Continuum Tree Asymptotics of Discrete Fragmentations and Applications to Phylogenetic Models
نویسنده
چکیده
Given any regularly varying dislocation measure, we identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application, we obtain continuum random tree limits of Aldous’s beta-splitting models and Ford’s alpha models for phylogenetic trees. This confirms in a strong way that the whole trees grow at the same speed as the mean height of a randomly chosen leaf.
منابع مشابه
Continuum Tree Asymptotics of Discrete Fragmentations and Applications to Phylogenetic Models by Bénédicte Haas, Grégory Miermont, Jim Pitman
Given any regularly varying dislocation measure, we identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application, we obtain continuum random tree limits of Aldous’s beta-splitting models and Ford’s alpha models for phylogenetic trees. This confirms in a strong way that the whole trees grow at the same speed as the ...
متن کامل2 00 6 Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models ∗
Given any regularly varying dislocation measure, we identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application we obtain continuum random tree limits of Aldous’s beta-splitting models and Ford’s alpha models for phylogenetic trees. This confirms in a strong way that the whole trees grow at the same speed as the m...
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متن کاملQuantitative Comparison of Tree Pairs Resulted from Gene and Protein Phylogenetic Trees for Sulfite Reductase Flavoprotein Alpha-Component and 5S rRNA and Taxonomic Trees in Selected Bacterial Species
Introduction: FAD is the cofactor of FAD-FR protein family. Sulfite reductase flavoprotein alpha-component is one of the main enzymes of this family. Based on applications of this enzyme in biotechnology and industry, it was chosen as the subject of evolutionary studies in 19 specific species. Method: Gene and protein sequences of sulfite reductase flavoprotein alpha-component, 5S rRNA sequence...
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Abstract. We consider the fragmentation at nodes of the Lévy continuous random tree introduced in a previous paper. In this framework we compute the asymptotic for the number of small fragments at time θ. This limit is increasing in θ and discontinuous. In the α-stable case the fragmentation is self-similar with index 1/α, with α ∈ (1, 2) and the results are close to those Bertoin obtained for ...
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