Improved Robustness to Gene Tree Incompleteness, Estimation Errors, and Systematic Homology Errors with Weighted TREE-QMC

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 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 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 QMC framework of Snir and Rao, introducing weighted TREE-QMC. The incorporation of weighting schemes into TREE-QMC required a small increase in time complexity compared with 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 2 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. Source code for weighted TREE-QMC is available on Github: https://github.com/molloy-lab/TREE-QMC.