Empirical Problems of the Hierarchical Likelihood Ratio Test for Model Selection

Advocates of maximum likelihood (ML) approaches to phylogenetics commonly cite as one of their primary advantages the use of objective statistical criteria for model selection. Currently, a particular implementation of the likelihood ratio test (LRT) is the most commonly used model-selection criterion in phylogenetics. This approach requires the choice of a starting point and a parameter addition (or removal) sequence that can affect all ML inferences (i.e., topology, model, and all evolutionary parameters). Here, several alternative starting points and parameter sequences are tested in empirical data sets to assess their influence on model selection and optimal topology. In the studied data sets, varying model-selection protocols leads to selection of different models that, in some cases, lead to different ML trees. Given the sensitivity of the LRT, some possible solutions to model selection (within the hypothesis testing approach) are outlined, and alternative model-selection criteria are discussed. Some of the suggested alternatives seem to lack these problems, although their behavior and adequacy for phylogenetics needs to be further explored.