Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models

Abstract

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.

Published in at http://dx.doi.org/10.1214/07-AOP377 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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Cited by in corpus (5)

• Spinal partitions and invariance under re-rooting of continuum random trees
• Gibbs fragmentation trees
• Distributions of linear functionals of two parameter Poisson--Dirichlet random measures
• Regenerative tree growth: Binary self-similar continuum random trees and Poisson--Dirichlet compositions
• Random tree growth by vertex splitting