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

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2013/12/3

Y1 - 2013/12/3

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.

UR - http://hdl.handle.net/10754/597628

UR - https://www.cambridge.org/core/product/identifier/S0308210510001629/type/journal_article

UR - http://www.scopus.com/inward/record.url?scp=84896906031&partnerID=8YFLogxK

U2 - 10.1017/S0308210510001629

DO - 10.1017/S0308210510001629

M3 - Article

SN - 0308-2105

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

IS - 6

ER -