An Approximately Unbiased Test of Phylogenetic Tree Selection

Abstract

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.

Evolution of the Relaxin/Insulin-like Gene Family in Placental Mammals: Implications for Its Early Evolution

“…Under the divergence post-WGD model we would expect genes on the same cluster to be monophyletic, whereas under the divergence pre-WGD model we would expect to find all RLN genes in one clade, and all INSL genes in another. The topology recovered in our ML and Bayesian analyses is congruent with the divergence post-WGD model, and the approximately unbiased topology test (Shimodaira 2002) was marginally significant in rejecting the divergence pre-WGD model in all cases (P = 0.0508).…”

“…3), and that the gene was secondarily lost in all Euarchontoglires other than catarrhine primates. This latter point was also supported by the approximately unbiased topology test (Shimodaira 2002), which rejected the placement of the INSL4 as sister to the catarrhine RLN1 and RLN2 clade (P \ 0.0001), but not as a sister group of the Euarchontoglires clade (P = 0.42).…”

An investigation of the co-variation in circulating levels of a large number of environmental contaminants

“…Cluster stability was assessed using multiscale, multistage bootstrapping. 16 The procedure assesses the frequency of which the observed clustering is similar in repeated resampling, with sampling fractions ranging from 0.5 to 1.4, from the original data. These observed frequencies correspond to bootstrap probability values (BP) and z-scores for the BP-values for each sampling fraction were calculated according to z ¼ F À1 (BP), where F À1 ( Á ) is the inverse of the standard normal distribution function.…”

The phylogenetic position and diversity of the enigmatic mongrel frog Nothophryne Poynton, 1963 (Amphibia, Anura)

“…Approximately Unbiased (AU) tests (Shimodaira, 2002) were used to evaluate the fit of our new and Scott's (2005) previously proposed hypothesis of the relationships of Nothophryne to the small-scale dataset. The tree with the best overall fit was our ML GTR + G tree.…”