Fig. 9. Scatter plots of 500 inferred rates versus their simulated values with a model tree with six sequences and d = 0.1 for (a) ML and (b) EB-EXP. The.

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Fig. 9. Scatter plots of 500 inferred rates versus their simulated values with a model tree with six sequences and d = 0.1 for (a) ML and (b) EB-EXP. The grey line marks the y = x line From: Comparison of Site-Specific Rate-Inference Methods for Protein Sequences: Empirical Bayesian Methods Are Superior Mol Biol Evol. 2004;21(9):1781-1791. doi:10.1093/molbev/msh194 Mol Biol Evol | Molecular Biology and Evolution vol. 21 no. 9 © Society for Molecular Biology and Evolution 2004; all rights reserved.

Fig. 8. The conservation pattern obtained for the Bcl-x<sub>L</sub>/Bak complex (PDB ID:1bxl) using (a) EB-EXP with BCL-BIG, (b) ML with BCL-BIG, (c) EB-EXP with BCL-SMALL, and (d) ML with BCL-SMALL. The Bcl-x<sub>L</sub> protein is presented as a spacefill model. Conservation scores are color-coded onto the van der Waals surface of the protein. The Bak peptide is shown as a yellow backbone model. The color-coding bar shows the coloring scheme: burgundy corresponds to maximal conservation, white corresponds to average conservation, and turquoise to maximal variability From: Comparison of Site-Specific Rate-Inference Methods for Protein Sequences: Empirical Bayesian Methods Are Superior Mol Biol Evol. 2004;21(9):1781-1791. doi:10.1093/molbev/msh194 Mol Biol Evol | Molecular Biology and Evolution vol. 21 no. 9 © Society for Molecular Biology and Evolution 2004; all rights reserved.

Fig. 7. Accuracy of predictions as a function of sequence length obtained with a model tree as in figure 2a and d = 0.1. The two inference methods are labeled as in figure 5. (a) When the branch lengths of the model tree were given to the two inference methods. (b) When the branch lengths of the model tree were optimized before the tree was given as input to the inference methods From: Comparison of Site-Specific Rate-Inference Methods for Protein Sequences: Empirical Bayesian Methods Are Superior Mol Biol Evol. 2004;21(9):1781-1791. doi:10.1093/molbev/msh194 Mol Biol Evol | Molecular Biology and Evolution vol. 21 no. 9 © Society for Molecular Biology and Evolution 2004; all rights reserved.

Fig. 6. Accuracy of predictions as functions of α Fig. 6. Accuracy of predictions as functions of α. The two inference methods are labeled as in figure 5. (a) The results obtained with a model tree as in figure 2a and d = 0.1. (b) The results obtained with a model tree as in figure 2b and d = 0.1 From: Comparison of Site-Specific Rate-Inference Methods for Protein Sequences: Empirical Bayesian Methods Are Superior Mol Biol Evol. 2004;21(9):1781-1791. doi:10.1093/molbev/msh194 Mol Biol Evol | Molecular Biology and Evolution vol. 21 no. 9 © Society for Molecular Biology and Evolution 2004; all rights reserved.

Fig. 5. Accuracy of predictions as a function of the branch lengths d Fig. 5. Accuracy of predictions as a function of the branch lengths d. The model tree used was as in figure 2a. The results obtained using EB-EXP and ML are marked with squares and circles, respectively From: Comparison of Site-Specific Rate-Inference Methods for Protein Sequences: Empirical Bayesian Methods Are Superior Mol Biol Evol. 2004;21(9):1781-1791. doi:10.1093/molbev/msh194 Mol Biol Evol | Molecular Biology and Evolution vol. 21 no. 9 © Society for Molecular Biology and Evolution 2004; all rights reserved.

Fig. 4. Accuracy of predictions as a function of the number of sequences. Accuracy was measured by using MSE. In all trees d = 0.1. (a) When the branch lengths are known prior to rate inference. (b) When the branch lengths are unknown. In this case the branch lengths of the model tree were optimized before the tree was given as input to the EB-EXP and ML inference methods. The results obtained using EB-EXP, ML, and ML-RICH are marked with squares, circles, and triangles, respectively From: Comparison of Site-Specific Rate-Inference Methods for Protein Sequences: Empirical Bayesian Methods Are Superior Mol Biol Evol. 2004;21(9):1781-1791. doi:10.1093/molbev/msh194 Mol Biol Evol | Molecular Biology and Evolution vol. 21 no. 9 © Society for Molecular Biology and Evolution 2004; all rights reserved.

Fig. 3. Accuracy of EB-EXP estimations as a function of number of categories. Accuracy was measured by using MSE. The data set number (table 1) is listed on the right-hand side of each curve. (a) Results obtained with a fixed phylogenetic tree. (b) Results obtained with trees and distributions inferred from real data sets From: Comparison of Site-Specific Rate-Inference Methods for Protein Sequences: Empirical Bayesian Methods Are Superior Mol Biol Evol. 2004;21(9):1781-1791. doi:10.1093/molbev/msh194 Mol Biol Evol | Molecular Biology and Evolution vol. 21 no. 9 © Society for Molecular Biology and Evolution 2004; all rights reserved.

Fig. 2. Illustrative unrooted model tree with (a) six sequences and (b) 18 sequences. The lengths of the internal and external branches are d and 3d, respectively From: Comparison of Site-Specific Rate-Inference Methods for Protein Sequences: Empirical Bayesian Methods Are Superior Mol Biol Evol. 2004;21(9):1781-1791. doi:10.1093/molbev/msh194 Mol Biol Evol | Molecular Biology and Evolution vol. 21 no. 9 © Society for Molecular Biology and Evolution 2004; all rights reserved.

Fig. 1. A four-taxon unrooted tree used to illustrate the likelihood calculations. The external nodes (leaves) are labelled 1 to 4; internal nodes are labelled 5 to 6. Branch lengths are marked by t<sub>i</sub>, where i is the branch identifier. Capital letters in parentheses are one-letter abbreviations for amino acids From: Comparison of Site-Specific Rate-Inference Methods for Protein Sequences: Empirical Bayesian Methods Are Superior Mol Biol Evol. 2004;21(9):1781-1791. doi:10.1093/molbev/msh194 Mol Biol Evol | Molecular Biology and Evolution vol. 21 no. 9 © Society for Molecular Biology and Evolution 2004; all rights reserved.