TY - JOUR

T1 - Asymptotics of steady states of a selection-mutation equation for small mutation rate

AU - Calsina, Àngel

AU - Cuadrado, Sílvia

AU - Desvillettes, Laurent

AU - Raoul, Gaël

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

U2 - 10.1017/S0308210510001629

DO - 10.1017/S0308210510001629

M3 - Article

VL - 143

SP - 1123

EP - 1146

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 6

ER -