BACKGROUND: The advent of next-generation and long-read sequencing technologies has provided an ever-increasing wealth of phylogenetic data that require specially designed algorithms to decipher the underlying evolutionary relationships. As large-scale data become increasingly accessible, there is a concomitant need for efficient computational libraries that facilitate the development and dissemination of specialized algorithms for phylogenetic comparative biology. RESULTS: We introduce Phylo-rs: a fast, extensible, general-purpose library for phylogenetic analysis and inference written in the Rust programming language. Phylo-rs leverages a combination of speed, memory-safety, and native WebAssembly support offered by Rust to provide a robust set of memory-efficient data structures and elementary phylogenetic algorithms. Phylo-rs focuses on the efficient and convenient deployment of software aimed at large-scale phylogenetic analysis and inference. Scalability analysis against popular libraries shows that Phylo-rs performs comparably or better on key algorithms. We utilized it to assess the phylogenetic diversity of influenza A virus in swine, identifying virus groups that are undergoing evolutionary expansion that could be targeted for control through multivalent vaccines. Additionally, we used Phylo-rs to enhance phylogenetic inference by visualizing tree space from Markov chain Monte Carlo (MCMC) Bayesian analysis, efficiently computing approximately five billion tree pair distances to evaluate convergence and select MCMC runs for genomic epidemiology. CONCLUSION: Phylo-rs enables the design and implementation of cutting-edge software for phylogenetic analysis, thereby facilitating the application and dissemination of theoretical advancements in biology. Phylo-rs is available under an open-source license on GitHub at https://github.com/sriram98v/phylo-rs , with documentation available at https://docs.rs/phylo/latest/phylo/ .

The cophenetic distance is a well-established metric in biology used to compare pairs of trees represented in a vector format. This distance was introduced by Cardona and his co-authors, building on the foundational work of Sokal and Rohlf, which dates back over 60 years. It is widely recognized for its versatility since it can analyze trees with edge weights using various vector norms. However, when comparing large-scale trees, the quadratic runtime of the current best-known (i.e., naïve) algorithm for computing the cophenetic distance can become prohibitive. Recently, a new algorithmic framework with near-linear time complexity has been developed to calculate the distances of a generalized class of cophenetic distances, which are derived from the work of Sokal and Rohlf. This improvement not only allows the cophenetic distance to be utilized in large-scale studies but also enhances the versatility of these studies by incorporating generalized variants of the cophenetic distance. However, the framework is limited to applying only the L1 and L2 vector norms, which significantly restricts the versatility of generalized cophenetic distances in large-scale applications. To address this limitation, we present a near-linear time algorithmic framework for computing the generalized cophenetic distances across all Lp vector norms. In our scalability study, we showcase the practical performance of our unrestricted algorithmic framework. Furthermore, we investigate the applicability of the generalized cophenetic distances by analyzing the distributions of key components of these distances under various vector norms.

The classic quantitative measure of phylogenetic diversity (PD) has been used to address problems in conservation biology, microbial ecology, and evolutionary biology. PD is the minimum total length of the branches in a phylogeny required to cover a specified set of taxa on the phylogeny. A general goal in the application of PD has been identifying a set of taxa of size k that maximize PD on a given phylogeny; this has been mirrored in active research to develop efficient algorithms for the problem. Other descriptive statistics, such as the minimum PD, average PD, and standard deviation of PD, can provide invaluable insight into the distribution of PD across a phylogeny (relative to a fixed value of k). However, there has been limited or no research on computing these statistics, especially when required for each clade in a phylogeny, enabling direct comparisons of PD between clades. We introduce efficient algorithms for computing PD and the associated descriptive statistics for a given phylogeny and each of its clades. In simulation studies, we demonstrate the ability of our algorithms to analyze large-scale phylogenies with applications in ecology and evolutionary biology. The software is available at https://github.com/flu-crew/PD_stats.

Diverse Natural Language Processing tasks employ constituency parsing to understand the syntactic structure of a sentence according to a phrase structure grammar. Many state-of-the-art constituency parsers are proposed, but they may provide different results for the same sentences, especially for corpora outside their training domains. This paper adopts the truth discovery idea to aggregate constituency parse trees from different parsers by estimating their reliability in the absence of ground truth. Our goal is to consistently obtain high-quality aggregated constituency parse trees. We formulate the constituency parse tree aggregation problem in two steps, structure aggregation and constituent label aggregation. Specifically, we propose the first truth discovery solution for tree structures by minimizing the weighted sum of Robinson-Foulds (RF) distances, a classic symmetric distance metric between two trees. Extensive experiments are conducted on benchmark datasets in different languages and domains. The experimental results show that our method, CPTAM, outperforms the state-of-the-art aggregation baselines. We also demonstrate that the weights estimated by CPTAM can adequately evaluate constituency parsers in the absence of ground truth.

MOTIVATION: A phylogenetic network is a powerful model to represent entangled evolutionary histories with both divergent (speciation) and convergent (e.g. hybridization, reassortment, recombination) evolution. The standard approach to inference of hybridization networks is to (i) reconstruct rooted gene trees and (ii) leverage gene tree discordance for network inference. Recently, we introduced a method called RF-Net for accurate inference of virus reassortment and hybridization networks from input gene trees in the presence of errors commonly found in phylogenetic trees. While RF-Net demonstrated the ability to accurately infer networks with up to four reticulations from erroneous input gene trees, its application was limited by the number of reticulations it could handle in a reasonable amount of time. This limitation is particularly restrictive in the inference of the evolutionary history of segmented RNA viruses such as influenza A virus (IAV), where reassortment is one of the major mechanisms shaping the evolution of these pathogens. RESULTS: Here, we expand the functionality of RF-Net that makes it significantly more applicable in practice. Crucially, we introduce a fast extension to RF-Net, called Fast-RF-Net, that can handle large numbers of reticulations without sacrificing accuracy. In addition, we develop automatic stopping criteria to select the appropriate number of reticulations heuristically and implement a feature for RF-Net to output error-corrected input gene trees. We then conduct a comprehensive study of the original method and its novel extensions and confirm their efficacy in practice using extensive simulation and empirical IAV evolutionary analyses. AVAILABILITY AND IMPLEMENTATION: RF-Net 2 is available at https://github.com/flu-crew/rf-net-2. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: The classic multispecies coalescent (MSC) model provides the means for theoretical justification of incomplete lineage sorting-aware species tree inference methods. This has motivated an extensive body of work on phylogenetic methods that are statistically consistent under MSC. One such particularly popular method is ASTRAL, a quartet-based species tree inference method. Novel studies suggest that ASTRAL also performs well when given multi-locus gene trees in simulation studies. Further, Legried et al. recently demonstrated that ASTRAL is statistically consistent under the gene duplication and loss model (GDL). GDL is prevalent in evolutionary histories and is the first core process in the powerful duplication-loss-coalescence evolutionary model (DLCoal) by Rasmussen and Kellis. RESULTS: In this work, we prove that ASTRAL is statistically consistent under the general DLCoal model. Therefore, our result supports the empirical evidence from the simulation-based studies. More broadly, we prove that the quartet-based inference approach is statistically consistent under DLCoal. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Solving median tree problems is a classic approach for inferring species trees from a collection of discordant gene trees. Median tree problems are typically NP-hard and dealt with by local search heuristics. Unfortunately, such heuristics generally lack provable correctness and precision. Algorithmic advances addressing this uncertainty have led to exact dynamic programming formulations suitable to solve a well-studied group of median tree problems for smaller phylogenetic analyses. However, these formulations allow computing only very few optimal species trees out of possibly many such trees, and phylogenetic studies often require the analysis of all optimal solutions through their consensus tree. Here, we describe a significant algorithmic modification of the dynamic programming formulations that compute the cluster counts of all optimal species trees from which various types of consensus trees can be efficiently computed. Through experimental studies, we demonstrate that our parallel implementation of the modified dynamic programming formulation is more efficient than a previous implementation of the original formulation. Finally, we show that the parallel implementation can rapidly identify novel reassorted influenza A viruses potentially facilitating pandemic preparedness efforts.

MOTIVATION: The evolution of complexity is one of the most fascinating and challenging problems in modern biology, and tracing the evolution of complex traits is an open problem. In bacteria, operons and gene blocks provide a model of tractable evolutionary complexity at the genomic level. Gene blocks are structures of co-located genes with related functions, and operons are gene blocks whose genes are co-transcribed on a single mRNA molecule. The genes in operons and gene blocks typically work together in the same system or molecular complex. Previously, we proposed a method that explains the evolution of orthologous gene blocks (orthoblocks) as a combination of a small set of events that take place in vertical evolution from common ancestors. A heuristic method was proposed to solve this problem. However, no study was done to identify the complexity of the problem. RESULTS: Here, we establish that finding the homologous gene block problem is NP-hard and APX-hard. We have developed a greedy algorithm that runs in polynomial time and guarantees an O(ln⁡n) approximation. In addition, we formalize our problem as an integer linear program problem and solve it using the PuLP package and the standard CPLEX algorithm. Our exploration of several candidate operons reveals that our new method provides more optimal results than the results from the heuristic approach, and is significantly faster. AVAILABILITY AND IMPLEMENTATION: The software and data accompanying this paper are available under the GPLv3 and CC0 license respectively on: https://github.com/nguyenngochuy91/Relevant-Operon.

Inference of phylogenetic networks - the evolutionary histories of species involving speciation as well as reticulation events - has proved to be an extremely challenging problem even for smaller datasets easily tackled by supertree inference methods. An effective way to boost the scalability of distance-based supertree methods originates from the Pareto (for clusters) property, which is a highly desirable property for phylogenetic consensus methods. In particular, one can employ strict consensus merger algorithms to boost the scalability and accuracy of supertree methods satisfying Pareto; cf. SuperFine. In this work, we establish a Pareto-like property for phylogenetic networks. Then we consider the recently introduced RF-Net method that heuristically solves the so-called RF-Network problem and which was demonstrated to be an efficient and effective tool for the inference of hybridization and reassortment networks. As our main result, we provide a constructive proof (entailing an explicit refinement algorithm) that the Pareto property applies to the RF-Network problem when the solution space is restricted to the popular class of tree-child networks. This result implies that strict consensus merger strategies, similar to SuperFine, can be directly applied to boost both accuracy and scalability of RF-Net significantly. Finally, we further investigate the optimum solutions to the RF-Network problem; in particular, we describe structural properties of all optimum (tree-child) RF-networks in relation to strict consensus clusters of the input trees.

Median tree problems are powerful tools for inferring large-scale phylogenetic trees that hold enormous promise for society at large. Such problems seek a median tree for a given collection of input trees under some problem-specific distance. Here, we introduce a median tree problem under the classic Manhattan path-difference distance. We show that this problem is NP-hard, devise an ILP formulation, and provide an effective local search heuristic that is based on solving a local search problem exactly. Our algorithm for the local search problem improves asymptotically by a factor of $n$n on the best-known (naïve) solution, where $n$n is the overall number of taxa in the input trees. Finally, comparative phylogenetic studies using considerably large empirical data and an accuracy analysis for smaller phylogenetic trees reveal the ability of our novel heuristic.

Synthesizing large-scale phylogenetic trees is a fundamental problem in evolutionary biology. Median tree problems have evolved as a powerful tool to reconstruct such trees. Such problems seek a median tree for a given collection of input trees under some problem-specific tree distance. There has been an increased interest in the median tree problem for the classical path-difference distance between trees. While this problem is NP-hard, standard local search heuristics have been described that are based on solving a local search problem exactly. For a more effective heuristic we devise a time efficient algorithm for the local search problem that improves on the best-known solution by a factor of $n$n, where $n$n is the size of the input trees. Furthermore, we introduce a novel hybrid version of the standard local search that is exploiting our new algorithm for a more refined heuristic search. Finally, we demonstrate the performance of our hybrid heuristic in a comparative study with other commonly used methods that synthesize species trees using published empirical data sets.

Median tree inference under path-difference metrics has shown great promise for large-scale phylogeny estimation. Similar to these metrics is the family of cophenetic metrics that originates from a classic dendrogram comparison method introduced more than 50 years ago. Despite the appeal of this family of metrics, the problem of computing median trees under cophenetic metrics has not been analyzed. Like other standard median tree problems relevant in practice, as we show here, this problem is also NP-hard. NP-hard median tree problems have been successfully addressed by local search heuristics that are solving thousands of instances of a corresponding (local neighborhood) search problem. For the local neighborhood search problem under a cophenetic metric, the best known (naïve) algorithm has a time complexity that is typically prohibitive for effective heuristic searches. Building on the pioneering work on path-difference median trees, we develop efficient algorithms for Manhattan and Euclidean cophenetic search problems that improve on the naïve solution by a linear and a quadratic factor, respectively. We demonstrate the performance and effectiveness of the resulting heuristic methods in a comparative study using benchmark empirical datasets.