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

Citation data:

Proceedings of the Royal Society of Edinburgh Section A: Mathematics, ISSN: 1473-7124, Vol: 143, Issue: 6, Page: 1123-1146

Publication Year:
2013
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Repository URL:
http://hdl.handle.net/10754/597628
DOI:
10.1017/s0308210510001629
Author(s):
Calsina, Àngel; Cuadrado, Sílvia; Desvillettes, Laurent; Raoul, Gaël
Publisher(s):
Cambridge University Press (CUP)
Tags:
Mathematics
article description
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.