Fig. 2

There are five possible tree shapes with four leaves. Three of these tree shapes (\({\mathcal {S}}_1\), \({\mathcal {S}}_2\), and \({\mathcal {S}}_3\)) have a non-trivial unrooted topology (quartet). The other two tree shapes (\({\mathcal {S}}_4\) and \({\mathcal {S}}_5\)) have a trivial unrooted topology (star). Looking at Fig. 1, tree shapes \({\mathcal {S}}_1\)–\({\mathcal {S}}_5\) are observed by sampling cells \(X_1 = \{1, 4, 10, 11\}\), \(X_2 = \{1, 7, 10, 11\}\), \(X_3 = \{1, 2, 10, 11\}\), \(X_4 = \{1, 9, 10, 11\}\), and \(X_5 = \{0, 1, 2, 3\}\), respectively