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Generalized Markov branching trees

Published online by Cambridge University Press:  17 March 2017

Harry Crane*
Affiliation:
Rutgers University
*
* Postal address: Department of Statistics and Biostatistics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA. Email address: [email protected]

Abstract

Motivated by the gene tree/species tree problem from statistical phylogenetics, we extend the class of Markov branching trees to a parametric family of distributions on fragmentation trees that satisfies a generalized Markov branching property. The main theorems establish important statistical properties of this model, specifically necessary and sufficient conditions under which a family of trees can be constructed consistently as sample size grows. We also consider the question of attaching random edge lengths to these trees.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2017 

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