Comparative performance of MEME and FEL on 16 empirical alignments (see Results and Text S1 for an extended discussion of each individual case).

<p> () reports the number of sequences (codons) in the alignment. () refers sites found by MEME to be positively (negatively) selected (). () denote sites found by FEL to be positively (negatively) selected (). references sites that are classified as neutrally evolving by FEL. Values in parentheses for the column show the mean p-values for FEL and MEME on this set of sites, respectively. Values reported in the rightmost column count the number of sites where MEME fits significantly better than FEL, based on a 2-degrees of freedom LRT (). Abbreviations: IAV = Influenza A virus, JEV = Japanese encephalitis virus.</p

Individual sites of the vertebrate rhodopsin alignment used to illustrate similarities and differences between FEL and MEME.

<p>Branches that have experienced substitutions, based on most likely joint maximum likelihood ancestral reconstructions at a given site, are labeled as count of synonymous substitutions:count of non-synonymous substitutions. The thickness of each branch is proportional to the minimal number of single nucleotide substitutions mapped to the branch. Branches are colored according to the magnitude of the empirical Bayes factor (EBF) for the event of positive selection: red – evidence for positive selection, teal – evidence for neutral evolution or negative selection, black –Ê no information. See <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1002764#s2" target="_blank">Methods</a> for more detail. All three sites were identified as experiencing positive diversifying selection by MEME. FEL reported site 54 as positively selected, site 273 as neutral, and site 210 as negatively selected.</p

Comparative performance of FEL and MEME on simulated data where varies along phylogenetic lineages.

<p>Power to detect sites under selection () are reported for FEL and MEME (in <b>boldface</b>) for each unique combination of negative selection (), positive selection (), and proportion of branches under positive selection () parameters.</p

Non-negative matrix factorization.

<p>Non-negative matrix factorization.</p

NNMF basis matrices.

<p>The set of NNMF basis matrices obtained for ranks ranging from 1 to 5. Amino acids are ordered according to their Stanfel classification <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028898#pone.0028898-Stanfel1" target="_blank">[25]</a>. Rates are indicated in grayscale, with pure white being a rate of zero and pure black being the maximum rate in the matrix.</p

scores for all models.

<p>Each table entry is the number of datasets with in that range. For any dataset, the best model has . A model with has essentially no support.</p

NNMF basis matrices correlate with amino acid properties.

<p>The correlations between amino acid properties and the basis matrices. The horizontal black line (at −0.16867) indicates the threshold for significant negative correlation (, one tailed, ).</p

Learning models of protein evolution with NNMF.

<p>A schematic overview of the procedure.</p

Interpretation of the matrix factorization in Figure 1.

<p>Interpretation of the matrix factorization in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028898#pone-0028898-g001" target="_blank">Figure 1</a>.</p

for all models with gamma rate variation (4 categories).

<p>Each table entry is the number of datasets with in that range. For any dataset, the best model has . A model with has essentially no support.</p