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Data from: Quartet-based species tree methods enable fast and consistent tree of blobs reconstruction under the network multispecies coalescent

Dai, Junyan1; Han, Yunheng1; Molloy, Erin1

Published Jun 25, 2026 on Dryad. https://doi.org/10.5061/dryad.cjsxksnnp

Data files

Jun 25, 2026 version files 9.31 GB

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Abstract

Hybridization between species is an important force in evolution, commonly modeled by the network multispecies coalescent. Reconstructing evolutionary histories under this model is computationally challenging, even for level-1 networks where hybridization events are isolated. Divide-and-conquer is a promising path forward, but current methods with statistical guarantees rely on an estimated tree of blobs (TOB) for the network, which compresses the non-tree-like parts into single vertices. TOB reconstruction is itself challenging, with the only available method TINNiK having time complexity O(n5 + n4k) for k genes and n species. Here, we present a new framework for scalable TOB reconstruction with statistical guarantees. Our approach operates by (1) seeking a refinement of the TOB and then (2) contracting edges in it. For step (1), we show that any optimal solution to Weighted Quartet Consensus is a TOB refinement almost surely, as the number of genes goes to infinity, motivating the use of methods, such as ASTRAL or TREE-QMC. For step (2), we show that applying the same hypothesis tests as TINNiK to just O(n) four-taxon subsets around each edge is sufficient for statistical consistency when the underlying network is level-1. Leveraging TREE-QMC for the first step gives our method time complexity O(n3k) and its name: TOB-QMC. On simulated data, TOB-QMC typically matches or exceeds TINNiK in accuracy while being more scalable. TOB-QMC also enables fast exploration of non-tree-like evolution, as demonstrated through re-analysis of three phylogenomic data sets. Lastly, our study clarifies the theoretical utility of quartet-based species tree methods in the context of hybridization, which is critical given the recent result that ASTRAL can be misleading.