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 -