The evolutionary limit for models of populations interacting competitively via several resources

Nicolas Champagnat, Pierre Emmanuel Jabin

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We consider an integro-differential nonlinear model that describes the evolution of a population structured by a quantitative trait. The interactions between individuals occur by way of competition for resources whose concentrations depend on the current state of the population. Following the formalism of Diekmann et al. (2005) [16], we study a concentration phenomenon arising in the limit of strong selection and small mutations. We prove that the population density converges to a sum of Dirac masses characterized by the solution φ of a Hamilton-Jacobi equation which depends on resource concentrations that we fully characterize in terms of the function φ.

Original languageEnglish (US)
Pages (from-to)176-195
Number of pages20
JournalJournal of Differential Equations
Volume251
Issue number1
DOIs
StatePublished - Jul 1 2011

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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