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Consistency of Topological Moves Based on the Balanced Minimum Evolution Principle of Phylogenetic Inference
January-March 2009 (vol. 6 no. 1)
pp. 110-117
Magnus Bordewich, University of Durham, Durham
Olivier Gascuel, CNRS-Université Montpellier II, Montpellier
Katharina T. Huber, University of East Anglia , Norwich
Vincent Moulton, University of East Anglia, Norwich
Many phylogenetic algorithms search the space of possible trees using topological rearrangements and some optimality criterion. FastME is such an approach that uses the {\em balanced minimum evolution (BME)} principle, which computer studies have demonstrated to have high accuracy. FastME includes two variants: {\em balanced subtree prune and regraft (BSPR)} and {\em balanced nearest neighbor interchange (BNNI)}. These algorithms take as input a distance matrix and a putative phylogenetic tree. The tree is modified using SPR or NNI operations, respectively, to reduce the BME length relative to the distance matrix, until a tree with (locally) shortest BME length is found. Following computer simulations, it has been conjectured that BSPR and BNNI are consistent, i.e. for an input distance that is a tree-metric, they converge to the corresponding tree. We prove that the BSPR algorithm is consistent. Moreover, even if the input contains small errors relative to a tree-metric, we show that the BSPR algorithm still returns the corresponding tree. Whether BNNI is consistent remains open.

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Index Terms:
phylogenetic tree, subtree prune and regraft (SPR), BSPR algorithm, Nearest Neighbor Interchange (NNI), BNNI algorithm, balanced minimum evolution principle (BME), tree-length, quartet-distance, Robinson Foulds distance, consistency, safety radius, topological move
Magnus Bordewich, Olivier Gascuel, Katharina T. Huber, Vincent Moulton, "Consistency of Topological Moves Based on the Balanced Minimum Evolution Principle of Phylogenetic Inference," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 6, no. 1, pp. 110-117, Jan.-March 2009, doi:10.1109/TCBB.2008.37
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