Title :

Stochastic dynamics of adaptive trait and neutral marker driven by eco-evolutionary feedbacks

Author(s) :

Billiard, Sylvain [Auteur correspondant]
Génétique et évolution des populations végétales [GEPV]
Ferriere, Regis [Auteur correspondant]
Eco-évolution mathématique - IBENS
Department of Ecology and Evolutionary Biology [University of Arizona]
Méléard, Sylvie [Auteur correspondant]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]
Tran, Chi [Auteur correspondant]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Journal of Mathematical Biology

Pages :

1211-1242

Publisher :

Springer

Publication date :

2015-11

ISSN :

0303-6812

English keyword(s) :

Substitution Fleming-Viot Process
measure-valued individual-based model
adaptive dynamics
selective sweeps
hitchhiking
limit theorems for multi-scale processes
neutral diversity
Mutation-selection

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]

How the neutral diversity is affected by selection and adaptation is investigated in an eco-evolutionary framework. In our model, we study a finite population in continuous time, where each individual is characterized by ...
Show more >How the neutral diversity is affected by selection and adaptation is investigated in an eco-evolutionary framework. In our model, we study a finite population in continuous time, where each individual is characterized by a trait under selection and a completely linked neutral marker. Population dynamics are driven by births and deaths, mutations at birth, and competition between individuals. Trait values influence ecological processes (demographic events, competition), and competition generates selection on trait variation, thus closing the eco-evolutionary feedback loop. The demographic effects of the trait are also expected to influence the generation and maintenance of neutral variation. We consider a large population limit with rare mutation, under the assumption that the neutral marker mutates faster than the trait under selection. We prove the convergence of the stochastic individual-based process to a new measure-valued diffusive process with jumps that we call Substitution Fleming-Viot Process (SFVP). When restricted to the trait space this process is the Trait Substitution Sequence first introduced by Metz et al. (1996). During the invasion of a favorable mutation, a genetical bottleneck occurs and the marker associated with this favorable mutant is hitchhiked. By rigorously analysing the hitchhiking effect and how the neutral diversity is restored afterwards, we obtain the condition for a time-scale separation; under this condition, we show that the marker distribution is approximated by a Fleming-Viot distribution between two trait substitutions. We discuss the implications of the SFVP for our understanding of the dynamics of neutral variation under eco-evolutionary feedbacks and illustrate the main phenomena with simulations. Our results highlight the joint importance of mutations, ecological parameters, and trait values in the restoration of neutral diversity after a selective sweep.Show less >

Language :

Anglais

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