Balanced Minimum Evolution Research Articles

PHYLOES an evolution strategy approach phylogenetic inference based on the balanced minimum evolution criterion

PHYLOES an evolution strategy approach phylogenetic inference based on the balanced minimum evolution criterion

PhyloBench: A Benchmark for Evaluating Phylogenetic Programs.

Phylogenetic inference based on protein sequence alignment is a widely used procedure. Numerous phylogenetic algorithms have been developed, most of which have many parameters and options. Choosing a program, options, and parameters can be a nontrivial task. No benchmark for comparison of phylogenetic programs on real protein sequences was publicly available. We have developed PhyloBench, a benchmark for evaluating the quality of phylogenetic inference, and used it to test a number of popular phylogenetic programs. PhyloBench is based on natural, not simulated, protein sequences of orthologous evolutionary domains. The measure of accuracy of an inferred tree is its distance to the corresponding species tree. A number of tree-to-tree distance measures were tested. The most reliable results were obtained using the Robinson-Foulds distance. Our results confirmed recent findings that distance methods are more accurate than maximum likelihood (ML) and maximum parsimony. We tested the bayesian program MrBayes on natural protein sequences and found that, on our datasets, it performs better than ML, but worse than distance methods. Of the methods we tested, the Balanced Minimum Evolution method implemented in FastME yielded the best results on our material. Alignments and reference species trees are available at https://mouse.belozersky.msu.ru/tools/phylobench/ together with a web-interface that allows for a semi-automatic comparison of a user's method with a number of popular programs.

An evolution strategy approach for the balanced minimum evolution problem.

The Balanced Minimum Evolution (BME) is a powerful distance based phylogenetic estimation model introduced by Desper and Gascuel and nowadays implemented in popular tools for phylogenetic analyses. It was proven to be computationally less demanding than more sophisticated estimation methods, e.g. maximum likelihood or Bayesian inference while preserving the statistical consistency and the ability to run with almost any kind of data for which a dissimilarity measure is available. BME can be stated in terms of a nonlinear non-convex combinatorial optimization problem, usually referred to as the Balanced Minimum Evolution Problem (BMEP). Currently, the state-of-the-art among approximate methods for the BMEP is represented by FastME (version 2.0), a software which implements several deterministic phylogenetic construction heuristics combined with a local search on specific neighbourhoods derived by classical topological tree rearrangements. These combinations, however, may not guarantee convergence to close-to-optimal solutions to the problem due to the lack of solution space exploration, a phenomenon which is exacerbated when tackling molecular datasets characterized by a large number of taxa. To overcome such convergence issues, in this article, we propose a novel metaheuristic, named PhyloES, which exploits the combination of an exploration phase based on Evolution Strategies, a special type of evolutionary algorithm, with a refinement phase based on two local search algorithms. Extensive computational experiments show that PhyloES consistently outperforms FastME, especially when tackling larger datasets, providing solutions characterized by a shorter tree length but also significantly different from the topological perspective. The software and the data are available at https://github.com/andygaspar/PHYLOES.

A massively parallel branch-&-bound algorithm for the balanced minimum evolution problem

We build upon recent theoretical advances in the Balanced Minimum Evolution Problem (BMEP) to design a new massively parallel exact solution algorithm that proves to be up to one order of magnitude faster than the current state-of-the-art under the same computing settings and environment.

Politopos en filogenética

We introduce mathematical notions used in phylogenetics and three sorts of phylogenetics polytopes. The Tight span and the Lipschitz polytope are both associated to finite metric spaces and can be connected to distance-preserving embeddings, while the balanced minimum evolution (BME) polytope is associated to natural numbers.

On the approximability of the fixed-tree balanced minimum evolution problem.

