• Corpus ID: 238857291

Confining integro-differential equations originating from evolutionary biology: ground states and long time dynamics

  title={Confining integro-differential equations originating from evolutionary biology: ground states and long time dynamics},
  author={Matthieu Alfaro and Pierre Gabriel and Otared Kavian},
We consider nonlinear mutation selection models, known as replicator-mutator equations in evolutionary biology. They involve a nonlocal mutation kernel and a confining fitness potential. We prove that the long time behaviour of the Cauchy problem is determined by the principal eigenelement of the underlying linear operator. The novelties compared to the literature on these models are about the case of symmetric mutations: Université de Rouen Normandie, CNRS, Laboratoire de Mathématiques Raphaël… 


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On the maintenance of genetic variation: global analysis of Kimura's continuum-of-alleles model
  • R. Bürger
  • Biology, Medicine
    Journal of mathematical biology
  • 1986
The present analysis provides the first proof that in Kimura's model an equilibrium in fact exists and, moreover, that it is globally stable and shows that continuum-of-alleles models may be excellent approximations to multiallele models, if analysed appropriately.