Another powerful general approach to phylogenetic reconstruction is analyzing quartets, which are subsets of four leaves in a tree. Quartet methods first infer a set of quartet trees and then combine them to build a tree on the full dataset [16, 23, 24]. Induced quartet trees have also been used [24–28] to combine a collection of input trees to build a so-called supertree . Quartet-based phylogeny estimation has been revived in recent years [3, 5, 30–32] because of its connections to coalescent-based analyses [33–35]. Under the MSC model, for unrooted species trees with four leaves, the most likely unrooted gene tree is identical to the species tree  (but this is not true for larger trees [34, 36]). Furthermore, the length of the internal branch in a quartet species tree (in coalescent units) defines the probabilities of the three possible gene tree quartet topologies . Some recent and statistically consistent quartet-based species tree estimation methods rely on these results. For example, ASTRAL seeks the species tree with the maximum number of quartet trees shared with input gene trees [3, 4].