Combinatorics of least squares trees
- Creators
- Mihaescu, Radu
- Pachter, Lior
Abstract
A recurring theme in the least squares approach to phylogenetics has been the discovery of elegant combinatorial formulas for the least squares estimates of edge lengths. These formulas have proved useful for the development of efficient algorithms, and have also been important for understanding connections among popular phylogeny algorithms. For example, the selection criterion of the neighbor-joining algorithm is now understood in terms of the combinatorial formulas of Pauplin for estimating tree length. We highlight a phylogenetically desirable property that weighted least squares methods should satisfy, and provide a complete characterization of methods that satisfy the property. The necessary and sufficient condition is a multiplicative four point condition that the the variance matrix needs to satisfy. The proof is based on the observation that the Lagrange multipliers in the proof of the Gauss–Markov theorem are tree-additive. Our results generalize and complete previous work on ordinary least squares, balanced minimum evolution and the taxon weighted variance model. They also provide a time optimal algorithm for computation.
Additional Information
© 2008 National Academy of Sciences. Edited by Peter J. Bickel, University of California, Berkeley, CA, and approved May 21, 2008 (received for review March 3, 2007) R.M. was supported by a National Science Foundation (NSF) Graduate Fellowship and partially by the Fannie and John Hertz. Author contributions: R.M. and L.P. designed research, performed research, and wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission.Attached Files
Published - 25464022.pdf
Submitted - 0802.2395.pdf
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Additional details
- PMCID
- PMC2533170
- Eprint ID
- 74805
- Resolver ID
- CaltechAUTHORS:20170306-144249240
- NSF Graduate Research Fellowship
- Fannie and John Hertz Foundation
- Created
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2017-03-07Created from EPrint's datestamp field
- Updated
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2021-11-11Created from EPrint's last_modified field