TREE-QMC: Improving quartet graph construction for scalable and accurate species tree estimation from gene trees

Abstract

Genome-scale data is increasingly available for species tree estimation, bringing attention to the fact that different regions of the genome can have evolutionary histories that differ from each other and from the species tree due to incomplete lineage sorting. This has led to the development of many new methods, some of which estimate the species tree from a collection of (estimated) gene trees. ASTRAL, the dominant method in this class, executes an exact algorithm for the Maximum Quartet Support Species Tree problem within a constrained solution space, constructed from the input gene trees. The other popular heuristics for this NP-hard problem, wQMC and wQFM, take a set of weighted quartets as input and construct the species tree in a divide-and-conquer fashion, for example via graph cuts. This approach has failed to compete with ASTRAL because it is less scalable when considering the time required to explicitly weight quartets based on the gene trees. Moreover, in prior studies, wQMC has been consistently less accurate than either wQFM or ASTRAL.Here, we address that the poor accuracy of wQMC by showing that the quartet graph should be normalized to account for “artificial taxa,” which are introduced during the divide phase so that solutions on subproblems can be combined during the conquer phase. This led us to design efficient techniques for uniform and non-uniform graph normalization, with the goal of the latter being improved robustness on data sets with large numbers of taxa and gene tree heterogeneity. We provide an algorithm to construct the normalized quartet graph directly from the input gene trees, enabling our new method TREE-QMC to run in O(n3k) time where n is the number of species and k is the number of gene trees (provided some assumptions on subproblem sizes). In an extensive simulation study, graph normalization enabled TREE-QMC to be competitive in terms of species tree accuracy with ASTRAL-III and FASTRAL, a recent method that runs ASTRAL-III using an aggressively constrained solution space to speedup analyses. Notably, when the number of taxa was large (> 500), TREE-QMC (with non-uniform graph normalization) produced more accurate species trees than either FASTRAL and ASTRAL-III, at speeds closer to FASTRAL. We also re-analyzed an avian data set of 3,679 ultraconserved elements, finding that the estimated trees differed only on the short branches suggestive of ILS, with the TREE-QMC tree being closer to the concatenation tree than the ASTRAL-III/FASTRAL tree. Overall, our study shows that wQMC’s divide-and-conquer framework can be competitive with the dynamic programming approach of ASTRAL.

Quartets enable statistically consistent estimation of cell lineage trees under an unbiased error and missingness model

“…This result has driven methodological development over the last decade, with some of the most popular approaches to date being based on quartets (Larget et al 2010;Mirarab et al 2014). Moreover, new and improved quartet-based methods are continually being developed (Mirarab and Warnow 2015;Zhang et al 2018;Dibaeinia et al 2021;Mahbub et al 2021;Han and Molloy 2023). Similar results exist for triplets (rooted, binary, three-leaf trees); see Degnan and Rosenberg (2006); Liu et al (2010); Islam et al (2020).…”

Quartet Fiduccia–Mattheyses revisited for larger phylogenetic studies

“… Le et al (2021) explored different variants of constrained-INC ( Zhang et al 2019 ) and found unsatisfactory gene tree accuracy and optimistic species tree quality when compared to conventional phylogenetic tree building approaches, despite the fact that just one model condition in their experiment included more than 1000 sequences. Han and Molloy (2023) have recently developed TREE-QMC, which is based on wQMC and offers a fast method for constructing the quartet graph directly from input gene trees without the need for explicitly computing the weighted quartet distributions as in the case of wQMC and wQFM.…”