The Fixed-Tree BMEP (FT-BMEP) is a special case of the Balanced Minimum Evolution Problem (BMEP) that consists of finding the assignment of a set of n taxa to the n leaves of a given unrooted binary tree so as to minimize the BMEP objective function. Deciding the computational complexity of the FT-BMEP has been an open problem for almost a decade. Here, we show that a few modifications to Fiorini and Joret’s proof of the mathcal {NP}-hardness of the BMEP suffice to prove the general mathcal {NP}-hardness of the FT-BMEP as well as its strong inapproximability.

An information theory perspective on the balanced minimum evolution problem

We show that the Balanced Minimum Evolution Problem (BMEP) is a cross-entropy minimization problem. This new perspective both extends the previous interpretations of the BMEP length function described in the literature and enables the identification of an efficiently computable family of lower bounds on the value of the optimal solution to the problem.

On the Balanced Minimum Evolution polytope

Recent advances on the polyhedral combinatorics of the Balanced Minimum Evolution Problem (BMEP) enabled the characterization of a number of facets of its convex hull (also referred to as the BMEP polytope) as well as the discovery of connections between this polytope and the permutoassociahedron. In this article, we extend these studies, by presenting new results concerning some fundamental characteristics of the BMEP polytope, new facet-defining inequalities in the case of six or more taxa, a number of valid inequalities, and a polynomial time oracle to recognize its vertices. Our aim is to broaden understanding of the polyhedral combinatorics of the BMEP with a view to developing new and more effective exact solution algorithms.

Level-1 phylogenetic networks and their balanced minimum evolution polytopes.

Balanced minimum evolution is a distance-based criterion for the reconstruction of phylogenetic trees. Several algorithms exist to find the optimal tree with respect to this criterion. One approach is to minimize a certain linear functional over an appropriate polytope. Here we present polytopes that allow a similar linear programming approach to finding phylogenetic networks. We investigate a two-parameter family of polytopes that arise from phylogenetic networks, and which specialize to the Balanced Minimum Evolution polytopes as well as the Symmetric Travelling Salesman polytopes. We show that the vertices correspond to certain level-1 phylogenetic networks, and that there are facets or faces for every split. We also describe lower bound faces and a family of faces for every dimension.

Enumerating vertices of the balanced minimum evolution polytope

Recent advances on the polyhedral combinatorics of the Balanced Minimum Evolution Problem (BMEP) enabled the identification of fundamental characteristics of the convex hull of the BMEP (or BMEP polytope) as well as the description of some of its facets. These results have been possible thanks to the assistance of general purpose softwares for polyhedral analyses, such as Polymake, whose running times however become quickly unpractical. In this article, we address the problem of designing tailored algorithms for the study of the BMEP polytope, with special focus on the problem of enumerating its vertices. To this end, by exploiting some results from the polyhedral combinatorics of the BMEP and a particular encoding scheme based on Prüfer coding, we present an iterative enumeration algorithm that is markedly faster than current general purpose softwares and that can be natively massively parallelized.

FastME 2.0: A Comprehensive, Accurate, and Fast Distance-Based Phylogeny Inference Program.

FastME provides distance algorithms to infer phylogenies. FastME is based on balanced minimum evolution, which is the very principle of Neighbor Joining (NJ). FastME improves over NJ by performing topological moves using fast, sophisticated algorithms. The first version of FastME only included Nearest Neighbor Interchange. The new 2.0 version also includes Subtree Pruning and Regrafting, while remaining as fast as NJ and providing a number of facilities: Distance estimation for DNA and proteins with various models and options, bootstrapping, and parallel computations. FastME is available using several interfaces: Command-line (to be integrated in pipelines), PHYLIP-like, and a Web server (http://www.atgc-montpellier.fr/fastme/).

