A multiple category model optimized by the mcBPPS sampler. (top) A tree representing the hierarchical relationships between functionally-divergent protein subgroups. Color code: internal nodes, blue; leaf nodes, red. Each subtree within the tree (i.e., each node and its descendents) corresponds to a set of sequences that generally conserve a pattern that sequences in the rest of the tree generally lack. For example, node 5 could represent a subfamily whose family, superfamily and class are represented by the subtrees rooted at nodes 4, 2 and 1, respectively. (middle) The corresponding functional divergence (FD-)table. A tree is converted into a FD-table, as follows: The subtree rooted at each node of the tree corresponds to the foreground (‘+’ rows) for that column in the table, whereas the rest of the subtree rooted at the parent of that node corresponds to the background (‘-‘rows). (A set of randomly-generated sequences serves as the background for the root node.) Each internal node in the tree corresponds to a miscellaneous category—that is to sequences sharing a common pattern with, but lacking patterns specific to each of its descendent subtrees. (bottom) Contrast alignment corresponding to column 4 of the table. Each subgroup corresponding to a row with a ‘+’ or a ‘-‘symbol in that column is assigned to the foreground or background, respectively; subgroups with an ‘o’ symbol are omitted from that contrast alignment.