Fig. 2

Example of MUL-tree correction using TRACTION-MT given a reference tree. Given a singly-labeled, binary tree T on leaf set S, we wish to correct a MUL-tree \(\mathcal {R}\) using TRACTION-MT. First, we build the extension of T with respect to \(\mathcal {R}\), called “Extended T.” Second, we re-label the leaves so that \(\mathcal {R}\) and Extended T become consistent full differentiations. Now we run TRACTION on the pair, producing the singly-labeled tree shown in (d). TRACTION-MT would then relabel the leaves again (i.e., \(s_i\) is relabeled s for all species s), to produce a MUL-tree that refines \(\mathcal {R}\)