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Research talks;Mathematics in Science and Technology;Probability and Statistics;Topology

A popular line of research in evolutionary biology is to use time-calibrated phylogenies in order to infer the underlying diversification process. This involves the use of stochastic models of ultrametric trees, i.e., trees whose tips lie at the same distance from the root. We recast some well-known models of ultrametric trees (infinite regular trees, exchangeable coalescents, coalescent point processes) in the framework of so-called comb metric spaces and give some applications of coalescent point processes to the phylogeny of bird species.

However, these models of diversification assume that species are exchangeable particles, and this always leads to the same (Yule) tree shape in distribution. Here, we propose a non-exchangeable, individual-based, point mutation model of diversification, where interspecific pairwise competition is only felt from the part of individuals belonging to younger species. As the initial (meta)population size grows to infinity, the properly rescaled dynamics of species lineages converge to a one-parameter family of coalescent trees interpolating between the caterpillar tree and the Kingman coalescent.

Keywords: ultrametric tree, inference, phylogenetic tree, phylogeny, birth-death process, population dynamics, evolution
A popular line of research in evolutionary biology is to use time-calibrated phylogenies in order to infer the underlying diversification process. This involves the use of stochastic models of ultrametric trees, i.e., trees whose tips lie at the same distance from the root. We recast some well-known models of ultrametric trees (infinite regular trees, exchangeable coalescents, coalescent point processes) in the framework of so-called comb metric ...

60J80 ; 60J85 ; 92D15 ; 92D25 ; 54E45 ; 54E70

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- ix; 105 p.
ISBN 978-0-8218-5248-4

Memoirs of the american mathematical society , 1003

Localisation : Collection 1er étage

matrices infinie # transformation # méthodes itératives

28A12 ; 34B45 ; 42C05 ; 42A82 ; 46E22 ; 47L30 ; 47l60 ; 47C10 ; 47S50 ; 54E70 ; 60J10 ; 60J20 ; 78M05 ; 81S30 ; 81Q15 ; 81T75 ; 82B44 ; 90B15

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Wiley series in probability and mathematical statistics

Localisation : Ouvrage RdC (BILL)

convergence faible # distribution # espace C # espace D # espace métrique # fonction de distribution empirique # mouvement brouwien # processus de la diffusion # représentati on de convergence faible # théorème de Prohorov # variable aléatoire # variable dépendant

54E70 ; 60B10 ; 60Hxx

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