Minimum Evolution Criterion 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

Fishing for minimum evolution trees with Neighbor-Nets

In evolutionary biology, biologists commonly use a phylogenetic tree to represent the evolutionary history of some set of species. A common approach taken to construct such a tree is to search through the space of all possible phylogenetic trees on the set so as to find one that optimizes some score function, such as the minimum evolution criterion. However, this is hampered by the fact that the space of phylogenetic trees is extremely large in general. Interestingly, an alternative approach, which has received somewhat less attention in the literature, is to instead search for trees within some set of bipartitions or splits of the set of species in question. Here we consider the problem of searching through a set of splits that is circular. Such sets can, for example, be generated by the NeighborNet algorithm for constructing phylogenetic networks. More specifically, we present an O(n4) time algorithm for finding an optimal minimum evolution tree in a circular set of splits on a set of species of size n. In addition, using simulations, we compare the performance of this algorithm when applied to NeighborNet output with that of FastME, a leading method for searching for minimum evolution trees in tree space. We find that, even though a circular set of splits represents just a tiny fraction of the total number of possible splits of a set, the trees obtained from circular sets compare quite favorably with those obtained with FastME, suggesting that the approach could warrant further investigation.

FastTree 2 – Approximately Maximum-Likelihood Trees for Large Alignments

BackgroundWe recently described FastTree, a tool for inferring phylogenies for alignments with up to hundreds of thousands of sequences. Here, we describe improvements to FastTree that improve its accuracy without sacrificing scalability.Methodology/Principal FindingsWhere FastTree 1 used nearest-neighbor interchanges (NNIs) and the minimum-evolution criterion to improve the tree, FastTree 2 adds minimum-evolution subtree-pruning-regrafting (SPRs) and maximum-likelihood NNIs. FastTree 2 uses heuristics to restrict the search for better trees and estimates a rate of evolution for each site (the “CAT” approximation). Nevertheless, for both simulated and genuine alignments, FastTree 2 is slightly more accurate than a standard implementation of maximum-likelihood NNIs (PhyML 3 with default settings). Although FastTree 2 is not quite as accurate as methods that use maximum-likelihood SPRs, most of the splits that disagree are poorly supported, and for large alignments, FastTree 2 is 100–1,000 times faster. FastTree 2 inferred a topology and likelihood-based local support values for 237,882 distinct 16S ribosomal RNAs on a desktop computer in 22 hours and 5.8 gigabytes of memory.Conclusions/SignificanceFastTree 2 allows the inference of maximum-likelihood phylogenies for huge alignments. FastTree 2 is freely available at http://www.microbesonline.org/fasttree.

The minimum evolution problem: Overview and classification

AbstractMolecular phylogenetics studies the hierarchical evolutionary relationships among organisms by means of molecular data. These relationships are typically described by means of weighted trees, or phylogenies, whose leaves represent the observed organisms, internal vertices the intermediate ancestors, and edges the evolutionary relationships between pairs of organisms. Molecular phylogenetics provides several criteria for selecting one phylogeny from among plausible alternatives. Usually, such criteria can be expressed in terms of objective functions, and the phylogenies that optimize them are referred to as optimal. One of the most important criteria is the minimum evolution (ME) criterion, which states that the optimal phylogeny for a given set of organisms is the one whose sum of edge weights is minimal. Finding the phylogeny that satisfies the ME criterion involves solving an optimization problem, called the minimum evolution problem (MEP), which is notoriously ${\cal N P}$‐Hard. This article offers an overview of the MEP and discusses the different versions of it that occur in the literature. © 2008 Wiley Periodicals, Inc. NETWORKS, 2009

Mathematical models to reconstruct phylogenetic trees under the minimum evolution criterion

AbstractA basic problem in molecular biology is to rebuild phylogenetic trees (PT) from a set of DNA or protein sequences. Among different criteria used for this purpose, the minimum evolution criterion is an optimality based criterion aiming to rebuild PT characterized by a minimal length. This problem is known to be 𝒩𝒫‐hard. We introduce in this article some mixed integer programming models, and we also study possible cuts and lower bounds for the optimal value. So far, the number of sequences that can be involved in optimal phylogenetic reconstruction is still limited to 10. © 2008 Wiley Periodicals, Inc. NETWORKS, 2009

Guided genome halving: hardness, heuristics and the history of the Hemiascomycetes.

