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H 1 Competitive populations with vertical and horizontal transmissions

Auteurs : Méléard, Sylvie (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Horizontal transfer of information is recognized as a major process in the evolution and adaptation of population, especially micro-organisms. There is a large literature but the previous models are either based on epidemiological models or population genetics stochastic models with constant population size. We propose a general stochastic eco-evolutionary model of population dynamics with horizontal and vertical transfers, inspired by the transfer of plasmids in bacteria. The transfer rates are either density-dependent (DD) or frequency-dependent (FD) or of Michaelis-Menten form (MM). Our model allows eco-evolutionary feedbacks. In the first part we present a two-traits (alleles or kinds of plasmids, etc.) model with horizontal transfer without mutation and study a large population limit. It’s a ODEs system. We show that the phase diagrams are different in the (DD), (FD) and (MM) cases. We interpret the results for the impact of horizontal transfer on the maintenance of polymorphism and the invasion or elimination of pathogens strains. We also propose a diffusive approximation of adaptation with transfer. In a second part, we study the impact of the horizontal transfer on the evolution. We explain why it can drastically affect the evolutionary outcomes. Joint work with S. Billiard,P. Collet, R. Ferrière, C.V. Tran.

    Codes MSC :
    60J75 - Jump processes
    60J80 - Branching processes (Galton-Watson, birth-and-death, etc.)
    92D15 - Problems related to evolution
    92D25 - Population dynamics (general)

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 30/06/15
      Date de captation : 16/06/15
      Collection : Research talks ; Mathematics in Science and Technology ; Probability and Statistics
      Sous collection : Research talks
      Format : quicktime ; audio/x-aac
      Durée : 00:53:02
      Domaine : Mathematics in Science & Technology ; Probability & Statistics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-06-16_Meleard.mp4

    Informations sur la rencontre

    Nom de la rencontre : Probability and biological evolution / Probabilités et évolution biologique
    Organisateurs de la rencontre : Pardoux, Etienne ; Wakolbinger, Anton
    Dates : 15/06/15 - 19/06/15
    Année de la rencontre : 2015
    URL Congrès : http://conferences.cirm-math.fr/1112.html

    Citation Data

    DOI : 10.24350/CIRM.V.18773803
    Cite this video as: Méléard, Sylvie (2015). Competitive populations with vertical and horizontal transmissions. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18773803
    URI : http://dx.doi.org/10.24350/CIRM.V.18773803


    1. Billiard, S., Ferrière, R., Méléard, S., Tran, C.V. (2014). Stochastic dynamics of adaptive trait and neutral marker driven by eco-evolutionary feedbacks. - http://arxiv.org/abs/1310.6274

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