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 -