Polymorphic evolution sequence and evolutionary branching - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Probability Theory and Related Fields Year : 2011

Polymorphic evolution sequence and evolutionary branching


We are interested in the study of models describing the evolution of a polymorphic population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The population size is assumed to be large and the mutation rate small. We prove that under a good combination of these two scales, the population process is approximated in the long time scale of mutations by a Markov pure jump process describing the successive trait equilibria of the population. This process, which generalizes the so-called trait substitution sequence, is called polymorphic evolution sequence. Then we introduce a scaling of the size of mutations and we study the polymorphic evolution sequence in the limit of small mutations. From this study in the neighborhood of evolutionary singularities, we obtain a full mathematical justification of a heuristic criterion for the phenomenon of evolutionary branching. To this end we finely analyze the asymptotic behavior of 3-dimensional competitive Lotka-Volterra systems.
Fichier principal
Vignette du fichier
TSS22032010v4.pdf (599.47 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

inria-00345399 , version 1 (09-12-2008)
inria-00345399 , version 2 (09-03-2016)





Nicolas Champagnat, Sylvie Méléard. Polymorphic evolution sequence and evolutionary branching. Probability Theory and Related Fields, 2011, 151 (1-2), pp.45-94. ⟨10.1007/s00440-010-0292-9⟩. ⟨inria-00345399v2⟩
197 View
241 Download



Gmail Facebook Twitter LinkedIn More