Motivation: Some present day species have incurred a whole genome doubling event in their evolutionary history, and this is reflected today in patterns of duplicated segments scattered throughout their chromosomes. These duplications may be used as data to ‘halve’ the genome, i.e. to reconstruct the ancestral genome at the moment of doubling, but the solution is often highly nonunique. To resolve this problem, we take account of outgroups, external reference genomes, to guide and narrow down the search.Results: We improve on a previous, computationally costly, ‘brute force’ method by adapting the genome halving algorithm of El-Mabrouk and Sankoff so that it rapidly and accurately constructs an ancestor close the outgroups, prior to a local optimization heuristic. We apply this to reconstruct the predoubling ancestor of Saccharomyces cerevisiae and Candida glabrata, guided by the genomes of three other yeasts that diverged before the genome doubling event. We analyze the results in terms (1) of the minimum evolution criterion, (2) how close the genome halving result is to the final (local) minimum and (3) how close the final result is to an ancestor manually constructed by an expert with access to additional information. We also visualize the set of reconstructed ancestors using classic multidimensional scaling to see what aspects of the two doubled and three unduplicated genomes influence the differences among the reconstructions.Availability: The experimental software is available on request.Contact: sankoff@uottawa.ca

On the optimality of the neighbor-joining algorithm

The popular neighbor-joining (NJ) algorithm used in phylogenetics is a greedy algorithm for finding the balanced minimum evolution (BME) tree associated to a dissimilarity map. From this point of view, NJ is "optimal" when the algorithm outputs the tree which minimizes the balanced minimum evolution criterion. We use the fact that the NJ tree topology and the BME tree topology are determined by polyhedral subdivisions of the spaces of dissimilarity maps to study the optimality of the neighbor-joining algorithm. In particular, we investigate and compare the polyhedral subdivisions for n ≤ 8. This requires the measurement of volumes of spherical polytopes in high dimension, which we obtain using a combination of Monte Carlo methods and polyhedral algorithms. Our results include a demonstration that highly unrelated trees can be co-optimal in BME reconstruction, and that NJ regions are not convex. We obtain the l2 radius for neighbor-joining for n = 5 and we conjecture that the ability of the neighbor-joining algorithm to recover the BME tree depends on the diameter of the BME tree.

Inferring horizontal transfers in the presence of rearrangements by the minimum evolution criterion

The evolution of viruses is very rapid and in addition to local point mutations (insertion, deletion, substitution) it also includes frequent recombinations, genome rearrangements and horizontal transfer of genetic materials (HGTS). Evolutionary analysis of viral sequences is therefore a complicated matter for two main reasons: First, due to HGTs and recombinations, the right model of evolution is a network and not a tree. Second, due to genome rearrangements, an alignment of the input sequences is not guaranteed. These facts encourage developing methods for inferring phylogenetic networks that do not require aligned sequences as input. In this work, we present the first computational approach which deals with both genome rearrangements and horizontal gene transfers and does not require a multiple alignment as input. We formalize a new set of computational problems which involve analyzing such complex models of evolution. We investigate their computational complexity, and devise algorithms for solving them. Moreover, we demonstrate the viability of our methods on several synthetic datasets as well as four biological datasets. The code is available from the authors upon request.

Trypanosoma cruzi: Exploring the nuclear genome of zymodeme 3 stocks by chromosome size polymorphism

Chagas disease is emerging in the Brazilian Amazon. We evaluated the position of eight zymodeme 3 isolates from Amazonian sylvatic vectors and one human case in relation to Trypanosoma cruzi I and II major groups and hybrid strains by chromosome size polymorphism. Nineteen isolates were analyzed by mapping nine coding sequences on chromosomal bands (0.6–3.3 Mbp). Numerical analysis was based on the absolute chromosomal size difference index (aCSDI). A dendrogram was obtained applying the minimum evolution criterion and considering the aCSDI values to estimate the branch lengths. The isolates were distributed in four groups. Group A clustered hybrid isolates; Groups B and C, T. cruzi II and T. cruzi I isolates, respectively. Seven Z3 stocks were clustered in Group D, which showed low intra-group diversity and was the most divergent. The proportion of two different-sized homologous chromosomes was determined. Wild vectors harboring Z3 stocks constitute a potential reservoir of human infection in the Amazon.

Topological Bias in Distance-Based Phylogenetic Methods: Problems with Over- and Underestimated Genetic Distances

I show several types of topological biases in distance-based methods that use the least-squares method to evaluate branch lengths and the minimum evolution (ME) or the Fitch-Margoliash (FM) criterion to choose the best tree. For a 6-species tree, there are two tree shapes, one with three cherries (a cherry is a pair of adjacent leaves descending from the most recent common ancestor), and the other with two. When genetic distances are underestimated, the 3-cherry tree shape is favored with either the ME or FM criterion. When the genetic distances are overestimated, the ME criterion favors the 2-cherry tree, but the direction of bias with the FM criterion depends on whether negative branches are allowed, i.e. allowing negative branches favors the 3-cherry tree shape but disallowing negative branches favors the 2-cherry tree shape. The extent of the bias is explored by computer simulation of sequence evolution.

On the optimization principle in phylogenetic analysis and the minimum-evolution criterion.

This paper discusses the optimization principle in phylogenetic analysis, in the case of distance data. We argue that the use of this principle cannot be called into question, except for computing time reasons. We show that the minimum-evolution criterion is not perfectly suited for distance data estimated from sequences, and we present another approach, implemented in the BIONJ algorithm, which allows the data features to be taken into account, while being less demanding in computing time. Simulations show that BIONJ significantly outperforms NJ.

Rapid Evaluation of Least-Squares and Minimum-Evolution Criteria on Phylogenetic Trees

We present fast new algorithms for evaluating trees with respect to least squares and minimum evolution (ME), the most commonly used criteria for inferring phylogenetic trees from distance data. These include: an optimal O(N2 ) time algorithm for calculating the branch (edge) lengths on a tree according to ordinary or unweighted least squares (OLS); an O(N3) time algorithm for edge lengths under weighted least squares (WLS) and the FitchMargoliash method; and an optimal O(N4) time algorithm for generalised least squares edge lengths. The Minimum Evolution criterion is based on the sum of edge lengths. Consequently, the edge lengths algorithms presented here lead directly to O(N2), O(N3) and O(N4) time algorithms for ME under OLS, WLS and GLS respectively. These algorithms are substantially faster than all those previously published, and the algorithms for OLS and GLS are the fastest possible (with respect to order of computational complexity). An optimal algorithm for determining path lengths in a tree with given edge lengths is also developed. This leads to an optimal O(N ) algorithm for OLS sums of squares evaluation and corresponding O(N3 ) and O(N4) time algorithms for WLS and GLS sums of squares, respectively. The GLS algorithm is time optimal if the covariance matrix is already inverted. The considerable increases in speed enable far more extensive tree searches and statistical evaluations (e.g. bootstrap, parametric bootstrap or jackknife). Hopefully, the fast algorithms for WLS and GLS will encourage their use for evaluating trees and their edge lengths ( e.g. for approximate divergence time estimates), since they should be more statistically efficient than OLS.

Statistical Tests of DNA Phylogenies

In this article, we review (1) statistical tests of DNA phylogenies inferred by the maximum- parsimony method, including tests that take into account the effect of different base compositions among lineages, (2) statistical tests based on the minimum-evolution criterion, i.e., the best tree is the tree with the smallest sum of branch-length estimates, and (3) the bootstrap technique for estimating the confidence level of a phylogenetic hypothesis based on either the maximum-parsimony or the neighbor-joining method. We explain why the bootstrap technique usually gives biased estimates and how to correct the bias. (DNA phylogenies; parsimony; neighbor joining; minimum evolution; statis? tical tests; bootstrap; bias correction.)

Statistical properties of the ordinary least-squares, generalized least-squares, and minimum-evolution methods of phylogenetic inference.

Statistical properties of the ordinary least-squares (OLS), generalized least-squares (GLS), and minimum-evolution (ME) methods of phylogenetic inference were studied by considering the case of four DNA sequences. Analytical study has shown that all three methods are statistically consistent in the sense that as the number of nucleotides examined (m) increases they tend to choose the true tree as long as the evolutionary distances used are unbiased. When evolutionary distances (dij's) are large and sequences under study are not very long, however, the OLS criterion is often biased and may choose an incorrect tree more often than expected under random choice. It is also shown that the variance-covariance matrix of dij's becomes singular as dij's approach zero and thus the GLS may not be applicable when dij's are small. The ME method suffers from neither of these problems, and the ME criterion is statistically unbiased. Computer simulation has shown that the ME method is more efficient in obtaining the true tree than the OLS and GLS methods and that the OLS is more efficient than the GLS when dij's are small, but otherwise the GLS is more efficient.