012012 TPM3u 5 Like TPM3 but unequal base freq. 010212 TPM3 2 AC=CG, AG=CT, AT=GT and equal base freq. 010212 TPM2u 5 Like TPM2 but unequal base freq. 012210 TPM2 2 AC=AT, AG=CT, CG=GT and equal base freq. 012210 K81u 5 Like K81 but unequal base freq. 010020 K81 or K3P 2 Three substitution types model and equal base freq. 010020 TNe 2 Like TN but equal base freq. 010010 TN or TN93 5 Like HKY but unequal purine/pyrimidine rates ( Tamura and Nei, 1993). 010010 HKY or HKY85 4 Unequal transition/transversion rates and unequal base freq. 000000 K80 or K2P 1 Unequal transition/transversion rates and equal base freq. 000000 F81 3 Equal rates but unequal base freq. Therefore, in that case, it is probably better to always use C50 or C60.IQ-TREE includes all common DNA models (ordered by complexity): Model df Explanation Code JC or JC69 0 Equal substitution rates and equal base frequencies ( Jukes and Cantor, 1969). Under PhyloBayes, on the other and, all models, from C20 to C60 have about the same computational efficiency. Under PhyML, the C20 model is a good compromise between efficiency and accuracy. They have been implemented in the two phylogenetic softwares PhyML and PhyloBayes. We demonstrate that these profile mixtures provide a better statistical fit than currently available empirical matrices (WAG, JTT), in particular on saturated data. In a way, we can say that they are to our previous CAT model what WAG or JTT are to the GTR model : simply, a pre-learnt version of the model, which can now be used for analysing small datasets, while explicitely accounting for site-specific effects. Here, we introduce a series of empirically determined profile mixture models, with number of components ranging from 20 to 60. To draw a parallel with standard models, we only implemented the equivalent of the GTR approach, which means that the model could be applied only on large datasets. In addition, thus far, no empirical information was stored a priori in the model concerning the shapes of the profiles. However, such profile mixture models were introduced only in a Bayesian context, and were not available in a Maximum Likelihood framework. They perform particularly well on saturated data, and for that reason, are more robust to phylogenetic artefacts due to the presence of fast evolving species in the dataset ( Lartillot et al, 2007). In several instances, we showed that such mixture models provide a better fit than standard models. And to each class is associated a probability profile over the 20 amino-acids. Through the underlying mixture, the model implicitely clusters sites according to their class of biochemical constraint (hydrophobic, polar, positively charged, etc.). Such mixture models explicitely account for the fact that distinct sites are under distinct evolutionary pressures. Over the last few years, we proposed a simple alternative to empirical rate matrices, by using mixtures of stationary probability profiles ( Lartillot and Philippe, 2004). Such pre-learnt empirical matrices are available from several sources (WAG, JTT, LG).Īn alternative approach : profile mixture models The empirical approach : the parameters of the matrix have been learnt on a separate database, based on several dozens of hundreds of single-gene alignments.Given the number of additional parameters entailed by a time-reversible 20x20 matrix, this works well only if the dataset is big enough. The GTR approach : all the parameters of the matrix are learnt directly on the dataset under investigation, along with the othe parameters of the model (topology of the tree, branch lengths, etc.).Concerning the exact values of those rates, there are two main attitudes : Biochemical realism of such matrices translates into higher rates of substitution between biochemically similar amino-acids (e.g. They are conveniently summarised in terms of a 20x20 rate-matrix, specifying the rate of substitution between each pair of amino-acids. Standard phylogenetic models used for analysing protein sequences assume that the patterns of amino-acid replacements are identical across the sequence. Introduction to Empirical Profile Mixture Models.
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