Data from: A new hierarchy of phylogenetic models consistent with heterogeneous substitution rates

When the process underlying DNA substitutions varies across evolutionary history, some standard Markov models underlying phylogenetic methods are mathematically inconsistent. The most prominent example is the general time-reversible model (GTR) together with some, but not all, of its submodels. To rectify this deficiency, nonhomogeneous Lie Markov models have been identified as the class of models that are consistent in the face of a changing process of DNA substitutions regardless of taxon sampling. Some well-known models in popular use are within this class, but are either overly simplistic (e.g., the Kimura two-parameter model) or overly complex (the general Markov model). On a diverse set of biological data sets, we test a hierarchy of Lie Markov models spanning the full range of parameter richness. Compared against the benchmark of the ever-popular GTR model, we find that as a whole the Lie Markov models perform well, with the best performing models having 8–10 parameters and the ability to recognize the distinction between purines and pyrimidines.Read Me fileJava_SourceJava source files for the likelihood analysis using Lie Markov modelsLie Markov model analysis with MathematicaVarious analyses of the Lie Markov models: Fourier-Motzkin elimination, nesting, equilibrium base frequencies, time reversibility, embeddability.LieMarkov.nbPDF of Mathematica fileMathematica file LieMarkov.nb printed out in PDF format, to provide some accessibility to those without Mathematica.LieMarkov.pdfLikelihood analysis spreadsheetSpreadsheet taking output of test.sh and calculating AIC, BIC scores, ranking models, and formatting results for inclusion in the paper.likelihoods.odsRunable Java jar file for likelihood analysisSee ReadMe.txt for details. Requires library jar file (https://github.com/MichaelWoodhams/pal-mdw/releases) to run.LMM.jarShell script to run likelihood analysisTakes multiple days to run.test.shSupplementary tables and figuresSupplementary tables and figures in support of the main paper. Includes information repackaged from likelihoods.ods and LieMarkov.nb.supplementary_material.pd