A new proof for the convergence of an individual based model to the Trait substitution sequence - Centre de mathématiques appliquées (CMAP) Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2012

A new proof for the convergence of an individual based model to the Trait substitution sequence

Résumé

We consider a stochastic individual based model for a population structured by a vector trait and with logistic interactions. We consider its limit in a context from adaptive dynamics: the population is large, the mutations are rare and we view the process in the timescale of mutations. Using averaging techniques due to Kurtz (1992), we give a new proof of the convergence of the individual based model to the Trait substitution sequence of Metz et al. (1992) and rigorously proved by Champagnat (2006): assuming that ''invasion implies fixation'', we obtain in the limit a process that jumps from one population equilibrum to another one when mutations occur and invade the population.
Fichier principal
Vignette du fichier
Classic-v4.pdf (282.48 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00678007 , version 1 (11-03-2012)
hal-00678007 , version 2 (12-03-2012)

Identifiants

Citer

Ankit Gupta, J.A.J. Metz, Viet Chi Tran. A new proof for the convergence of an individual based model to the Trait substitution sequence. 2012. ⟨hal-00678007v1⟩
303 Consultations
126 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More