δ Plots: A Tool for Analyzing Phylogenetic Distance Data

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 delta 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. delta Plots and taxon rankings are applied to three biological data sets using distances derived from sequence alignment, gene order, and fragment length polymorphism.

The statistical geometry of transcriptome divergence in cell-type evolution and cancer

“…Tree structure of distance matrices has been investigated extensively in the field of statistical geometry 10,11 . If a distance matrix is to be precisely described by a tree, it should satisfy the four-point condition.…”

“…Trees are limiting cases of box graphs, that is, a tree is a box graph in which one and only one of the inner edges is of zero length. Let the inner edges of the box graph be e and f, then the measure of treeness is the so-called delta statistic, d ¼ e/f, erf, which can be calculated directly from the distances 11 . For example, the tetrad in fig.…”

How do obligate parasites evolve? A multi-gene phylogenetic analysis of downy mildews

“…As Holland et al (2002) remarked, the best-Wt maximum likelihood model needs not result in pair-wise distance estimates optimal for phylogenetic inference with neighbour-joining or other distance methods. Since most distance methods are guaranteed to infer the correct tree from completely additive distances, one could instead use the substitution model resulting in the distance matrix with the least departure from additivity to infer the tree (SwoVord et al, 1996, p. 458;Holland et al, 2002) and use the best ML model only to estimate branch lengths. Holland et al (2002) computed a "Delta Value" from each distance matrix which is minimal (0) in the optimal case.…”

“…Since most distance methods are guaranteed to infer the correct tree from completely additive distances, one could instead use the substitution model resulting in the distance matrix with the least departure from additivity to infer the tree (SwoVord et al, 1996, p. 458;Holland et al, 2002) and use the best ML model only to estimate branch lengths. Holland et al (2002) computed a "Delta Value" from each distance matrix which is minimal (0) in the optimal case. Here, we used PAUP¤ in conjunction with DeltaStats, a Python script written by B.…”

Fishing for minimum evolution trees with Neighbor-Nets

“…To simulate treelike matrices, we followed the procedure described in [15]. In particular, we evolved molecular sequences of length 1000 along a tree (with probability r of recombination set to 0), and computed a distance matrix The bar chart shows the number of distance matrices (out of 100) for which the ME score of the phylogenetic tree produced for NNet was equal (light gray), smaller (dark gray) or larger (white) than the ME score of the tree produced by FastME.…”