Then, the supplementary distance matrix is transformed into a supplementary cross-product matrix which is in turn transformed into a factor matrix (Figure 1).
This supplementary distance matrix was transformed as described in the Methods section to obtain the coordinates of the supplementary sequences when they are projected onto the human active space.
In order to avoid excessive redundancy, we denote only one gene of a homologous cluster in brackets, which can be further assessed using either the GECO LisDB server (http://bioinfo.mikrobio.med.uni-giessen.de/geco2lisdb) or the supplementary homology matrix (Additional file 1).
The aim of our method is to identify a diagonal positive semi-definite matrix (supplementary text, Supplementary Material online) parameterizing Mahalanobis distance metric such that it maximizes the Spearman's rank correlation coefficient between the resulting distances and the phenetic distances within the reference taxonomy.
Ancestral states were reconstructed for all traits of the character matrix (supplementary table 7, Supplementary Material online) comparing the GLS, PIC, and maximum likelihood methods implemented in APE.
This method did not have the scope to reconstruct evolutionary distance but was able to group strains based on which genes were present or absent using a Jaccard distance matrix (supplementary file S3, Supplementary Material online).
We conducted a phylogenetic analysis of the final matrix (supplementary data set S2, Supplementary Material online) using RAxML through CIPRES with the following settings: -p 1648144 -x 2465477 -N 5000 -k -f a -m GTRGAMMA.
The ML phylogenetic tree of the 19 mycobacteria was estimated using information of one thousand and eleven 1 1 orthologs (364,491 amino acids; fig. 2) and our estimated MYC-GTR amino acid substitution matrix (supplementary fig. S1, Supplementary Material online).
The probability of an exchange for the given pair of clades at the current depth level R was computed using the formula p i = d i -α /C with the preset value of α, d i = D i − R, where D i is the distance between the compared clades in the fixed distance matrix (supplementary fig. S6, Supplementary Material online) and C = ∑ d i -α.
We analyzed this final matrix (supplementary data set S1, Supplementary Material online) by utilizing CIPRES resources (Miller et al. 2010) to run RAxML v. 7.6.3 (Stamatakis 2006; Stamatakis et al. 2008) with the following settings: -p 6540444 -x 18884 -N 1000 -k -f a -m GTRCAT.
