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Systematic Biology 2006 55(4):652-661; doi:10.1080/10635150600889617
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© 2006 Society of Systematic Biologists

A Geometric Approach to Tree Shape Statistics

Frederick A. Matsen

1 Program for Evolutionary Dynamics and Department of Mathematics, Harvard University One Brattle Square, 6th Floor, Cambridge, Massachusetts, 02138, USA E-mail: matsen{at}math.harvard.edu

Edited by Mike Steel: Associate Editor


   Abstract

This article presents a new way to quantify the descriptive ability of tree shape statistics. Where before, tree shape statistics were chosen by their ability to distinguish between macroevolutionary models, the resolution presented in this paper quantifies the ability of a statistic to differentiate between similar and different trees. This is termed the geometric approach to differentiate it from the model-based approach previously explored. A distinct advantage of this perspective is that it allows evaluation of multiple tree shape statistics describing different aspects of tree shape. After developing the methodology, it is applied here to make specific recommendations for a suite of three statistics that may prove useful in applications. The article ends with an application of the statistics to clarify the impact of taxa omission on tree shape.

Keywords: Macroevolutionary models; multidimensional scaling; nearest neighbor interchange metric; phylogenetic tree shape; tree estimation bias

Received December 17, 2005; Revised February 8, 2006; Accepted March 9, 2006
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