Asymptotics of steady states of a selection–mutation equation for small mutation rate
Type
ArticleKAUST Grant Number
KUK-I1-007-43Date
2013-12-03Online Publication Date
2013-12-03Print Publication Date
2013-12Permanent link to this record
http://hdl.handle.net/10754/597628
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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.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.Publisher
Cambridge University Press (CUP)ae974a485f413a2113503eed53cd6c53
10.1017/S0308210510001629