Schematic of the iterative algorithm.

A: Construction of the naive MCCs. Circles indicate the root of the five clades that match exactly in the two trees (slightly highlighted branches). Trying to grow one of these clades gives inconsistent results in the two trees: e.g. growing the MCC (B1,B2) gives clade (A,B1,B2) in the first tree and (A,D1,D2,B1,B2) in the second. B: Trees obtained after reducing trees of A to their naive MCCs: each clade is represented by a single effective leaf. C: Counting incompatibilities in the reduced trees. For each effective leaf, the clades defined by its direct ancestor in the two trees are compared, and each mismatch counts as one incompatibility. D: Enforcing reassortments on some leaves to remove incompatibilities. A configuration is associated to each set of removed leaves. The scoring function adds the number of remaining incompatibilities given and the number of removed leaves multiplied by γ. The optimal set of reassortments is found by minimizing , e.g. removing D is optimal if γ < 5.