University of Science and Technology (KAUST). Finally, all authors were partly supported by the bilateral PICASSO project POLYCELL, Grant no. 22978WA.en
dc.publisherCambridge University Press (CUP)en
dc.titleAsymptotics of steady states of a selection–mutation equation for small mutation rateen
dc.typeArticleen
dc.identifier.journalProceedings of the Royal Society of Edinburgh: Section A Mathematicsen
dc.contributor.institutionUniversidad Autonoma de Barcelona, Barcelona, Spainen
dc.contributor.institutionEcole Normale Superieure de Cachan, Cachan, Franceen
dc.contributor.institutionCEFE Centre d'Ecologie Fonctionnelle et Evolutive UMR 5175, Montpellier, Franceen
kaust.grant.numberKUK-I1-007-43en
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