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Gene trees can be different from the species tree due to biological processes and inference errors. One way to obtain a species tree is to find one that maximizes some measure of similarity to a set of gene trees. The number of shared quartets between a potential species tree and gene trees provides a statistically justifiable score; if maximized properly, it could result in a statistically consistent estimator of the species tree under several statistical models of discordance. However, finding the median quartet score tree, one that maximizes this score, is NP-Hard, motivating several existing heuristic algorithms. These heuristics do not follow the hill-climbing paradigm used extensively in phylogenetics. In this paper, we make theoretical contributions that enable an efficient hill-climbing approach. Specifically, we show that a subtree of size m can be placed optimally on a tree of size n in quasi-linear time with respect to n and (almost) independently of m. This result enables us to perform subtree prune and regraft (SPR) rearrangements as part of a hill-climbing search. We show that this approach can slightly improve upon the results of widely-used methods such as ASTRAL in terms of the optimization score but not necessarily accuracy., (© 2024. The Author(s).)

Background: To account for genome-wide discordance among gene trees, several widely-used methods seek to find a species tree with the minimum distance to input gene trees. To efficiently explore the large space of species trees, some of these methods, including ASTRAL, use dynamic programming (DP). The DP paradigm can restrict the search space, and thus, ASTRAL and similar methods use heuristic methods to define a restricted search space. However, arbitrary constraints provided by the user on the output tree cannot be trivially incorporated into such restrictions. The ability to infer trees that honor user-defined constraints is needed for many phylogenetic analyses, but no solution currently exists for constraining the output of ASTRAL., Results: We introduce methods that enable the ASTRAL dynamic programming to infer constrained trees in an effective and scalable manner. To do so, we adopt a recently developed tree completion algorithm and extend it to allow multifurcating input and output trees. In simulation studies, we show that the approach for honoring constraints is both effective and fast. On real data, we show that constrained searches can help interrogate branches not recovered in the optimal ASTRAL tree to reveal support for alternative hypotheses., Conclusions: The new algorithm is added ASTRAL to all user-provided constraints on the species tree.

Background: Sequence data used in reconstructing phylogenetic trees may include various sources of error. Typically errors are detected at the sequence level, but when missed, the erroneous sequences often appear as unexpectedly long branches in the inferred phylogeny., Results: We propose an automatic method to detect such errors. We build a phylogeny including all the data then detect sequences that artificially inflate the tree diameter. We formulate an optimization problem, called the k-shrink problem, that seeks to find k leaves that could be removed to maximally reduce the tree diameter. We present an algorithm to find the exact solution for this problem in polynomial time. We then use several statistical tests to find outlier species that have an unexpectedly high impact on the tree diameter. These tests can use a single tree or a set of related gene trees and can also adjust to species-specific patterns of branch length. The resulting method is called TreeShrink. We test our method on six phylogenomic biological datasets and an HIV dataset and show that the method successfully detects and removes long branches. TreeShrink removes sequences more conservatively than rogue taxon removal and often reduces gene tree discordance more than rogue taxon removal once the amount of filtering is controlled., Conclusions: TreeShrink is an effective method for detecting sequences that lead to unrealistically long branch lengths in phylogenetic trees. The tool is publicly available at https://github.com/uym2/TreeShrink .

Background: Evolutionary histories can be discordant across the genome, and such discordances need to be considered in reconstructing the species phylogeny. ASTRAL is one of the leading methods for inferring species trees from gene trees while accounting for gene tree discordance. ASTRAL uses dynamic programming to search for the tree that shares the maximum number of quartet topologies with input gene trees, restricting itself to a predefined set of bipartitions., Results: We introduce ASTRAL-III, which substantially improves the running time of ASTRAL-II and guarantees polynomial running time as a function of both the number of species (n) and the number of genes (k). ASTRAL-III limits the bipartition constraint set (X) to grow at most linearly with n and k. Moreover, it handles polytomies more efficiently than ASTRAL-II, exploits similarities between gene trees better, and uses several techniques to avoid searching parts of the search space that are mathematically guaranteed not to include the optimal tree. The asymptotic running time of ASTRAL-III in the presence of polytomies is [Formula: see text] where D=O(nk) is the sum of degrees of all unique nodes in input trees. The running time improvements enable us to test whether contracting low support branches in gene trees improves the accuracy by reducing noise. In extensive simulations, we show that removing branches with very low support (e.g., below 10%) improves accuracy while overly aggressive filtering is harmful. We observe on a biological avian phylogenomic dataset of 14K genes that contracting low support branches greatly improve results., Conclusions: ASTRAL-III is a faster version of the ASTRAL method for phylogenetic reconstruction and can scale up to 10,000 species. With ASTRAL-III, low support branches can be removed, resulting in improved accuracy.

