Computing the Distribution of a Tree Metric

Author

Bryant, David ; Steel, Mike

Author_Institution

Dept. of Math., Univ. of Auckland, Auckland, New Zealand

Volume

6

Issue

3

fYear

2009

Firstpage

420

Lastpage

426

Abstract

The Robinson-Foulds (RF) distance is by far the most widely used measure of dissimilarity between trees. Although the distribution of these distances has been investigated for 20 years, an algorithm that is explicitly polynomial time has yet to be described for computing the distribution for trees around a given tree. In this paper, we derive a polynomial-time algorithm for this distribution. We show how the distribution can be approximated by a Poisson distribution determined by the proportion of leaves that lie in ldquocherriesrdquo of the given tree. We also describe how our results can be used to derive normalization constants that are required in a recently proposed maximum likelihood approach to supertree construction.

Keywords

bioinformatics; genetics; trees (mathematics); Poisson distribution; Robinson-Foulds distance; biology; discrete mathematics application; maximum likelihood approach; normalization constant; phylogenetics; polynomial-time algorithm; supertree construction; tree dissimilarity; tree metric distribution; Biology and genetics; Poisson approximation; Robinson-Foulds distance; discrete mathematics applications; normalization constant.; phylogenetics; trees; Algorithms; Models, Genetic; Phylogeny; Poisson Distribution;

fLanguage

English

Journal_Title

Computational Biology and Bioinformatics, IEEE/ACM Transactions on

Publisher

ieee

ISSN

1545-5963

Type

jour

DOI

10.1109/TCBB.2009.32

Filename

4799772