Titre :

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

Auteur(s) :

Gupta, Ankit [Auteur correspondant]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]
Metz, J.A.J. [Auteur]
Mathematical institute
Tran, Chi [Auteur correspondant]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Titre de la revue :

Acta Applicandae Mathematicae

Pagination :

1-27

Éditeur :

Springer Verlag

Date de publication :

2014-06

ISSN :

0167-8019

Mot(s)-clé(s) en anglais :

birth and death process
structured population
adaptive dynamics
individual based model
averaging technique
trait substitution sequence

Discipline(s) HAL :

Mathématiques [math]/Probabilités [math.PR]
Sciences du Vivant [q-bio]/Biodiversité/Evolution [q-bio.PE]

Résumé en anglais : [en]

We consider a continuous time stochastic individual based model for a population structured only by an inherited vector trait and with logistic interactions. We consider its limit in a context from adaptive dynamics: the ...
Lire la suite >We consider a continuous time stochastic individual based model for a population structured only by an inherited 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) first worked out by Dieckman and Law (1996) and rigorously proved by Champagnat (2006): rigging the model such that ''invasion implies substitution'', we obtain in the limit a process that jumps from one population equilibrium to another when mutations occur and invade the population.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Commentaire :

23 pages

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL