Illustration of how the elements of the distance matrices correspond to distances between leaves on the phylogenetic trees. In matrix A, element (i, j) corresponds to a pair of neighboring genomes, whereas element (i', j') to a pair of genomes that are distantly positioned in the protein A tree, which can be reconstructed from matrix A using the standard methods, such as neighbor-joining algorithm. Likewise, elements (i, j) and (i', j') in matrix B have similar interpretation as corresponding to the respective pairs of genomes in the protein B tree. When comparing two proteins A and B by calculating the Pearson correlation coefficients between the two corresponding matrices, the elements (i, j) and (i', j') should be weighted according to their "importance" dictated by the positions in the trees. It is noted that although the two protein trees shown here have different branch lengths but the same topology, in more complicated cases the tree topologies can also be different. In this study, however, the indices of the two matrices are mapped to the same tree, the species tree. The justification and effect of using the species tree is explained in the text.