New Mathematical Framework Enables Comparison of Phylogenetic Networks from Evolutionary Data
Researchers have independently posted two preprints introducing faster, more accurate computational algorithms — one for comparing topological structures in scientific data (MS-COOT) and one for reconstructing evolutionary networks from genomic data (NetCS). MS-COOT uses co-optimal transport on hypergraphs to compare Morse-Smale complexes, while NetCS leverages majority voting and merge sort to reconstruct hybridization events in phylogenetic networks far more efficiently than existing methods. Both works address longstanding scalability bottlenecks in their respective fields.
The first preprint, posted to arXiv, introduces MS-COOT, a method for comparing Morse-Smale complexes — topological decompositions of scalar fields used in scientific visualization. By representing these complexes as hypergraphs rather than standard graphs, MS-COOT can explicitly match regions (not just critical points) using a co-optimal transport framework, enabling detection of structural events like region splitting and merging. The method was evaluated on five datasets spanning 2D simulations, 3D meshes, and volumetric data, outperforming graph-based distances on tasks such as classification and resolution discrimination. The second preprint, posted to bioRxiv, presents NetCS, an algorithm for reconstructing level-1 phylogenetic networks — evolutionary histories that include hybridization events — once a 'tree of blobs' is known. Using only majority voting and merge sort, NetCS achieves accuracy comparable to the established NANUQ+ method while being dramatically faster, handling 200 taxa and 1,000 genes in minutes. Notably, both methods revealed that the harder unsolved problem in their domain lies upstream: for NetCS, accurate tree-of-blobs reconstruction remains the primary bottleneck, and even direct network reconstruction methods struggled with hybrid ancestry prediction.
What's missing
MS-COOT: The preprint does not report computational runtime or scalability benchmarks relative to existing graph-based methods, leaving practical efficiency unclear. NetCS: The simulations assume level-1 networks specifically; performance on higher-level networks with more complex hybridization is not assessed. Neither preprint has yet undergone peer review.
What different sources said
- arXiv stat.MLCenter
Conic Formulations of Transport Metrics for Unbalanced Measure Networks and Hypernetworks
- bioRxivCenter
Is level-1 blob reconstruction under the network multispecies coalescent easy?
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