Methodology article

Topology testing of phylogenies using least squares methods

Aleksandra Czarna¹ , Rafael Sanjuán² , Fernando González-Candelas³ and Borys Wróbel^1,3

¹Department of Marine Genetics and Biotechnology, Institute of Oceanology, Polish Academy of Sciences, Powstanców Warszawy 55, PL-81712 Sopot, Poland

²Instituto de Biología Molecular y Celular de Plantas, CSIC/Universidad Politécnica de Valencia, Valencia, Spain

³Institut Cavanilles de Biodiversitat i Biologia Evolutiva, Universitat de València, Spain

author email corresponding author email

BMC Evolutionary Biology 2006, 6:105doi:10.1186/1471-2148-6-105

Published:	6 December 2006

Abstract

Background

The least squares (LS) method for constructing confidence sets of trees is closely related to LS tree building methods, in which the goodness of fit of the distances measured on the tree (patristic distances) to the observed distances between taxa is the criterion used for selecting the best topology. The generalized LS (GLS) method for topology testing is often frustrated by the computational difficulties in calculating the covariance matrix and its inverse, which in practice requires approximations. The weighted LS (WLS) allows for a more efficient albeit approximate calculation of the test statistic by ignoring the covariances between the distances.

Results

The goal of this paper is to assess the applicability of the LS approach for constructing confidence sets of trees. We show that the approximations inherent to the WLS method did not affect negatively the accuracy and reliability of the test both in the analysis of biological sequences and DNA-DNA hybridization data (for which character-based testing methods cannot be used). On the other hand, we report several problems for the GLS method, at least for the available implementation. For many data sets of biological sequences, the GLS statistic could not be calculated. For some data sets for which it could, the GLS method included all the possible trees in the confidence set despite a strong phylogenetic signal in the data. Finally, contrary to WLS, for simulated sequences GLS showed undercoverage (frequent non-inclusion of the true tree in the confidence set).

Conclusion

The WLS method provides a computationally efficient approximation to the GLS useful especially in exploratory analyses of confidence sets of trees, when assessing the phylogenetic signal in the data, and when other methods are not available.