Titre :

Stochastic dynamics for adaptation and evolution of microorganisms

Auteur(s) :

Billiard, Sylvain [Auteur]
Évolution, Écologie et Paléontologie (Evo-Eco-Paleo) - UMR 8198 [Evo-Eco-Paléo (EEP)]
Collet, Pierre [Auteur]
Centre de Physique Théorique [CPHT]
Ferrière, Régis [Auteur]
Department of Ecology and Evolutionary Biology [University of Arizona]
Eco-évolution mathématique - IBENS
Méléard, Sylvie [Auteur]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]
Tran, Chi [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Éditeur(s) ou directeur(s) scientifique(s) :

V. Mehrmann and M. Skutella eds.

Titre de la manifestation scientifique :

European Congress of Mathematics

Ville :

Berlin

Pays :

Allemagne

Date de début de la manifestation scientifique :

2016

Éditeur :

European Mathematical Society

Date de publication :

2018

Mot(s)-clé(s) en anglais :

large population approximation
bacterial conjugation
trait substitution sequence
fixation probability
canonical equation
adaptive dynamics
stochastic individual-based models
horizontal gene transfer
interactions

Discipline(s) HAL :

Mathématiques [math]/Probabilités [math.PR]
Sciences de l'environnement/Biodiversité et Ecologie
Sciences du Vivant [q-bio]/Biodiversité/Evolution [q-bio.PE]

Résumé en anglais : [en]

We present a model for the dynamics of a population of bacteria with a continuum of traits, who compete for resources and exchange horizontally (transfer) an otherwise vertically inherited trait with possible mutations. ...
Lire la suite >We present a model for the dynamics of a population of bacteria with a continuum of traits, who compete for resources and exchange horizontally (transfer) an otherwise vertically inherited trait with possible mutations. Competition influences individual demographics, affecting population size, which feeds back on the dynamics of transfer. We consider a stochastic individual-based pure jump process taking values in the space of point measures, and whose jump events describe the individual reproduction, transfer and death mechanisms. In a large population scale, the stochastic process is proved to converge to the solution of a nonlinear integro-differential equation. When there are only two different traits and no mutation, this equation reduces to a non-standard two-dimensional dynamical system. We show how crucial the forms of the transfer rates are for the long-term behavior of its solutions. We describe the dynamics of invasion and fixation when one of the two traits is initially rare, and compute the invasion probabilities. Then, we study the process under the assumption of rare mutations. We prove that the stochastic process at the mutation time scale converges to a jump process which describes the successive invasions of successful mutants. We show that the horizontal transfer can have a major impact on the distribution of the successive mutational fixations, leading to dramatically different behaviors, from expected evolution scenarios to evolutionary suicide. Simulations are given to illustrate these phenomena.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL