Fast neighbor joining

AbstractReconstructing the evolutionary history of a set of species is a fundamental problem in biology and methods for solving this problem are gaged based on two characteristics: accuracy and efficiency. Neighbor Joining (NJ) is a so-called distance-based method that, thanks to its good accuracy and speed, has been embraced by the phylogeny community. It takes the distances between n taxa and produces in Θ(n3) time a phylogenetic tree, i.e., a tree which aims to describe the evolutionary history of the taxa. In addition to performing well in practice, the NJ algorithm has optimal reconstruction radius.The contribution of this paper is twofold: (1) we present an algorithm called Fast Neighbor Joining (FNJ) with optimal reconstruction radius and optimal run time complexity O(n2) and (2) we present a greatly simplified proof for the correctness of NJ. Initial experiments show that FNJ in practice has almost the same accuracy as NJ, indicating that the property of optimal reconstruction radius has great importance to their good performance. Moreover, we show how improved running time can be achieved for computing the so-called correction formulas

Three-Dimensional Phylogeny Explorer: Distinguishing paralogs, lateral transfer, and violation of "molecular clock" assumption with 3D visualization

<p>Abstract</p> <p>Background</p> <p>Construction and interpretation of phylogenetic trees has been a major research topic for understanding the evolution of genes. Increases in sequence data and complexity are creating a need for more powerful and insightful tree visualization tools.</p> <p>Results</p> <p>We have developed 3D Phylogeny Explorer (3DPE), a novel phylogeny tree viewer that maps trees onto three spatial axes (species on the X-axis; paralogs on Z; evolutionary distance on Y), enabling one to distinguish at a glance evolutionary features such as speciation; gene duplication and paralog evolution; lateral gene transfer; and violation of the "molecular clock" assumption. Users can input any tree on the online 3DPE, then rotate, scroll, rescale, and explore it interactively as "live" 3D views. All objects in 3DPE are clickable to display subtrees, connectivity path highlighting, sequence alignments, and gene summary views, and etc. To illustrate the value of this visualization approach for microbial genomes, we also generated 3D phylogeny analyses for all clusters from the public COG database. We constructed tree views using well-established methods and graph algorithms. We used Scientific Python to generate VRML2 3D views viewable in any web browser.</p> <p>Conclusion</p> <p>3DPE provides a novel phylogenetic tree projection method into 3D space and its web-based implementation with live 3D features for reconstruction of phylogenetic trees of COG database.</p

Evolutionary distances in the twilight zone -- a rational kernel approach

Phylogenetic tree reconstruction is traditionally based on multiple sequence alignments (MSAs) and heavily depends on the validity of this information bottleneck. With increasing sequence divergence, the quality of MSAs decays quickly. Alignment-free methods, on the other hand, are based on abstract string comparisons and avoid potential alignment problems. However, in general they are not biologically motivated and ignore our knowledge about the evolution of sequences. Thus, it is still a major open question how to define an evolutionary distance metric between divergent sequences that makes use of indel information and known substitution models without the need for a multiple alignment. Here we propose a new evolutionary distance metric to close this gap. It uses finite-state transducers to create a biologically motivated similarity score which models substitutions and indels, and does not depend on a multiple sequence alignment. The sequence similarity score is defined in analogy to pairwise alignments and additionally has the positive semi-definite property. We describe its derivation and show in simulation studies and real-world examples that it is more accurate in reconstructing phylogenies than competing methods. The result is a new and accurate way of determining evolutionary distances in and beyond the twilight zone of sequence alignments that is suitable for large datasets.Comment: to appear in PLoS ON

Alignment-free phylogenetic reconstruction: Sample complexity via a branching process analysis

We present an efficient phylogenetic reconstruction algorithm allowing insertions and deletions which provably achieves a sequence-length requirement (or sample complexity) growing polynomially in the number of taxa. Our algorithm is distance-based, that is, it relies on pairwise sequence comparisons. More importantly, our approach largely bypasses the difficult problem of multiple sequence alignment.Comment: Published in at http://dx.doi.org/10.1214/12-AAP852 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Using Avida to test the effects of natural selection on phylogenetic reconstruction methods

Phylogenetic trees group organisms by their ancestral relationships. There are a number of distinct algorithms used to reconstruct these trees from molecular sequence data, but different methods sometimes give conflicting results. Since there are few precisely known phylogenies, simulations are typically used to test the quality of reconstruction algorithms. These simulations randomly evolve strings of symbols to produce a tree, and then the algorithms are run with the tree leaves as inputs. Here we use Avida to test two widely used reconstruction methods, which gives us the chance to observe the effect of natural selection on tree reconstruction. We find that if the organisms undergo natural selection between branch points, the methods will be successful even on very large time scales. However, these algorithms often falter when selection is absent

