Figure 9.

Ratchets based on reference tree distance. Comparison of a rooted reference tree (a) with an unrooted test tree (b) shows that five internal edges in the reference tree imply bipartitionings of taxa that are not consistent with the test tree (note that since they imply the exact same bipartition, the two edges connected to the root of the reference tree only contribute a single count), corresponding to a reference tree distance of 5. Two SPR operations that could be proposed by EEEP are indicated with dashed arrows: the resulting modified reference trees are indicated for arrow number 1 in panel (c), and for arrow number 2 in panel (d). These two trees have reference tree distances of 4 and 3 respectively from the test tree, and are therefore not treated equally if a ratchet is being used. Under a permissive ratchet, both edits would be accepted and used for subsequent SPR moves, because both yielded a decrease in the overall reference tree distance. However, under a strict ratchet, only the edit that yielded a reference tree distance of 3 would be accepted, because it yielded the largest decrease in reference tree distance.