Fig. 2

Geometric view of CFs for 4-taxon network models, with dashed lines outlining the simplex \(\Delta ^2\). Each point in \(\Delta ^2\) arises as a CF under the NMSC, even when restricting to level-1 networks [26]. (L) The cut model consists of 3 blue line segments, with each formed by CFs arising from 4-networks with a specific resolved tree of blobs topology. CFs off the cut model arise only from networks with unresolved trees of blobs. (R) The T3 submodel is those cut CFs with smallest entry occurring exactly twice. Using it as the null hypothesis in the TINNiK algorithm may lead to more sets of 4 taxa initially judged as B-quartets than using the cut test