δ Plots: A Tool for Analyzing Phylogenetic Distance Data

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Abstract
A method is described that allows the assessment of treelikeness of phylogenetic distance data before tree estimation. This method is related to statistical geometry as introduced by Eigen, Winkler-Oswatitsch, and Dress (1988 [Proc. Natl. Acad. Sci. USA. 85:5913–5917]), and in essence, displays a measure for treelikeness of quartets in terms of a histogram that we call a δ plot. This allows identification of nontreelike data and analysis of noisy data sets arising from processes such as, for example, parallel evolution, recombination, or lateral gene transfer. In addition to an overall assessment of treelikeness, individual taxa can be ranked by reference to the treelikeness of the quartets to which they belong. Removal of taxa on the basis of this ranking results in an increase in accuracy of tree estimation. Recombinant data sets are simulated, and the method is shown to be capable of identifying single recombinant taxa on the basis of distance information alone, provided the parents of the recombinant sequence are sufficiently divergent and the mixture of tree histories is not strongly skewed toward a single tree. δ Plots and taxon rankings are applied to three biological data sets using distances derived from sequence alignment, gene order, and fragment length polymorphism.