2011-10-01, English, Article, Report edition: Polymorphic evolution sequence and evolutionary branching.(Report) Champagnat, Nicolas; Meleard, Sylvie

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Physical Description
  • Report
  • Magazine/​Journal article
Published
  • Springer, 2011 Oct
Language
  • English

Edition details

Title
  • Polymorphic evolution sequence and evolutionary branching.(Report)
Also Titled
  • Polymorphic evolution sequence and evolutionary branching.
Appears In
  • Probability Theory and Related Fields, v.151, no.1-2, 2011 Oct, p.45(50) (ISSN: 0178-8051)
Author
  • Champagnat, Nicolas
  • Meleard, Sylvie
Published
  • Springer, 2011 Oct
Physical Description
  • Report
  • Magazine/​Journal article
Subjects
Target Audience
  • Academic
Summary
  • Byline: Nicolas Champagnat (1), Sylvie Meleard (2) Keywords: Mutation-selection individual-based model; Fitness of invasion; Adaptive dynamics; Polymorphic evolution sequence; Competitive Lotka--Volterra system; Evolutionary branching; 92D25; 60J80; 37N25; 92D15; 60J75 Abstract: 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 (TSS), is called polymorphic evolution sequence (PES). Then we introduce a scaling of the size of mutations and we study the PES 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. This phenomenon corresponds to the situation where the population, initially essentially single modal, is driven by the selective forces to divide into two separate subpopulations. To this end we finely analyze the asymptotic behavior of three-dimensional competitive Lotka--Volterra systems. Author Affiliation: (1) EPI TOSCA, INRIA Sophia Antipolis, Mediterranee, 2004 route des Lucioles, BP. 93, 06902, Sophia Antipolis Cedex, France (2) CMAP, Ecole Polytechnique, CNRS, route de Saclay, 91128, Palaiseau Cedex, France Article History: Registration Date: 30/​03/​2010 Received Date: 26/​11/​2009 Online Date: 14/​04/​2010
Terms of Use
  • COPYRIGHT 2011 Springer
Language
  • English
Database
  • Gale Academic OneFile
Identifier
  • 267037822

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