NANUQ+: A divide-and-conquer approach to network estimation.

Inference of a species network from genomic data remains a difficult problem, with recent progress mostly limited to the level-1 case. However, inference of the Tree of Blobs of a network, showing only the network's cut edges, can be performed for any network by TINNiK, suggesting a divide-and-conquer approach to network inference where the tree's multifurcations are individually resolved to give more detailed structure. Here we develop a method, ${\text{NANUQ}}^{+}$ , to quickly perform such a level-1 resolution. Viewed as part of the NANUQ pipeline for fast level-1 inference, this gives tools for both understanding when the level-1 assumption is likely to be met and for exploring all highly-supported resolutions to cycles.