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 and the rate of mutations. We show that depending on , the limit with can lead to population number densities which are either Gaussian-like (when is small) or Cauchy-like (when is large).
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| http://dx.doi.org/10.1016/j.jmaa.2016.07.028 | DOI Listing |
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