Testing robustness of relative complexity measure method constructing robust phylogenetic trees for Galanthus L. Using the relative complexity measure

Background: Most phylogeny analysis methods based on molecular sequences use multiple alignment where the quality of the alignment, which is dependent on the alignment parameters, determines the accuracy of the resulting trees. Different parameter combinations chosen for the multiple alignment may result in different phylogenies. A new non-alignment based approach, Relative Complexity Measure (RCM), has been introduced to tackle this problem and proven to work in fungi and mitochondrial DNA. Result: In this work, we present an application of the RCM method to reconstruct robust phylogenetic trees using sequence data for genus Galanthus obtained from different regions in Turkey. Phylogenies have been analyzed using nuclear and chloroplast DNA sequences. Results showed that, the tree obtained from nuclear ribosomal RNA gene sequences was more robust, while the tree obtained from the chloroplast DNA showed a higher degree of variation. Conclusions: Phylogenies generated by Relative Complexity Measure were found to be robust and results of RCM were more reliable than the compared techniques. Particularly, to overcome MSA-based problems, RCM seems to be a reasonable way and a good alternative to MSA-based phylogenetic analysis. We believe our method will become a mainstream phylogeny construction method especially for the highly variable sequence families where the accuracy of the MSA heavily depends on the alignment parameters

Consistency and convergence rate of phylogenetic inference via regularization

It is common in phylogenetics to have some, perhaps partial, information about the overall evolutionary tree of a group of organisms and wish to find an evolutionary tree of a specific gene for those organisms. There may not be enough information in the gene sequences alone to accurately reconstruct the correct "gene tree." Although the gene tree may deviate from the "species tree" due to a variety of genetic processes, in the absence of evidence to the contrary it is parsimonious to assume that they agree. A common statistical approach in these situations is to develop a likelihood penalty to incorporate such additional information. Recent studies using simulation and empirical data suggest that a likelihood penalty quantifying concordance with a species tree can significantly improve the accuracy of gene tree reconstruction compared to using sequence data alone. However, the consistency of such an approach has not yet been established, nor have convergence rates been bounded. Because phylogenetics is a non-standard inference problem, the standard theory does not apply. In this paper, we propose a penalized maximum likelihood estimator for gene tree reconstruction, where the penalty is the square of the Billera-Holmes-Vogtmann geodesic distance from the gene tree to the species tree. We prove that this method is consistent, and derive its convergence rate for estimating the discrete gene tree structure and continuous edge lengths (representing the amount of evolution that has occurred on that branch) simultaneously. We find that the regularized estimator is "adaptive fast converging," meaning that it can reconstruct all edges of length greater than any given threshold from gene sequences of polynomial length. Our method does not require the species tree to be known exactly; in fact, our asymptotic theory holds for any such guide tree.Comment: 34 pages, 5 figures. To appear on The Annals of Statistic

Phase transition in the sample complexity of likelihood-based phylogeny inference

Reconstructing evolutionary trees from molecular sequence data is a fundamental problem in computational biology. Stochastic models of sequence evolution are closely related to spin systems that have been extensively studied in statistical physics and that connection has led to important insights on the theoretical properties of phylogenetic reconstruction algorithms as well as the development of new inference methods. Here, we study maximum likelihood, a classical statistical technique which is perhaps the most widely used in phylogenetic practice because of its superior empirical accuracy. At the theoretical level, except for its consistency, that is, the guarantee of eventual correct reconstruction as the size of the input data grows, much remains to be understood about the statistical properties of maximum likelihood in this context. In particular, the best bounds on the sample complexity or sequence-length requirement of maximum likelihood, that is, the amount of data required for correct reconstruction, are exponential in the number, $n$, of tips---far from known lower bounds based on information-theoretic arguments. Here we close the gap by proving a new upper bound on the sequence-length requirement of maximum likelihood that matches up to constants the known lower bound for some standard models of evolution. More specifically, for the $r$-state symmetric model of sequence evolution on a binary phylogeny with bounded edge lengths, we show that the sequence-length requirement behaves logarithmically in $n$ when the expected amount of mutation per edge is below what is known as the Kesten-Stigum threshold. In general, the sequence-length requirement is polynomial in $n$. Our results imply moreover that the maximum likelihood estimator can be computed efficiently on randomly generated data provided sequences are as above.Comment: To appear in Probability Theory and Related Field