Minimal Values for Reliability of Bootstrap and Jackknife Proportions, Decay Index, and Bayesian Posterior Probability

Although optimal cladograms based on real data sets are readily demonstrated to be well loaded with phylogenetic data, statistical means of evaluating dependability of details of branch arrangements have been problematic. Exact values of four measures of branch arrangement reliability nonparametric bootstrap and jackknife proportions, the Decay Index, and Bayesian posterior probabilities were obtained from artificial 4-taxon data sets predetermined to have .95 confidence limits through a separate standard: an exact binomial calculation. Minimum values required for a .95 binomial confidence interval for each of these four metrics for internode lengths of 3 through 60 steps varied between 1.00 and .88 for bootstrap and jackknife; for Decay Index between 3 and 15; and for Bayesian posterior probabilities between 1.00 and .91. Binomial analysis involved the relative support for the optimal branch arrangement and a pool of support for the two alternative arrangements obtainable through nearest neighbor interchange with a null at probability 1/3. Any imbalance between the numbers of steps for the two non-optimal branch arrangements (of the three possible arrangements) lowers these four reliability measurements without affecting the binomial confidence interval, but such low values alone do not necessarily mean high reliability. In the literature, if any of these four common branch reliability measures and the branch lengths are given, unambiguous maximum binomial confidence intervals can now be estimated for those cladogram internodes. More exact confidence levels can be ascertained by recalculation with constraint trees using nearest neighbor interchange.