Estimating Uncertainty in Evolutionary Trees from Manhattan-Distance Triads

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Abstract
A simple way is needed to indicate the approximate uncertainty in phylogenetic diagrams. The reliability of reconstructed phylogenetic trees is considered with respect to sampling error. A measure of uncertainty is developed for a triad of integral Manhattan distances surrounding an inner node of a tree, using three statistical models based on the Poisson and binomial distributions. The three models give broadly similar results. The methods give very approximate estimates that indicate the order of magnitude of the standard error of the central node''s position, as well as a rough estimate of the probability that another random sample of characters would lead to a local change in tree topology. The uncertainty can be shown graphically, and illustrations are given on trees from cytochrome and myoglobin sequences, Hennigian analysis of morphology, and DNA pairing data. The sampling errors for the first three are substantial; that for DNA data is in theory very small, but experimental error is shown to have a noticeable effect. [Phylogenetic trees; Manhattan distance; sampling error; experimental error.].