Performance Study of Phylogenetic Methods

Journal of Classification, 2010

We present a new distance based quartet method for phylogenetic tree reconstruction, called Minimum Tree Cost Quartet Puzzling. Starting from a distance matrix computed from natural data, the algorithm incrementally constructs a tree by adding one taxon at a time to the intermediary tree using a cost function based on the relaxed 4-point condition for weighting quartets. Different input orders of taxa lead to trees having distinct topologies which can be evaluated using a maximum likelihood or weighted least squares optimality criterion. Using reduced sets of quartets and a simple heuristic tree search strategy we obtain an overall complexity of O(n 5 log 2 n) for the algorithm. We evaluate the performances of the method through comparative tests and show that our method outperforms NJ when a weighted least squares optimality criterion is employed. We also discuss the theoretical boundaries of the algorithm.

2006

Abstract This paper describes a parallel implementation of our recently developed algorithm for phylogenetic analysis on the IBM BlueGene/L cluster. This algorithm constructs evolutionary trees for a given set of DNA or protein sequences based on the topological information of every possible quartet trees. Our experimental results showed that it has several advantages over many popular algorithms.

Molecular Biology and Evolution, 1999

A new quartet method is described for building phylogenetic trees, making use of a numerical measure of local inconsistency. For each quartet consisting of four species, the user chooses numbers indicating evidence for each of the three possible completely resolved trees. These numbers may be, for example, tree lengths or likelihoods. From these numbers, I describe how to measure the ''local inconsistency'' that results from placing a new species into a particular position in a phylogenetic tree. The best placements are those with low local inconsistency. A phylogenetic tree for a collection of taxa may be constructed by picking a random order of species and adding the species in this order, each time using the placement with the lowest local inconsistency. To summarize the results, one may select a majority-rule consensus tree or the tree most frequently obtained. Alternatively, taxa can be added in the order that maximizes the signal strength. Advantages of the method may include flexibility and better resolution. Studies are performed for artificial data sets for which long-branch attractions are a serious problem; comparisons show performance much superior to maximum parsimony and somewhat superior to quartet puzzling. A case study with real data also illustrates the method.

IEEE/ACM transactions on computational biology and bioinformatics, 2016

Quartet trees displayed by larger phylogenetic trees have long been used as inputs for species tree and supertree reconstruction. Computational constraints prevent the use of all displayed quartets in many practical problems with large numbers of taxa. We introduce the notion of an Efficient Quartet System (EQS) to represent a phylogenetic tree with a subset of the quartets displayed by the tree. We show mathematically that the set of quartets obtained from a tree via an EQS contains all of the combinatorial information of the tree itself. Using performance tests on simulated datasets, we also demonstrate that using an EQS to reduce the number of quartets in both summary method pipelines for species tree inference as well as methods for supertree inference results in only small reductions in accuracy.

Lecture Notes in Computer Science, 2002

The benefits of experimental algorithmics and algorithm engineering need to be extended to applications in the computational sciences. In this paper, we present on one such application: the reconstruction of evolutionary histories (phylogenies) from molecular data such as DNA sequences. Our presentation is not a survey of past and current work in the area, but rather a discussion of what we see as some of the important challenges in experimental algorithmics that arise from computational phylogenetics.

Molecular Biology and Evolution, 2001

From the DNA sequences for N taxa, the (generally unknown) phylogenetic tree T that gave rise to them is to be reconstructed. Various methods give rise, for each quartet J consisting of exactly four taxa, to a predicted tree L(J) based only on the sequences in J, and these are then used to reconstruct T. The author defines an ''error-correcting map'' (Ec), which replaces each L(J) with a new tree, Ec(L)(J), which has been corrected using other trees, L(K), in the list L. The ''quartet distance'' between two trees is defined as the number of quartets J on which the two trees differ, and two distinct trees are shown to always have quartet distance of at least N Ϫ 3. If L has quartet distance at most (N Ϫ 4)/2 from T, then Ec(L) will coincide with the correct list for T; and this result cannot be improved. In general, Ec can correct many more errors in L. Iteration of the map Ec may produce still more accurate lists. Simulations are reported which often show improvement even when the quartet distance considerably exceeds (N Ϫ 4)/2. Moreover, the Buneman tree for Ec(L) is shown to refine the Buneman tree for L, so that strongly supported edges for L remain strongly supported for Ec(L). Simulations show that if methods such as the C-tree or hypercleaning are applied to Ec(L), the resulting trees often have more resolution than when the methods are applied only to L. ''most'' choices of J and then corrects individual L(J)

New Achievements in Evolutionary Computation, 2010

Communications of The Korean Mathematical Society, 2010

Among the distance based algorithms in phylogenetic tree reconstruction, the neighbor-joining algorithm has been a widely used and effective method. We propose a new algorithm which counts the number of consistent quartets for cherry picking with tie breaking. We show that the success rate of the new algorithm is almost equal to that of neighbor-joining. This gives an explanation of the qualitative nature of neighbor-joining and that of dissimilarity maps from DNA sequence data. Moreover, the new algorithm always reconstructs correct trees from quartet consistent dissimilarity maps.

4OR, 2018

The minimum quartet tree cost (MQTC) problem is a graph combinatorial optimization problem where, given a set of n ≥ 4 data objects and their pairwise costs (or distances), one wants to construct an optimal tree from the 3 • n 4 quartet topologies on n, where optimality means that the sum of the costs of the embedded (or consistent) quartet topologies is minimal. The MQTC problem is the foundation of the quartet method of hierarchical clustering, a novel hierarchical clustering method for non tree-like (non-phylogeny) data in various domains, or for heterogeneous data across domains. The MQTC problem is NP-complete and some heuristics have been already proposed in the literature. The aim of this paper is to present a first exact solution approach for the MQTC problem. Although the algorithm is able to get exact solutions only for relatively small problem instances, due to the high problem complexity, it can be used as a benchmark for validating the performance of any heuristic proposed for the MQTC problem.

Molecular Biology and Evolution, 1998

The maximum-likelihood (ML) method for inferring molecular phylogenies (Felsenstein 1981) is being used extensively in the wide field of phylogenetics. The method has a sound statistical basis (e.g., Felsenstein 1983; Goldman 1990; Yang 1994) and has proved to be powerful in recovering correct tree topologies in computer simulation studies (e.g.