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MBE Advance Access published online on October 13, 2004
Molecular Biology and Evolution, doi:10.1093/molbev/msi010
Molecular Biology and Evolution © Society for Molecular Biology and Evolution 2004; all rights reserved
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Accepted October 4, 2004

Research Article

The MinMax Squeeze: Guaranteeing a Minimal Tree for Population Data

B.R. Holland 1*, K.T. Huber 2, D. Penny 1, and V. Moulton 2

1 Allan Wilson Centre for Molecular Ecology and Evolution, Massey University, New Zealand
2 School of Computing Sciences, University of East Anglia, Norwich, NR4 7TJ, UK

* To whom correspondence should be addressed. E-mail: B.R.Holland{at}massey.ac.nz.


  Abstract

We report that for population data, where sequences are very similar to one another, it is often possible to use a two-pronged (MinMax Squeeze) approach to prove that a tree is the shortest possible under the parsimony criterion. Such population data can be in a range where parsimony is a maximum likelihood estimator. This is in sharp contrast to the case with species data where sequences are much further apart, and the problem of guaranteeing an optimal phylogenetic tree is known to be computationally prohibitive for realistic numbers of species, irrespective of whether likelihood or parsimony is the optimality criterion. The Squeeze uses both an upper bound (the length of the shortest tree known) and a lower bound derived from partitions of the columns (the length of the shortest tree possible). If the two bounds meet the shortest known tree is thus proven to be a shortest possible tree. The implementation is first tested on simulated datasets and then applied to 53 complete human mitochondrial genomes. The shortest possible trees for that data have several significant improvements from the published tree. Namely, a pair of Australian lineages comes deeper in the tree (in agreement with archaeological data), and the non-African part of the tree shows greater agreement with the geographical distribution of lineages.

Keywords: Lower bounds; Parsimony; Phylogeny estimation; human mtDNA.
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M. J. Pierson, R. Martinez-Arias, B. R. Holland, N. J. Gemmell, M. E. Hurles, and D. Penny
Deciphering Past Human Population Movements in Oceania: Provably Optimal Trees of 127 mtDNA Genomes
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