An Ultrafast Tool for Minimum Reticulate Networks

Improved Practical Algorithms for Rooted Subtree Prune and Regraft (rSPR) Distance and Hybridization Number

The problem of computing the rooted subtree prune and regraft (rSPR) distance of two phylogenetic trees is computationally hard and so is the problem of computing the hybridization number of two phylogenetic trees (denoted by Hybridization Number Computation [HNC]). Since they are important problems in phylogenetics, they have been studied extensively in the literature. Indeed, quite a number of exact or approximation algorithms have been designed and implemented for them. In this article, we design and implement several approximation algorithms for them and one exact algorithm for HNC. Our experimental results show that the resulting exact program is much faster (namely, more than 80 times faster for the easiest dataset used in the experiments) than the previous best and its superiority in speed becomes even more significant for more difficult instances. Moreover, the resulting approximation program's output has much better results than the previous bests; indeed, the outputs are always nearly optimal and often optimal. Of particular interest is the usage of the Monte Carlo tree search (MCTS) method in the design of our approximation algorithms. Our experimental results show that with MCTS, we can often solve HNC exactly within short time.

Faster Exact Computation of rSPR Distance via Better Approximation

Due to hybridization events in evolution, studying two different genes of a set of species may yield two related but different phylogenetic trees for the set of species. In this case, we want to measure the dissimilarity of the two trees. The rooted subtree prune and regraft (rSPR) distance of the two trees has been used for this purpose. The problem of computing the rSPR distance of two given trees has many applications but is NP-hard. Accordingly, a number of programs have been developed for solving the problem either exactly or approximately. In this paper, we develop two new programs one of which solves the problem exactly and outperforms the previous best (namely, Whidden et al.'s rSPR-v1.3.0) significantly, while the other solves the problem approximately and outputs significantly better lower and upper bounds on the rSPR distance of the two given trees than the previous best due to Schalekamp et al. Our programs can be downloaded at http://rnc.r.dendai.ac.jp/rspr.html.

Supertrees Based on the Subtree Prune-and-Regraft Distance

Supertree methods reconcile a set of phylogenetic trees into a single structure that is often interpreted as a branching history of species. A key challenge is combining conflicting evolutionary histories that are due to artifacts of phylogenetic reconstruction and phenomena such as lateral gene transfer (LGT). Many supertree approaches use optimality criteria that do not reflect underlying processes, have known biases, and may be unduly influenced by LGT. We present the first method to construct supertrees by using the subtree prune-and-regraft (SPR) distance as an optimality criterion. Although calculating the rooted SPR distance between a pair of trees is NP-hard, our new maximum agreement forest-based methods can reconcile trees with hundreds of taxa and>50 transfers in fractions of a second, which enables repeated calculations during the course of an iterative search. Our approach can accommodate trees in which uncertain relationships have been collapsed to multifurcating nodes. Using a series of benchmark datasets simulated under plausible rates of LGT, we show that SPR supertrees are more similar to correct species histories than supertrees based on parsimony or Robinson-Foulds distance criteria. We successfully constructed an SPR supertree from a phylogenomic dataset of 40,631 gene trees that covered 244 genomes representing several major bacterial phyla. Our SPR-based approach also allowed direct inference of highways of gene transfer between bacterial classes and genera. A Small number of these highways connect genera in different phyla and can highlight specific genes implicated in long-distance LGT. [Lateral gene transfer; matrix representation with parsimony; phylogenomics; prokaryotic phylogeny; Robinson-Foulds; subtree prune-and-regraft; supertrees.].

A practical approximation algorithm for solving massive instances of hybridization number for binary and nonbinary trees

BACKGROUND

Reticulate events play an important role in determining evolutionary relationships. The problem of computing the minimum number of such events to explain discordance between two phylogenetic trees is a hard computational problem. Even for binary trees, exact solvers struggle to solve instances with reticulation number larger than 40-50.

RESULTS

Here we present CycleKiller and NonbinaryCycleKiller, the first methods to produce solutions verifiably close to optimality for instances with hundreds or even thousands of reticulations.

