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 (US)|
|Number of pages||24|
|Journal||Proceedings of the Royal Society of Edinburgh: Section A Mathematics|
|State||Published - Dec 3 2013|
Bibliographical noteKAUST 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.