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: 03082105, Vol: 143, Issue: 06, Page: 11231146
 Publication Year:
 2013
 Repository URL:
 http://hdl.handle.net/10754/597628
 DOI:
 10.1017/s0308210510001629
 Author(s):
 Publisher(s):
 Tags:
 Mathematics
article description
We consider a selectionmutation 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 infinitedimensional 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.