A phylogenetic network represents evolutionary relationships involving hybridization, gene flow, or admixture. While the full network may not be identifiable from genomic data under common coalescent models, its tree of blobs, depicting only the tree-like portions of the network structure, is. We introduce ECToBlob (Edge Contraction for Tree of Blobs), a new statistically-consistent algorithm to estimate the tree of blobs from quartet concordance factors. Starting from a resolved tree, ECToBlob successively contracts edges which statistical tests indicate do not belong in the tree of blobs, due to reticulate or polytomous signal. We show that ASTRAL provides a valid starting tree under common assumptions, in that, asymptotically in the number of loci, trees optimizing ASTRAL’s criterion refine the tree of blobs. We describe several algorithm variants, differing in how evidence from multiple tests are combined to determine if the edge should be contracted, and provide software implementations.
