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

Àngel Calsina, Sílvia Cuadrado, Laurent Desvillettes, Gaël Raoul

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5 Citations (Scopus)


© 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).
Original languageEnglish
Pages (from-to)1515-1541
JournalJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - 15 Dec 2016


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


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