Fig. 3

Two cases where TRACTION-MT does not have good accuracy on multi-labeled gene trees. In the first case (left column), a duplication event (red circle) occurs at the root of the species tree shown in a, producing the true gene tree shown in b. If TRACTION-MT is given the estimated gene tree shown in c and the unrooted true species tree (a) as input, then TRACTION-MT will randomly refine the estimated gene tree, because it cannot add any bipartitions from the species tree. In the second case (right column), a duplication event (red circle) occurs towards the leaves of the species tree shown in d, producing the true gene tree shown in e. If TRACTION-MT is given the estimated gene tree shown in f and the unrooted true species tree (d) as input, then TRACTION-MT will add two branches as shown in blue in g, producing an incorrect gene tree. Furthermore, the addition of these two incorrect branches would imply two duplication events, one occurring at leaf d and one occurring at leaf e, in the true species tree, so that the gene tree returned by TRACTION-MT will not minimize the number of duplication events.