Background: Inferring species trees from gene trees using the coalescent-based summary methods has been the subject of much attention, yet new scalable and accurate methods are needed., Results: We introduce DISTIQUE, a new statistically consistent summary method for inferring species trees from gene trees under the coalescent model. We generalize our results to arbitrary phylogenetic inference problems; we show that two arbitrarily chosen leaves, called anchors, can be used to estimate relative distances between all other pairs of leaves by inferring relevant quartet trees. This results in a family of distance-based tree inference methods, with running times ranging between quadratic to quartic in the number of leaves., Conclusions: We show in simulated studies that DISTIQUE has comparable accuracy to leading coalescent-based summary methods and reduced running times.

Background: Given a new biological sequence, detecting membership in a known family is a basic step in many bioinformatics analyses, with applications to protein structure and function prediction and metagenomic taxon identification and abundance profiling, among others. Yet family identification of sequences that are distantly related to sequences in public databases or that are fragmentary remains one of the more difficult analytical problems in bioinformatics., Results: We present a new technique for family identification called HIPPI (Hierarchical Profile Hidden Markov Models for Protein family Identification). HIPPI uses a novel technique to represent a multiple sequence alignment for a given protein family or superfamily by an ensemble of profile hidden Markov models computed using HMMER. An evaluation of HIPPI on the Pfam database shows that HIPPI has better overall precision and recall than blastp, HMMER, and pipelines based on HHsearch, and maintains good accuracy even for fragmentary query sequences and for protein families with low average pairwise sequence identity, both conditions where other methods degrade in accuracy., Conclusion: HIPPI provides accurate protein family identification and is robust to difficult model conditions. Our results, combined with observations from previous studies, show that ensembles of profile Hidden Markov models can better represent multiple sequence alignments than a single profile Hidden Markov model, and thus can improve downstream analyses for various bioinformatic tasks. Further research is needed to determine the best practices for building the ensemble of profile Hidden Markov models. HIPPI is available on GitHub at https://github.com/smirarab/sepp .

Background: Species tree estimation is challenged by gene tree heterogeneity resulting from biological processes such as duplication and loss, hybridization, incomplete lineage sorting (ILS), and horizontal gene transfer (HGT). Mathematical theory about reconstructing species trees in the presence of HGT alone or ILS alone suggests that quartet-based species tree methods (known to be statistically consistent under ILS, or under bounded amounts of HGT) might be effective techniques for estimating species trees when both HGT and ILS are present., Results: We evaluated several publicly available coalescent-based methods and concatenation under maximum likelihood on simulated datasets with moderate ILS and varying levels of HGT. Our study shows that two quartet-based species tree estimation methods (ASTRAL-2 and weighted Quartets MaxCut) are both highly accurate, even on datasets with high rates of HGT. In contrast, although NJst and concatenation using maximum likelihood are highly accurate under low HGT, they are less robust to high HGT rates., Conclusion: Our study shows that quartet-based species-tree estimation methods can be highly accurate under the presence of both HGT and ILS. The study suggests the possibility that some quartet-based methods might be statistically consistent under phylogenomic models of gene tree heterogeneity with both HGT and ILS.

Background: Species tree estimation is challenging in the presence of incomplete lineage sorting (ILS), which can make gene trees different from the species tree. Because ILS is expected to occur and the standard concatenation approach can return incorrect trees with high support in the presence of ILS, "coalescent-based" summary methods (which first estimate gene trees and then combine gene trees into a species tree) have been developed that have theoretical guarantees of robustness to arbitrarily high amounts of ILS. Some studies have suggested that summary methods should only be used on "c-genes" (i.e., recombination-free loci) that can be extremely short (sometimes fewer than 100 sites). However, gene trees estimated on short alignments can have high estimation error, and summary methods tend to have high error on short c-genes. To address this problem, Chifman and Kubatko introduced SVDquartets, a new coalescent-based method. SVDquartets takes multi-locus unlinked single-site data, infers the quartet trees for all subsets of four species, and then combines the set of quartet trees into a species tree using a quartet amalgamation heuristic. Yet, the relative accuracy of SVDquartets to leading coalescent-based methods has not been assessed., Results: We compared SVDquartets to two leading coalescent-based methods (ASTRAL-2 and NJst), and to concatenation using maximum likelihood. We used a collection of simulated datasets, varying ILS levels, numbers of taxa, and number of sites per locus. Although SVDquartets was sometimes more accurate than ASTRAL-2 and NJst, most often the best results were obtained using ASTRAL-2, even on the shortest gene sequence alignments we explored (with only 10 sites per locus). Finally, concatenation was the most accurate of all methods under low ILS conditions., Conclusions: ASTRAL-2 generally had the best accuracy under higher ILS conditions, and concatenation had the best accuracy under the lowest ILS conditions. However, SVDquartets was competitive with the best methods under conditions with low ILS and small numbers of sites per locus. The good performance under many conditions of ASTRAL-2 in comparison to SVDquartets is surprising given the known vulnerability of ASTRAL-2 and similar methods to short gene sequences.

