Asymptotic profile in selection-mutation equations: Gauss versus Cauchy distributions

作者：Calsina Angel; Cuadrado Silvia^*; Desvillettes Laurent; Raoul Gael

来源：Journal of Mathematical Analysis and Applications, 2016, 444(2): 1515-1541.

DOI：10.1016/j.jmaa.2016.07.028

• Selection-mutation equations
• Asymptotic behaviour
• Spectral theory
• Population dynamics

In this paper, we study the asymptotic (large time) behaviour of a selection mutation competition model for a population structured with respect to a phenotypic trait when the rate of mutation is very small. We assume that the reproduction is asexual, and that the mutations can be described by a linear integral operator. We are interested in the interplay between the time variable t and the rate epsilon of mutations. We show that depending on alpha > 0, the limit epsilon -> 0 with t = epsilon(-alpha) can lead to population number densities which are either Gaussian-like (when a is small) or Cauchy-like (when a is large).

• 出版日期2016-12-15