1,129 research outputs found

    Maximal clades in random binary search trees

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    We study maximal clades in random phylogenetic trees with the Yule-Harding model or, equivalently, in binary search trees. We use probabilistic methods to reprove and extend earlier results on moment asymptotics and asymptotic normality. In particular, we give an explanation of the curious phenomenon observed by Drmota, Fuchs and Lee (2014) that asymptotic normality holds, but one should normalize using half the variance.Comment: 25 page

    Fringe trees, Crump-Mode-Jagers branching processes and mm-ary search trees

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    This survey studies asymptotics of random fringe trees and extended fringe trees in random trees that can be constructed as family trees of a Crump-Mode-Jagers branching process, stopped at a suitable time. This includes random recursive trees, preferential attachment trees, fragmentation trees, binary search trees and (more generally) mm-ary search trees, as well as some other classes of random trees. We begin with general results, mainly due to Aldous (1991) and Jagers and Nerman (1984). The general results are applied to fringe trees and extended fringe trees for several particular types of random trees, where the theory is developed in detail. In particular, we consider fringe trees of mm-ary search trees in detail; this seems to be new. Various applications are given, including degree distribution, protected nodes and maximal clades for various types of random trees. Again, we emphasise results for mm-ary search trees, and give for example new results on protected nodes in mm-ary search trees. A separate section surveys results on height, saturation level, typical depth and total path length, due to Devroye (1986), Biggins (1995, 1997) and others. This survey contains well-known basic results together with some additional general results as well as many new examples and applications for various classes of random trees

    Tropical Geometry of Phylogenetic Tree Space: A Statistical Perspective

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    Phylogenetic trees are the fundamental mathematical representation of evolutionary processes in biology. As data objects, they are characterized by the challenges associated with "big data," as well as the complication that their discrete geometric structure results in a non-Euclidean phylogenetic tree space, which poses computational and statistical limitations. We propose and study a novel framework to study sets of phylogenetic trees based on tropical geometry. In particular, we focus on characterizing our framework for statistical analyses of evolutionary biological processes represented by phylogenetic trees. Our setting exhibits analytic, geometric, and topological properties that are desirable for theoretical studies in probability and statistics, as well as increased computational efficiency over the current state-of-the-art. We demonstrate our approach on seasonal influenza data.Comment: 28 pages, 5 figures, 1 tabl

    Circumstances in which parsimony but not compatibility will be provably misleading

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    Phylogenetic methods typically rely on an appropriate model of how data evolved in order to infer an accurate phylogenetic tree. For molecular data, standard statistical methods have provided an effective strategy for extracting phylogenetic information from aligned sequence data when each site (character) is subject to a common process. However, for other types of data (e.g. morphological data), characters can be too ambiguous, homoplastic or saturated to develop models that are effective at capturing the underlying process of change. To address this, we examine the properties of a classic but neglected method for inferring splits in an underlying tree, namely, maximum compatibility. By adopting a simple and extreme model in which each character either fits perfectly on some tree, or is entirely random (but it is not known which class any character belongs to) we are able to derive exact and explicit formulae regarding the performance of maximum compatibility. We show that this method is able to identify a set of non-trivial homoplasy-free characters, when the number nn of taxa is large, even when the number of random characters is large. By contrast, we show that a method that makes more uniform use of all the data --- maximum parsimony --- can provably estimate trees in which {\em none} of the original homoplasy-free characters support splits.Comment: 37 pages, 2 figure

    Edit distance metrics for measuring dissimilarity between labeled gene trees

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    Les arbres phylogénétiques sont des instruments de biologie évolutive offrant de formidables moyens d'étude pour la génomique comparative. Ils fournissent des moyens de représenter des mécanismes permettant de modéliser les relations de parenté entre les espèces ou les membres de familles de gènes en fonction de la diversité taxonomique, ainsi que des observations et des renseignements sur l'histoire évolutive, la structure et la variation des processus biologiques. Cependant, les méthodes traditionnelles d'inférence phylogénétique ont la réputation d'être sensibles aux erreurs. Il est donc indispensable de comparer les arbres phylogénétiques et de les analyser pour obtenir la meilleure interprétation des données biologiques qu'ils peuvent fournir. Nous commençons par aborder les travaux connexes existants pour déduire, comparer et analyser les arbres phylogénétiques, en évaluant leurs bonnes caractéristiques ainsi que leurs défauts, et discuter des pistes d'améliorations futures. La deuxième partie de cette thèse se concentre sur le développement de mesures efficaces et précises pour analyser et comparer des paires d'arbres génétiques avec des nœuds internes étiquetés. Nous montrons que notre extension de la métrique bien connue de Robinson-Foulds donne lieu à une bonne métrique pour la comparaison d'arbres génétiques étiquetés sous divers modèles évolutifs, et qui peuvent impliquer divers événements évolutifs.Phylogenetic trees are instruments of evolutionary biology offering great insight for comparative genomics. They provide mechanisms to model the kinship relations between species or members of gene families as a function of taxonomic diversity. They also provide evidence and insights into the evolutionary history, structure, and variation of biological processes. However, traditional phylogenetic inference methods have the reputation to be prone to errors. Therefore, comparing and analysing phylogenetic trees is indispensable for obtaining the best interpretation of the biological information they can provide. We start by assessing existing related work to infer, compare, and analyse phylogenetic trees, evaluating their advantageous traits and flaws, and discussing avenues for future improvements. The second part of this thesis focuses on the development of efficient and accurate metrics to analyse and compare pairs of gene trees with labeled internal nodes. We show that our attempt in extending the popular Robinson-Foulds metric is useful for the preliminary analysis and comparison of labeled gene trees under various evolutionary models that may involve various evolutionary events

    Optimal Completion and Comparison of Incomplete Phylogenetic Trees Under Robinson-Foulds Distance

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    Efficient inference of bacterial strain trees from genome-scale multilocus data

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    Motivation: In bacterial evolution, inferring a strain tree, which is the evolutionary history of different strains of the same bacterium, plays a major role in analyzing and understanding the evolution of strongly isolated populations, population divergence and various evolutionary events, such as horizontal gene transfer and homologous recombination. Inferring a strain tree from multilocus data of these strains is exceptionally hard since, at this scale of evolution, processes such as homologous recombination result in a very high degree of gene tree incongruence
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