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Bulletin of Mathematical Biology

, Volume 73, Issue 6, pp 1202–1226

First Online: 17 July 2010Received: 28 January 2010Accepted: 28 May 2010

Abstract

It is well known among phylogeneticists that adding an extra taxon e.g. species to a data set can alter the structure of the optimal phylogenetic tree in surprising ways. However, little is known about this -rogue taxon- effect. In this paper we characterize the behavior of balanced minimum evolution BME phylogenetics on data sets of this type using tools from polyhedral geometry. First we show that for any distance matrix there exist distances to a -rogue taxon- such that the BME-optimal tree for the data set with the new taxon does not contain any nontrivial splits bipartitions of the optimal tree for the original data. Second, we prove a theorem which restricts the topology of BME-optimal trees for data sets of this type, thus showing that a rogue taxon cannot have an arbitrary effect on the optimal tree. Third, we computationally construct polyhedral cones that give complete answers for BME rogue taxon behavior when our original data fits a tree on four, five, and six taxa. We use these cones to derive sufficient conditions for rogue taxon behavior for four taxa, and to understand the frequency of the rogue taxon effect via simulation.

KeywordsMinimum evolution Distance-based phylogenetic inference Linear programming Polytope Normal fan The first author was supported by a UC Berkeley Chancellor’s Fellowship. The second author was supported by the Miller Institute for Basic Research at UC Berkeley.

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Author: María Angélica Cueto - Frederick A. Matsen

Source: https://link.springer.com/article/10.1007/s11538-010-9556-x







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