CONCLUSIONS

Using simulations, we demonstrate that these algorithms run quickly for large and difficult instances, producing solutions that are very close to optimality. As a spin-off from our simulations we also present TerminusEst, which is the fastest exact method currently available that can handle nonbinary trees: this is used to measure the accuracy of the NonbinaryCycleKiller algorithm. All three methods are based on extensions of previous theoretical work (SIDMA 26(4):1635-1656, TCBB 10(1):18-25, SIDMA 28(1):49-66) and are publicly available. We also apply our methods to real data.

An algorithm for constructing parsimonious hybridization networks with multiple phylogenetic trees

A phylogenetic network is a model for reticulate evolution. A hybridization network is one type of phylogenetic network for a set of discordant gene trees and "displays" each gene tree. A central computational problem on hybridization networks is: given a set of gene trees, reconstruct the minimum (i.e., most parsimonious) hybridization network that displays each given gene tree. This problem is known to be NP-hard, and existing approaches for this problem are either heuristics or making simplifying assumptions (e.g., work with only two input trees or assume some topological properties). In this article, we develop an exact algorithm (called PIRNC) for inferring the minimum hybridization networks from multiple gene trees. The PIRNC algorithm does not rely on structural assumptions (e.g., the so-called galled networks). To the best of our knowledge, PIRNC is the first exact algorithm implemented for this formulation. When the number of reticulation events is relatively small (say, four or fewer), PIRNC runs reasonably efficient even for moderately large datasets. For building more complex networks, we also develop a heuristic version of PIRNC called PIRNCH. Simulation shows that PIRNCH usually produces networks with fewer reticulation events than those by an existing method. PIRNC and PIRNCH have been implemented as part of the software package called PIRN and is available online.

Cherry picking: a characterization of the temporal hybridization number for a set of phylogenies

Recently, we have shown that calculating the minimum-temporal-hybridization number for a set [Formula: see text] of rooted binary phylogenetic trees is NP-hard and have characterized this minimum number when [Formula: see text] consists of exactly two trees. In this paper, we give the first characterization of the problem for [Formula: see text] being arbitrarily large. The characterization is in terms of cherries and the existence of a particular type of sequence. Furthermore, in an online appendix to the paper, we show that this new characterization can be used to show that computing the minimum-temporal hybridization number for two trees is fixed-parameter tractable.

What does the 5S rRNA multigene family tell us about the origin of the annual Triticeae (Poaceae)?

We have investigated the complex relationships among the annual genera within the tribe Triticeae through phylogenetic analyses of the 5S rRNA multigene family. Cloned sequences were assigned to groups of orthologous sequences, called unit classes, that were subjected to several analyses including BLAST (Basic Local Alignment Search Tool) searches to assess possible ancestral relationships with perennial genera; phylogenetic analyses using parsimony (Pars), maximum likelihood (ML), and Bayesian methods; and minimum reticulation networks from the Pars, ML, and Bayesian trees. In this study, we included genera with both annual and perennial species, such as Dasypyrum, Hordeum, and Secale. BLAST pointed to Pseudoroegneria (carrier of the St genome) and possibly Thinopyrum (carrier of the J genome) as the potential next of kin. However, Thinopyrum and Pseudoroegneria have never fallen together on the individual trees with the former generally associated with Crithopsis, Aegilops, Triticum, and Dasypyrum, while the latter is usually associated with the rest of the genera within Triticeae. The "long" unit classes placed Dasypyrum breviaristatum together with Dasypyrum villosum, whereas the "short" unit classes put them far apart on the trees. None of the gene trees alone was able to summarize the complex relationships among the genera, in line with previous results in the Triticeae. However, the application of tools designed to display phylogenetic networks was able to depict the complex links among the genera based on the short and the long gene trees, including the close link between Thinopyrum and Pseudoroegneria suggested by the phylogenetic analyses. In addition, our analyses provide support for the hypothesis that at least some annual Triticeae taxa are derived from their perennial relatives.