Fig. 3.

—Correspondence of OTU splits and tested root partitions. (a) In CSC gene trees; (b) in PSC gene trees; and (c) in CMC gene trees. PMC gene trees entail both the b and c operations. OTU splits refer to branches in gene trees and are represented as black circles and white squares. Species partitions refer to possible branches in the hypothetical species tree, with unknown topology, and are represented as gray shades. In CSC gene trees, all branches (including internal and external) can be mapped to species partitions in a one-to-one manner (green arrows in a; note that only several splits are illustrated). For mapping branches from PSC gene trees (b) to species partitions, we remove from the species partitions the species missing in the gene tree and term the reduced version of the species partitions as OTU partitions. In CMC gene trees (c), only branches that form species splits can be mapped onto species partitions. A species splits in a CMC gene tree is a branch for which all gene copies of any one species are present on the same side of the split.