Background: Species tree estimation can be challenging in the presence of gene tree conflict due to incomplete lineage sorting (ILS), which can occur when the time between speciation events is short relative to the population size. Of the many methods that have been developed to estimate species trees in the presence of ILS, *BEAST, a Bayesian method that co-estimates the species tree and gene trees given sequence alignments on multiple loci, has generally been shown to have the best accuracy. However, *BEAST is extremely computationally intensive so that it cannot be used with large numbers of loci; hence, *BEAST is not suitable for genome-scale analyses., Results: We present BBCA (boosted binned coalescent-based analysis), a method that can be used with *BEAST (and other such co-estimation methods) to improve scalability. BBCA partitions the loci randomly into subsets, uses *BEAST on each subset to co-estimate the gene trees and species tree for the subset, and then combines the newly estimated gene trees together using MP-EST, a popular coalescent-based summary method. We compare time-restricted versions of BBCA and *BEAST on simulated datasets, and show that BBCA is at least as accurate as *BEAST, and achieves better convergence rates for large numbers of loci., Conclusions: Phylogenomic analysis using *BEAST is currently limited to datasets with a small number of loci, and analyses with even just 100 loci can be computationally challenging. BBCA uses a very simple divide-and-conquer approach that makes it possible to use *BEAST on datasets containing hundreds of loci. This study shows that BBCA provides excellent accuracy and is highly scalable.

Background: Scientists rarely reuse expert knowledge of phylogeny, in spite of years of effort to assemble a great "Tree of Life" (ToL). A notable exception involves the use of Phylomatic, which provides tools to generate custom phylogenies from a large, pre-computed, expert phylogeny of plant taxa. This suggests great potential for a more generalized system that, starting with a query consisting of a list of any known species, would rectify non-standard names, identify expert phylogenies containing the implicated taxa, prune away unneeded parts, and supply branch lengths and annotations, resulting in a custom phylogeny suited to the user's needs. Such a system could become a sustainable community resource if implemented as a distributed system of loosely coupled parts that interact through clearly defined interfaces., Results: With the aim of building such a "phylotastic" system, the NESCent Hackathons, Interoperability, Phylogenies (HIP) working group recruited 2 dozen scientist-programmers to a weeklong programming hackathon in June 2012. During the hackathon (and a three-month follow-up period), 5 teams produced designs, implementations, documentation, presentations, and tests including: (1) a generalized scheme for integrating components; (2) proof-of-concept pruners and controllers; (3) a meta-API for taxonomic name resolution services; (4) a system for storing, finding, and retrieving phylogenies using semantic web technologies for data exchange, storage, and querying; (5) an innovative new service, DateLife.org, which synthesizes pre-computed, time-calibrated phylogenies to assign ages to nodes; and (6) demonstration projects. These outcomes are accessible via a public code repository (GitHub.com), a website (http://www.phylotastic.org), and a server image., Conclusions: Approximately 9 person-months of effort (centered on a software development hackathon) resulted in the design and implementation of proof-of-concept software for 4 core phylotastic components, 3 controllers, and 3 end-user demonstration tools. While these products have substantial limitations, they suggest considerable potential for a distributed system that makes phylogenetic knowledge readily accessible in computable form. Widespread use of phylotastic systems will create an electronic marketplace for sharing phylogenetic knowledge that will spur innovation in other areas of the ToL enterprise, such as annotation of sources and methods and third-party methods of quality assessment.

Background: Supertree methods combine trees on subsets of the full taxon set together to produce a tree on the entire set of taxa. Of the many supertree methods, the most popular is MRP (Matrix Representation with Parsimony), a method that operates by first encoding the input set of source trees by a large matrix (the "MRP matrix") over {0,1, ?}, and then running maximum parsimony heuristics on the MRP matrix. Experimental studies evaluating MRP in comparison to other supertree methods have established that for large datasets, MRP generally produces trees of equal or greater accuracy than other methods, and can run on larger datasets. A recent development in supertree methods is SuperFine+MRP, a method that combines MRP with a divide-and-conquer approach, and produces more accurate trees in less time than MRP. In this paper we consider a new approach for supertree estimation, called MRL (Matrix Representation with Likelihood). MRL begins with the same MRP matrix, but then analyzes the MRP matrix using heuristics (such as RAxML) for 2-state Maximum Likelihood., Results: We compared MRP and SuperFine+MRP with MRL and SuperFine+MRL on simulated and biological datasets. We examined the MRP and MRL scores of each method on a wide range of datasets, as well as the resulting topological accuracy of the trees. Our experimental results show that MRL, coupled with a very good ML heuristic such as RAxML, produced more accurate trees than MRP, and MRL scores were more strongly correlated with topological accuracy than MRP scores., Conclusions: SuperFine+MRP, when based upon a good MP heuristic, such as TNT, produces among the best scores for both MRP and MRL, and is generally faster and more topologically accurate than other supertree methods we tested.