Disparate parametric branch-support values from ambiguous characters

- SH-like aLRT > bootstrap for identification of ambiguous likelihood support.
- Bootstrap support when only hold 1 tree is less robust to changes in taxon sampling.
- PAUP∗ ML is most resilient to producing high support from ambiguous characters.
- Frequent discrepancies among methods that only show 1 fully resolved tree.

The greater power of parametric methods over parsimony is frequently observed in empirical phylogenetic analyses by providing greater resolution and higher branch support. This greater power is provided by several different factors, including some that are generally regarded as disadvantageous. In this study we used both empirical and (modified) simulated matrices to examine how Bayesian MCMC, maximum likelihood, and parsimony methods interpret ambiguous optimization of character states. We describe the information content in “redundant” terminals as well as a novel approach to help identify clades that cannot be unequivocally supported by synapomorphies in empirical matrices. Four of our main conclusions are as follows. First, the SH-like approximate likelihood ratio test is a more reliable indicator than the bootstrap of branches that are only ambiguously supported in likelihood analyses wherein only a single fully resolved optimal tree is presented. Second, bootstrap values generated by methods that only ever present a single fully resolved optimal tree are less robust to differences in taxon sampling than are those generated by more conservative methods. Third, PAUP∗ likelihood is more resilient to producing apparently unambiguous resolution and high support from ambiguous characters than is GARLI collapse 1 and MrBayes, which in turn are more resilient than PhyML. GARLI collapse 0, IQ-TREE, and RAxML are the least resilient bootstrapping methods examined. Fourth, frequent discrepancies with respect to resolution and/or branch support may be obtained by methods that only ever present a single fully resolved optimal tree in different contexts that are apparently unique to the specific program and/or method of quantifying branch support.