A branch-price-and-cut algorithm for the minimum evolution problem

We investigate the Minimum Evolution Problem (MEP), an NP-hard network design problem arising from computational biology. The MEP consists in finding a weighted unrooted binary tree having n leaves, minimal length, and such that the sum of the edge weights belonging to the unique path between each pair of leaves is greater than or equal to a prescribed value. We study the polyhedral combinatorics of the MEP and investigate its relationships with the Balanced Minimum Evolution Problem. We develop an exact solution approach for the MEP based on a nontrivial combination of a parallel branch-price-and-cut scheme and a non-isomorphic enumeration of all possible solutions to the problem. Computational experiments show that the new solution approach outperforms the best mixed integer linear programming formulation for the MEP currently described in the literature. Our results give a perspective on the combinatorics of the MEP and suggest new directions for the development of future exact solution approaches that may turn out useful in practical applications. We also show that the MEP is statistically consistent.

Accuracy Guarantees for Phylogeny Reconstruction Algorithms Based on Balanced Minimum Evolution

Distance-based phylogenetic methods attempt to reconstruct an accurate phylogenetic tree from an estimated matrix of pairwise distances between taxa. This paper examines two distance-based algorithms (GreedyBME and FastME) that are based on the principle of minimizing the balanced minimum evolution score of the output tree in relation to the given estimated distance matrix. This is also the principle that underlies the neighbor-joining (NJ) algorithm. We show that GreedyBME and FastME both reconstruct the entire correct tree if the input data are quartet consistent, and also that if the maximum error of any distance estimate is epsilon, then both algorithms output trees containing all sufficiently long edges of the true tree: those having length at least 3epsilon. That is to say, the algorithms have edge safety radius 1/3. In contrast, quartet consistency of the data is not sufficient to guarantee the NJ algorithm reconstructs the correct tree, and moreover, the NJ algorithm has edge safety radius of 1/4: Only edges of the true tree of length at least 4epsilon can be guaranteed to appear in the output. These results give further theoretical support to the experimental evidence suggesting FastME is a more suitable distance-based phylogeny reconstruction method than the NJ algorithm.

The balanced minimum evolution problem under uncertain data

We investigate the Robust Deviation Balanced Minimum Evolution Problem (RDBMEP), a combinatorial optimization problem that arises in computational biology when the evolutionary distances from taxa are uncertain and varying inside intervals. By exploiting some fundamental properties of the objective function, we present a mixed integer programming model to exactly solve instances of the RDBMEP and discuss the biological impact of uncertainty on the solutions to the problem. Our results give perspective on the mathematics of the RDBMEP and suggest new directions to tackle phylogeny estimation problems affected by uncertainty.

The Balanced Minimum Evolution Problem

Aphylogeny is an unrooted binary tree that represents the evolutionary relationships of a set of n species. Phylogenies find applications in several scientific areas ranging from medical research, to drug discovery, to epidemiology, to systematics, and to population dynamics. In such applications, the available information is usually restricted to the leaves of a phylogeny and is represented by molecular data extracted from the analyzed species, such as DNA, RNA, amino acid, or codon fragments. On the contrary, the information about the phylogeny itself is generally missing and is determined by solving an optimization problem, called the phylogeny estimation problem (PEP), whose versions depend on the criterion used to select a phylogeny from among plausible alternatives. In this paper, we investigate a recent version of the PEP, called the balanced minimum evolution problem (BMEP). We present a mixed-integer linear programming model to exactly solve instances of the BMEP and develop branching rules and families of valid inequalities to further strengthen the model. Our results give perspective on the mathematics of the BMEP and suggest new directions on the development of future efficient exact approaches to solutions of the problem.

Approximating the balanced minimum evolution problem

We prove a strong inapproximability result for the Balanced Minimum Evolution Problem. Our proof also implies that the problem remains NP-hard even when restricted to metric instances. Furthermore, we give a MST-based 2-approximation algorithm for the problem for such instances.

