| Type de publication : |
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Articles dans des revues avec comité de lecture |
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| Domaine : |
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Mathématiques/Probabilités
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| Titre : |
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Nonlinear historical superprocess approximations for population models with past dependence |
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| Auteur(s) : |
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Sylvie Méléard ( ) 1, Viet Chi Tran ( ) 1, 2 |
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| Laboratoire : |
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| Résumé : |
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We are interested in the evolving genealogy of a birth and death process with trait structure and ecological interactions. Traits are hereditarily transmitted from a parent to its offspring unless a mutation occurs. The dynamics may depend on the trait of the ancestors and on its past and allows interactions between individuals through their lineages. We define an interacting historical particle process describing the genealogies of the living individuals; it takes values in the space of point measures on an infinite dimensional càdlàg path space. This individual-based process can be approximated by a nonlinear historical superprocess, under the assumptions of large populations, small individuals and allometric demographies. Because of the interactions, the branching property fails and we use martingale problems and fine couplings between our population and independent branching particles. Our convergence theorem is illustrated by two examples of current interest in biology. The first one relates the biodiversity history of a population and its phylogeny, while the second treats a spatial model with competition between individuals through their past trajectories. |
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Langue du texte
intégral : |
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Anglais |
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Date de production,
écriture : |
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09/07/2011 |
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| Journal : |
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| Audience : |
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internationale |
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| Date de publication : |
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19/06/2012 |
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Date de publication
électronique : |
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19/06/2012 |
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| Volume : |
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17 |
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| Numéro : |
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47 |
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| Page, identifiant, ... : |
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1-32 |
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| Mots Clés : |
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Nonlinear historical superprocess – Genealogical interacting particle system – Limit theorem – Evolution models |
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| Classification : |
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60J80, 60J68, 60K35 |
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| Commentaire : |
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31 pages |
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| Contrat, financement : |
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Chaire Modélisation Mathématique et Biodiversité (Veolia Environnement-Ecole Polytechnique-Museum National d'Histoire Naturelle-Fondation X) |
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| Projet ANR : |
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| Référence du projet |
ANR MANEGE (ANR-09-BLAN-0215) |
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