Success of maximum likelihood phylogeny inference in the four-taxon case

We used simulated data to investigate a number of properties of maximum- likelihood (ML) phylogenetic tree estimation for the case of four taxa. Simulated data were generated under a broad range of conditions, including wide variation in branch lengths, differences in the ratio of transition and transversion substitutions, and the absence of presence of gamma-distributed site-to-site rate variation. Data were analyzed in the ML framework with two different substitution models, and we compared the ability of the two models to reconstruct the correct topology. Although both models were inconsistent for some branch-length combinations in the presence of site-to-site variation, the models were efficient predictors of topology under most simulation conditions. We also examined the performance of the likelihood ratio (LR) test for significant positive interior branch length. This test was found to be misleading under many simulation conditions, rejecting too often under some simulation conditions. Under the null hypothesis of zero length internal branch, LR statistics are assumed to be asymptotically distributed chi 2(1); with limited data, the distribution of LR statistics under the null hypothesis varies from chi 2(1).