Summary methods are widely used to reconstruct species trees from gene tres while accommodating discordance from incomplete lineage sorting; however, it is increasingly recognized that their accuracy can be negatively impacted by incomplete and/or error-ridden gene trees. To address the latter, Zhang and Mirarab (2022) updated the popular summary method ASTRAL so that it weights quartets based on gene tree branch lengths and support values. The implementation of these weighting schemes presented computational challenges, leading Zhang and Mirarab (2022) to replace ASTRAL's original algorithm (i.e., computing an exact solution within a constrained search space) in favor of search heuristics based on phylogenetic placement. Here, we show that these weighting schemes can be effectively leveraged within the Quartet Max Cut framework of Snir and Rao (2010), introducing weighted TREE-QMC. The incorporation of weighting schemes into TREE-QMC required only a small increase in time complexity compared to the unweighted algorithm; fortunately, the increase in runtime was also small, behaving more like a constant factor in our simulation study. Moreover, weighted TREE-QMC was fast and highly competitive with weighted ASTRAL, even outperforming it in terms of species tree accuracy on some challenging simulation conditions, such as large numbers of taxa. In reanalyzing two avian data sets, we found that weighting quartets by gene tree branch lengths can improve robustness to systematic homology errors and can be as effective as removing the impacted taxa from individual gene trees or removing the impacted gene trees entirely. Lastly, our study revealed that TREE-QMC was robust to extreme rates of missing taxa, suggesting its utility as a supertree method.

Funding provided by: State of MarylandROR ID: https://ror.org/04ja8je85Award Number: