An Approximately Unbiased Test of Phylogenetic Tree Selection

An approximately unbiased (AU) test that uses a newly devised multiscale bootstrap technique was developed for general hypothesis testing of regions in an attempt to reduce test bias. It was applied to maximum-likelihood tree selection for obtaining the confidence set of trees. The AU test is based on the theory of Efron et al. (Proc. Natl. Acad. Sci. USA 93:13429–13434; 1996), but the new method provides higher-order accuracy yet simpler implementation. The AU test, like the Shimodaira–Hasegawa (SH) test, adjusts the selection bias overlooked in the standard use of the bootstrap probability and Kishino–Hasegawa tests. The selection bias comes from comparing many trees at the same time and often leads to overconfidence in the wrong trees. The SH test, though safe to use, may exhibit another type of bias such that it appears conservative. Here I show that the AU test is less biased than other methods in typical cases of tree selection. These points are illustrated in a simulation study as well as in the analysis of mammalian mitochondrial protein sequences. The theoretical argument provides a simple formula that covers the bootstrap probability test, the Kishino–Hasegawa test, the AU test, and the Zharkikh–Li test. A practical suggestion is provided as to which test should be used under particular circumstances.