Statistics Papers

Document Type

Journal Article

Date of this Version

5-2008

Publication Source

Bulletin of Mathematical Biology

Volume

70

Issue

4

Start Page

1115

Last Page

1139

DOI

10.1007/s11538-007-9293-y

Abstract

In this paper, we apply new geometric and combinatorial methods to the study of phylogenetic mixtures. The focus of the geometric approach is to describe the geometry of phylogenetic mixture distributions for the two state random cluster model, which is a generalization of the two state symmetric (CFN) model. In particular, we show that the set of mixture distributions forms a convex polytope and we calculate its dimension; corollaries include a simple criterion for when a mixture of branch lengths on the star tree can mimic the site pattern frequency vector of a resolved quartet tree. Furthermore, by computing volumes of polytopes we can clarify how “common” non-identifiable mixtures are under the CFN model. We also present a new combinatorial result which extends any identifiability result for a specific pair of trees of size six to arbitrary pairs of trees. Next we present a positive result showing identifiability of rates-across-sites models. Finally, we answer a question raised in a previous paper concerning “mixed branch repulsion” on trees larger than quartet trees under the CFN model.

Copyright/Permission Statement

The final publication is available at Springer via http://dx.doi.org/10.1007/s11538-007-9293-y.

Keywords

phylogenetics, model identifiability, mixture model, polytope, discrete Fourier analysis

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Date Posted: 27 November 2017

This document has been peer reviewed.