© 2016 Elsevier Inc. 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 ε of mutations. We show that depending on α>0, the limit ε→0 with t=ε−α can lead to population number densities which are either Gaussian-like (when α is small) or Cauchy-like (when α is large).
- Asymptotic behaviour
- Population dynamics
- Selection–mutation equations
- Spectral theory
Calsina, À., Cuadrado, S., Desvillettes, L., & Raoul, G. (2016). Asymptotic profile in selection–mutation equations: Gauss versus Cauchy distributions. Journal of Mathematical Analysis and Applications, 444(2), 1515-1541. https://doi.org/10.1016/j.jmaa.2016.07.028