Treeness triangles: visualizing the loss of phylogenetic signal.

It is well known that molecular data "saturates" with increasing sequence divergence (thereby losing phylogenetic information) and that in addition the accumulation of misleading information due to chance similarities or to systematic bias may accompany saturation as well. Exploratory data analysis methods that can quantify the extent of signal loss or convergence for a given data set are scarce. Such methods are needed because genomics delivers very long sequence alignments spanning substantial phylogenetic depth, where site saturation may be compounded by systematic biases or other alternative signals. Here we introduce the Treeness Triangle (TT) graph, in which signals detectable by Hadamard (spectral) analysis are summed into 3 categories--those supporting 1) external and 2) internal branches in the optimal tree, in addition to 3) the residuals (potential internal branches not present in the optimal tree). These 3 values are plotted in a standard ternary coordinate system. The approach is illustrated with simulated and real data sets, the latter from complete chloroplast genomes, where potential problems of paralogy or lateral gene acquisition can be excluded. The TT uncovers the divergence-dependent loss of phylogenetic signal as subsets of chloroplast genomes are investigated that span increasingly deeper evolutionary timescales. The rate of signal loss (or signal retention) varies with the gene and/or the method of analysis.