title: Stochastic dynamics of adaptive trait and neutral marker driven by eco-evolutionary feedbacks.
abstract: 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.
authors.affiliation: Laboratoire EEP, UFR de Biologie, Université des Sciences et Technologies Lille 1, Cité scientifique, 59655, Villeneuve d'Ascq Cedex, France. sylvain.billiard@univ-lille1.fr.
authors.forename: Sylvain
authors.initials: S
authors.lastname: Billiard
authors.affiliation: Eco-Evo-Math International Laboratory, Institut de Biologie de l'ENS, CNRS INSERM ENS UMR 8197, 46 rue d'Ulm, 75230, Paris, France. ferriere@biologie.ens.fr.|Department of Ecology and Evolutionary Biology, University of Arizona, Tucson, USA. ferriere@biologie.ens.fr.
authors.forename: Régis
authors.initials: R
authors.lastname: Ferrière
authors.affiliation: CMAP, Ecole Polytechnique, CNRS, route de Saclay, 91128, Palaiseau Cedex, France. sylvie.meleard@polytechnique.edu.
authors.forename: Sylvie
authors.initials: S
authors.lastname: Méléard
authors.affiliation: Laboratoire P. Painlevé, UFR de Mathématiques, Université des Sciences et Technologies Lille 1, Cité scientifique, 59655, Villeneuve d'Ascq Cedex, France. chi.tran@math.univ-lille1.fr.
authors.forename: Viet Chi
authors.initials: VC
authors.lastname: Tran
mesh_terms: D000220:Adaptation, Biological / Q000235:genetics; D044822:Biodiversity; D003198:Computer Simulation; D017753:Ecosystem; D019143:Evolution, Molecular; D025461:Feedback, Physiological; D005819:Genetic Markers; D005828:Genetics, Population; D055641:Mathematical Concepts; D008957:Models, Genetic; D009154:Mutation; D011157:Population Dynamics; D012641:Selection, Genetic; D013269:Stochastic Processes
chemical_list: D005819:Genetic Markers
keywords: Adaptive dynamics; Hitchhiking; Limit theorems for multi-scale processes; Measure-valued individual-based model; Mutation-selection; Neutral diversity; Selective sweeps; Substitution Fleming–Viot Process