A Sharp Error Probability Estimate for the Reconstruction of Phylogenetic Quartets by the Four-Point Method

Despite the continued development of advanced algorithms for phylogeny reconstruction, the assessment of topological accuracy remains a challenging problem. New tools are needed to assist researchers in the prediction and evaluation of phylogenetic performance, particularly when short alignments are considered. We present a probabilistic analysis of quartet accuracy by the four-point method (FPM) for the Jukes-Cantor model for nucleotide substitution, developing a sharp error estimate as a function of the quartet edge lengths and the number of nucleotide positions available. Our multivariate product (MVP) estimate offers significant improvements over existing bounds and performs well even for short sequence lengths. Results demonstrate that the MVP may be employed in predicting the performance of several popular phylogeny reconstruction methods, and we illustrate a potential application of the MVP to larger datasets using a seven-taxa tree derived from a mitochondrial DNA distance matrix.