Abstract not found

Abstract not found

Bayesian inference (BI) of phylogenetic relationships uses the same probabilistic models of evolution as its precursor maximum likelihood (ML), so BI has generally been assumed to share ML’s desirable statistical properties, such as largely unbiased inference of topology given an accurate model and increasingly reliable inferences as the amount of data increases. Here we show that BI, unlike ML, is biased in favor of topologies that group long branches together, even when the true model and prior distributions of evolutionary parameters over a group of phylogenies are known. Using experimental simulation studies and numerical and mathematical analyses, we show that this bias becomes more severe as more data are analyzed, causing BI to infer an incorrect tree as the maximum a posteriori phylogeny with asymptotically high support as sequence length approaches infinity. BI’s long branch attraction bias is relatively weak when the true model is simple but becomes pronounced when sequence sites evolve heterogeneously, even when this complexity is incorporated in the model. This bias—which is apparent under both controlled simulation conditions and in analyses of empirical sequence data—also makes BI less efficient and less robust to the use of an incorrect evolutionary model than ML. Surprisingly, BI’s bias is caused by one of the method’s stated advantages—that it incorporates uncertainty about branch lengths by integrating over a distribution of possible values instead of estimating them from the data, as ML does. Our findings suggest that trees inferred using BI should be interpreted with caution and that ML may be a more reliable

Phylogenetic inference for molecular data by the maximum-likelihood approach has been attacked from a theoretical point of view, because the likelihood functions take different forms for different trees, so that optimised likelihood values for different trees do not appear directly comparable (Nei, 1987). Here, a new "super-tree" perspective is introduced to refute these criticisms. A super-tree likelihood expression is constructed which is a function of all possible bipartition lengths; it reduces to the individual tree likelihood functions when bipartitions not in a given tree are set to zero. From this perspective, the problem of phylogeny inference is seen to be a classical statistical problem involving selection between composite hypotheses. In particular, the usual ML procedure is welljustified, and, moreover, the likelihood ratio between two trees does indeed indicate the posterior odds of the trees. This "literal" interpretation of the likelihood values shown by simulation to provide a more intuitive indication of tree selection accuracy than the "integrated" likelihood posterior probabilities of Rannala and Yang (1996) and bootstrap supports. Thus, the likelihood framework for phylogenetic inference for molecular

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