Title :

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

Author(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]

Journal title :

Acta Applicandae Mathematicae

Pages :

1-27

Publisher :

Springer Verlag

Publication date :

2014-06

ISSN :

0167-8019

English keyword(s) :

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

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Comment :

23 pages

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL