One of the Grand Challenges in Science is the construction of the Tree of Life, an evolutionary tree containing several million species, spanning all life on earth. However, the construction of the Tree of Life is enormously computationally challenging, as all the current most accurate methods are either heuristics for NP-hard optimization problems or Bayesian MCMC methods that sample from tree space. One of the most promising approaches for improving scalability and accuracy for phylogeny estimation uses divide-and-conquer: a set of species is divided into overlapping subsets, trees are constructed on the subsets, and then merged together using a "supertree method". Here, we present Exact-RFS-2, the first polynomial-time algorithm to find an optimal supertree of two trees, using the Robinson-Foulds Supertree (RFS) criterion (a major approach in supertree estimation that is related to maximum likelihood supertrees), and we prove that finding the RFS of three input trees is NP-hard. We also present GreedyRFS (a greedy heuristic that operates by repeatedly using Exact-RFS-2 on pairs of trees, until all the trees are merged into a single supertree). We evaluate Exact-RFS-2 and GreedyRFS, and show that they have better accuracy than the current leading heuristic for RFS.

MOTIVATION: While each cancer is the result of an isolated evolutionary process, there are repeated patterns in tumorigenesis defined by recurrent driver mutations and their temporal ordering. Such repeated evolutionary trajectories hold the potential to improve stratification of cancer patients into subtypes with distinct survival and therapy response profiles. However, current cancer phylogeny methods infer large solution spaces of plausible evolutionary histories from the same sequencing data, obfuscating repeated evolutionary patterns. RESULTS: To simultaneously resolve ambiguities in sequencing data and identify cancer subtypes, we propose to leverage common patterns of evolution found in patient cohorts. We first formulate the Multiple Choice Consensus Tree problem, which seeks to select a tumor tree for each patient and assign patients into clusters in such a way that maximizes consistency within each cluster of patient trees. We prove that this problem is NP-hard and develop a heuristic algorithm, Revealing Evolutionary Consensus Across Patients (RECAP), to solve this problem in practice. Finally, on simulated data, we show RECAP outperforms existing methods that do not account for patient subtypes. We then use RECAP to resolve ambiguities in patient trees and find repeated evolutionary trajectories in lung and breast cancer cohorts. AVAILABILITY AND IMPLEMENTATION: https://github.com/elkebir-group/RECAP. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Gene tree correction aims to improve the accuracy of a gene tree by using computational techniques along with a reference tree (and in some cases available sequence data). It is an active area of research when dealing with gene tree heterogeneity due to duplication and loss (GDL). Here, we study the problem of gene tree correction where gene tree heterogeneity is instead due to incomplete lineage sorting (ILS, a common problem in eukaryotic phylogenetics) and horizontal gene transfer (HGT, a common problem in bacterial phylogenetics). We introduce TRACTION, a simple polynomial time method that provably finds an optimal solution to the RF-Optimal Tree Refinement and Completion Problem, which seeks a refinement and completion of an input tree t with respect to a given binary tree T so as to minimize the Robinson-Foulds (RF) distance. We present the results of an extensive simulation study evaluating TRACTION within gene tree correction pipelines on 68,000 estimated gene trees, using estimated species trees as reference trees. We explore accuracy under conditions with varying levels of gene tree heterogeneity due to ILS and HGT. We show that TRACTION matches or improves the accuracy of well-established methods from the GDL literature under conditions with HGT and ILS, and ties for best under the ILS-only conditions. Furthermore, TRACTION ties for fastest on these datasets. TRACTION is available at https://github.com/pranjalv123/TRACTION-RF and the study datasets are available at https://doi.org/10.13012/B2IDB-1747658_V1.

Here we introduce the Optimal Tree Completion Problem, a general optimization problem that involves completing an unrooted binary tree (i.e., adding missing leaves) so as to minimize its distance from a reference tree on a superset of the leaves. More formally, given a pair of unrooted binary trees (T,t) where T has leaf set S and t has leaf set R, a subset of S, we wish to add all the leaves from S \ R to t so as to produce a new tree t' on leaf set S that has the minimum distance to T. We show that when the distance is defined by the Robinson-Foulds (RF) distance, an optimal solution can be found in polynomial time. We also present OCTAL, an algorithm that solves this RF Optimal Tree Completion Problem exactly in quadratic time. We report on a simulation study where we complete estimated gene trees using a reference tree that is based on a species tree estimated from a multi-locus dataset. OCTAL produces completed gene trees that are closer to the true gene trees than an existing heuristic approach, but the accuracy of the completed gene trees computed by OCTAL depends on how topologically similar the estimated species tree is to the true gene tree. Hence, under conditions with relatively low gene tree heterogeneity, OCTAL can be used to provide highly accurate completions of estimated gene trees. We close with a discussion of future research.