Fig. 3

NJMerge siblinghood proposal example. In this example, NJMerge evaluates the siblinghood proposal (C, D). Because \(C \in T_i\) and \(D \in T_j\), NJMerge first updates the constraint trees \(T_i\) and \(T_j\) based on the proposed siblinghood to get \(T'_i\) and \(T'_j\). Specifically, both \(C \in T_i\) and \(D \in T_j\) are replaced by X, representing the siblinghood (C, D). The compatibility of the updated constraint trees can be tested by rooting the trees at leaf X and using the algorithm proposed in [34]. Because the updated constraint trees (\(T'_i\) and \(T'_j\)) are indeed compatible, NJMerge will accept siblinghood proposal (C, D). Importantly, when NJMerge evaluates the next siblinghood proposal, the two constraint trees will no longer be on disjoint leaf sets