Hidetoshi Shimodaira

The maximum-likelihood method for inferring mo-lecular phylogeny (Felsenstein 1981) is being widelyused. The probabilistic model for generating the molec-ular sequences is specified by the substitution processand the tree topology. The parameters for the substitu-tion process and the branch lengths are estimated bymaximizing the likelihood, and then the tree topology isestimated by maximizing the maximized likelihood. Toobtain the confidence limit of the topology, the test ofKishino and Hasegawa (1989), referred to as the KHtest, is often used in practice. The same idea that is thebasis for the KH test is also found in the statistical lit-erature (Linhart 1988; Vuong 1989). The KH test wasdesigned for comparing two topologies but is often usedfor comparing many topologies. This use of the KH testleads to overconfidence for a wrong tree, because thesampling error due to the selection of the topology isoverlooked in it. In this note, we present a modificationof the KH test to take into account a multiplicity oftestings.Let a index the topologies and L

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.

Abstract Summary: Pvclust is an add-on package for a statistical software R to assess the uncertainty in hierarchical cluster analysis. Pvclust can be used easily for general statistical problems, such as DNA microarray analysis, to perform the bootstrap analysis of clustering, which has been popular in phylogenetic analysis. Pvclust calculates probability values (p-values) for each cluster using bootstrap resampling techniques. Two types of p-values are available: approximately unbiased (AU) p-value and bootstrap probability (BP) value. Multiscale bootstrap resampling is used for the calculation of AU p-value, which has superiority in bias over BP value calculated by the ordinary bootstrap resampling. In addition the computation time can be enormously decreased with parallel computing option. Availability: The program is freely distributed under GNU General Public License (GPL) and can directly be installed from CRAN (), the official R package archive. The instruction and program source code are available at Contact: ryota.suzuki@is.titech.ac.jp

UNLABELLED: CONSEL is a program to assess the confidence of the tree selection by giving the p-values for the trees. The main thrust of the program is to calculate the p-value of the Approximately Unbiased (AU) test using the multi-scale bootstrap technique. This p-value is less biased than the other conventional p-values such as the Bootstrap Probability (BP), the Kishino-Hasegawa (KH) test, the Shimodaira-Hasegawa (SH) test, and the Weighted Shimodaira-Hasegawa (WSH) test. CONSEL calculates all these p-values from the output of the phylogeny program packages such as Molphy, PAML, and PAUP*. Furthermore, CONSEL is applicable to a wide class of problems where the BPs are available. AVAILABILITY: The programs are written in C language. The source code for Unix and the executable binary for DOS are found at http://www.ism.ac.jp/~shimo/ CONTACT: shimo@ism.ac.jp