Approximate Likelihood-Ratio Test for Branches: A Fast, Accurate, and Powerful Alternative

Abstract

We revisit statistical tests for branches of evolutionary trees reconstructed upon molecular data. A new, fast, approximate likelihood-ratio test (aLRT) for branches is presented here as a competitive alternative to nonparametric bootstrap and Bayesian estimation of branch support. The aLRT is based on the idea of the conventional LRT, with the null hypothesis corresponding to the assumption that the inferred branch has length 0. We show that the LRT statistic is asymptotically distributed as a maximum of three random variables drawn from the chi(0)2 + chi(1)2 distribution. The new aLRT of interior branch uses this distribution for significance testing, but the test statistic is approximated in a slightly conservative but practical way as 2(l1- l2), i.e., double the difference between the maximum log-likelihood values corresponding to the best tree and the second best topological arrangement around the branch of interest. Such a test is fast because the log-likelihood value l2 is computed by optimizing only over the branch of interest and the four adjacent branches, whereas other parameters are fixed at their optimal values corresponding to the best ML tree. The performance of the new test was studied on simulated 4-, 12-, and 100-taxon data sets with sequences of different lengths. The aLRT is shown to be accurate, powerful, and robust to certain violations of model assumptions. The aLRT is implemented within the algorithm used by the recent fast maximum likelihood tree estimation program PHYML (Guindon and Gascuel, 2003).

Estimating Maximum Likelihood Phylogenies with PhyML

“…PhyML v3.0 also provides users with a fast approximate likelihood ratio test (aLRT) for branches (8), which proves to be a good alternative to the (time-consuming) bootstrap analysis. The aLRT is closely related to the conventional LRT, with the null hypothesis corresponding to the assumption that the tested branch has length 0.…”

“…The rational behind the aLRT clearly differs from non-parametric bootstrap, as detailed in (8). Basically, while aLRT values are derived from testing hypotheses, the bootstrap proportion is a repeatability measure; when the bootstrap proportion of a given clade is high, we are quite confident that this clade would be inferred again if another original data sample was available and analysed by the same tree-building method (which does not mean that the clade exists in the true tree).…”

Wolbachia enhances insect‐specific flavivirus infection in Aedes aegypti mosquitoes

“…The aligned sequences were manually trimmed and then imported into Phylogeny.fr together with other common flaviviruses (Dereeper, Audic, Claverie, & Blanc, 2010; Dereeper et al., 2008). The one click mode of Phylogeny.fr that uses MUSCLE for sequence alignment and maximum likelihood (PhyML) for tree building with aLRT (approximate likelihood‐ratio test) statistical test for branch support values, and TreeDyn for tree drawing was used for the phylogeny tree (Anisimova & Gascuel, 2006; Chevenet, Brun, Banuls, Jacq, & Christen, 2006; Guindon & Gascuel, 2003). …”

First detection and molecular characterization of a DENV‐1/DENV‐4 co‐infection during an epidemic in Rio de Janeiro, Brazil

“…The reliability of the phylogenies was estimated with the approximate likelihood‐ratio (aLRT) SH‐like test12 and trees were visualized with FigTree v1.4.2 program 13. Strains representative from the other DENV‐1 and DENV‐4 genotypes available in GenBank were also used for the analysis as outgroups.…”