Title :

Stochastic dynamics for adaptation and evolution of microorganisms

Author(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]

Scientific editor(s) :

V. Mehrmann and M. Skutella eds.

Conference title :

European Congress of Mathematics

City :

Berlin

Country :

Allemagne

Start date of the conference :

2016

Publisher :

European Mathematical Society

Publication date :

2018

English keyword(s) :

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

HAL domain(s) :

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

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

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL