wQFM-TREE: highly accurate and scalable quartet-based species tree inference from gene trees.

Motivation: methods are becoming increasingly popular for species tree estimation from multi-locus data in the presence of gene tree discordance. Accurate Species TRee Algorithm (ASTRAL), a leading method in this class, solves the Maximum Quartet Support Species Tree problem within a constrained solution space, while heuristics like Weighted Quartet Fiduccia-Mattheyses (wQFM) and Weighted Quartet MaxCut (wQMC) use weighted quartets and a divide-and-conquer strategy. Recent studies showed wQFM to be more accurate than ASTRAL and wQMC, though its scalability is hindered by the computational demands of explicitly generating and weighting $\Theta \left(n^4\right)$ quartets. Here, we introduce wQFM-TREE, a novel summary method that enhances wQFM by avoiding explicit quartet generation and weighting, enabling its application to large datasets.

Results: Extensive simulations under diverse and challenging model conditions, with hundreds or thousands of taxa and genes, consistently demonstrate that wQFM-TREE matches or improves upon the accuracy of ASTRAL. It outperformed ASTRAL in 25 of 27 model conditions (statistically significant in 20) involving 200-1000 taxa. Moreover, applying wQFM-TREE to re-analyze the green plant dataset from the One Thousand Plant Transcriptomes Initiative produced a tree highly congruent with established evolutionary relationships of plants. wQFM-TREE's remarkable accuracy and scalability make it a strong competitor to leading methods. Its algorithmic and combinatorial innovations also enhance quartet-based computations, advancing phylogenetic estimation.

Availability and implementation: wQFM-TREE is freely available in open source form at https://github.com/abdur-rafi/wQFM-TREE.