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

Àngel Calsina, Sílvia Cuadrado, Laurent Desvillettes, Gaël Raoul

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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.
Original languageEnglish (US)
Pages (from-to)1123-1146
Number of pages24
JournalProceedings of the Royal Society of Edinburgh: Section A Mathematics
Issue number6
StatePublished - Dec 3 2013
Externally publishedYes

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