Optimality of the Neighbor Joining Algorithm and Faces of the Balanced Minimum Evolution Polytope

Balanced minimum evolution (BME) is a statistically consistent distance-based method to reconstruct a phylogenetic tree from an alignment of molecular data. In 2000, Pauplin showed that the BME method is equivalent to optimizing a linear functional over the BME polytope, the convex hull of the BME vectors obtained from Pauplin's formula applied to all binary trees. The BME method is related to the Neighbor Joining (NJ) Algorithm, now known to be a greedy optimization of the BME principle. Further, the NJ and BME algorithms have been studied previously to understand when the NJ Algorithm returns a BME tree for small numbers of taxa. In this paper we aim to elucidate the structure of the BME polytope and strengthen knowledge of the connection between the BME method and NJ Algorithm. We first prove that any subtree-prune-regraft move from a binary tree to another binary tree corresponds to an edge of the BME polytope. Moreover, we describe an entire family of faces parameterized by disjoint clades. We show that these clade-faces are smaller dimensional BME polytopes themselves. Finally, we show that for any order of joining nodes to form a tree, there exists an associated distance matrix (i.e., dissimilarity map) for which the NJ Algorithm returns the BME tree. More strongly, we show that the BME cone and every NJ cone associated to a tree T have an intersection of positive measure.

Optimal solutions for the balanced minimum evolution problem

Phylogenies are trees representing the evolutionary relationships of a set of species (called taxa). Phylogenies find application in several scientific areas ranging from medical research to drug discovery, epidemiology, systematics and population dynamics. In these applications the available information is usually restricted to the leaves of a phylogeny and is represented by molecular data extracted from the species analyzed. On the contrary, the information about the phylogeny itself is generally missing and must be determined by solving an optimization problem, called the phylogeny estimation problem (PEP), whose versions depend on the criterion used to select a phylogeny among plausible alternatives.In this paper, we investigate one of the most significant versions of the PEP, called the balanced minimum evolution problem. We propose an exact algorithm based on the enumeration of non-isomorphic trees and the subsequent solution of quadratic assignment problems. Furthermore, by exploiting the underlying parallelism of the algorithm, we present a parallel version of the algorithm which shows a linear speed-up with respect to the sequential version. Extensive computational results prove the effectiveness of the proposed algorithms.

Polyhedral Geometry of Phylogenetic Rogue Taxa

It is well known among phylogeneticists that adding an extra taxon (e.g. species) to a data set can alter the structure of the optimal phylogenetic tree in surprising ways. However, little is known about this "rogue taxon" effect. In this paper we characterize the behavior of balanced minimum evolution (BME) phylogenetics on data sets of this type using tools from polyhedral geometry. First we show that for any distance matrix there exist distances to a "rogue taxon" such that the BME-optimal tree for the data set with the new taxon does not contain any nontrivial splits (bipartitions) of the optimal tree for the original data. Second, we prove a theorem which restricts the topology of BME-optimal trees for data sets of this type, thus showing that a rogue taxon cannot have an arbitrary effect on the optimal tree. Third, we computationally construct polyhedral cones that give complete answers for BME rogue taxon behavior when our original data fits a tree on four, five, and six taxa. We use these cones to derive sufficient conditions for rogue taxon behavior for four taxa, and to understand the frequency of the rogue taxon effect via simulation.

Robustness of Phylogenetic Inference Based on Minimum Evolution

Minimum evolution is the guiding principle of an important class of distance-based phylogeny reconstruction methods, including neighbor-joining (NJ), which is the most cited tree inference algorithm to date. The minimum evolution principle involves searching for the tree with minimum length, where the length is estimated using various least-squares criteria. Since evolutionary distances cannot be known precisely but only estimated, it is important to investigate the robustness of phylogenetic reconstruction to imprecise estimates for these distances. The safety radius is a measure of this robustness: it consists of the maximum relative deviation that the input distances can have from the correct distances, without compromising the reconstruction of the correct tree structure. Answering some open questions, we here derive the safety radius of two popular minimum evolution criteria: balanced minimum evolution (BME) and minimum evolution based on ordinary least squares (OLS + ME). Whereas BME has a radius of 1/2, which is the best achievable, OLS + ME has a radius tending to 0 as the number of taxa increases. This difference may explain the gap in reconstruction accuracy observed in practice between OLS + ME and BME (which forms the basis of popular programs such as NJ and FastME).