Abstract
Phylogenetic inference and evaluating support for inferred relationships is at the core of many studies testing evolutionary hypotheses. Despite the popularity of nonparametric bootstrap frequencies and Bayesian posterior probabilities, the interpretation of these measures of tree branch support remains a source of discussion. Furthermore, both methods are computationally expensive and become prohibitive for large datasets. Recent fast approximate likelihood-based measures of branch supports (aLRT and SH-aLRT) provide a compelling alternative to these slower conventional methods, offering not only speed advantages but also excellent levels of accuracy and power. Here we propose an additional method: a Bayesian-like transformation of aLRT (aBayes). Considering both probabilistic and frequentist frameworks, we compare the performance of the three fast likelihood-based methods with the standard bootstrap, the Bayesian approach, and the recently introduced rapid bootstrap. Our simulations and real data analyses show that with moderate model violations all tests are sufficiently accurate, but aLRT and aBayes offer the highest statistical power and are very fast. With severe model violations aLRT, aBayes and Bayesian posteriors can produce elevated false-positive rates. With datasets for which such violation can be detected, we recommend using SH-aLRT, the non-parametric version of aLRT based on test similar to Shimodaira-Hasegawa's. In general, the standard bootstrap seems to be excessively conservative, and is much slower than our approximate likelihood-based methods.