The evolutionary history of a set of taxa is usually represented by a phylogenetic tree, and this model has greatly facilitated the discussion and testing of hypotheses. However, it is well known that more complex evolutionary scenarios are poorly described by such models. Further, even when evolution proceeds in a tree-like manner, analysis of the data may not be best served by using methods that enforce a tree structure but rather by a richer visualization of the data to evaluate its properties, at least as an essential first step. Thus, phylogenetic networks should be employed when reticulate events such as hybridization, horizontal gene transfer, recombination, or gene duplication and loss are believed to be involved, and, even in the absence of such events, phylogenetic networks have a useful role to play. This article reviews the terminology used for phylogenetic networks and covers both split networks and reticulate networks, how they are defined, and how they can be interpreted. Additionally, the article outlines the beginnings of a comprehensive statistical framework for applying split network methods. We show how split networks can represent confidence sets of trees and introduce a conservative statistical test for whether the conflicting signal in a network is treelike. Finally, this article describes a new program, SplitsTree4, an interactive and comprehensive tool for inferring different types of phylogenetic networks from sequences, distances, and trees.

https://bioinformatics.cs.vt.edu/~easychair/HusonBryant_MBE_2006.pdf

Application of Phylogenetic Networks in Evolutionary Studies

BOLD: The Barcode of Life Data System: Barcoding

KEGG(Kyoto Encyclopedia of Genes and Genomes)〔和文〕 (特集 ゲノム医学の現在と未来--基礎と臨床) -- (データベース)

Gene families are growing rapidly, but standard methods for inferring phylogenies do not scale to alignments with over 10,000 sequences. We present FastTree, a method for constructing large phylogenies and for estimating their reliability. Instead of storing a distance matrix, FastTree stores sequence profiles of internal nodes in the tree. FastTree uses these profiles to implement Neighbor-Joining and uses heuristics to quickly identify candidate joins. FastTree then uses nearest neighbor interchanges to reduce the length of the tree. For an alignment with N sequences, L sites, and a different characters, a distance matrix requires O(N2) space and O(N2L) time, but FastTree requires just O(NLa + N) memory and O(Nlog (N)La) time. To estimate the tree's reliability, FastTree uses local bootstrapping, which gives another 100-fold speedup over a distance matrix. For example, FastTree computed a tree and support values for 158,022 distinct 16S ribosomal RNAs in 17 h and 2.4 GB of memory. Just computing pairwise Jukes–Cantor distances and storing them, without inferring a tree or bootstrapping, would require 17 h and 50 GB of memory. In simulations, FastTree was slightly more accurate than Neighbor-Joining, BIONJ, or FastME; on genuine alignments, FastTree's topologies had higher likelihoods. FastTree is available at http://microbesonline.org/fasttree.

/pdf/fasttree-computing-large-minimum-evolution-trees-with-eo2tre5l8r.pdf

FastTree: Computing Large Minimum Evolution Trees with Profiles instead of a Distance Matrix

Gene families are growing rapidly, but standard methods for inferring phylogenies do not scale to alignments with over 10,000 sequences. We present FastTree, a method for constructing large phylogenies and for estimating their reliability. Instead of storing a distance matrix, FastTree stores sequence profiles of internal nodes in the tree. FastTree uses these profiles to implement neighbor-joining and uses heuristics to quickly identify candidate joins. FastTree then uses nearest-neighbor interchanges to reduce the length of the tree. For an alignment with N sequences, L sites, and a different characters, a distance matrix requires O(N^2) space and O(N^2 L) time, but FastTree requires just O( NLa + N sqrt(N) ) memory and O( N sqrt(N) log(N) L a ) time. To estimate the tree's reliability, FastTree uses local bootstrapping, which gives another 100-fold speedup over a distance matrix. For example, FastTree computed a tree and support values for 158,022 distinct 16S ribosomal RNAs in 17 hours and 2.4 gigabytes of memory. Just computing pairwise Jukes-Cantor distances and storing them, without inferring a tree or bootstrapping, would require 17 hours and 50 gigabytes of memory. In simulations, FastTree was slightly more accurate than neighbor joining, BIONJ, or FastME; on genuine alignments, FastTree's topologies had higher likelihoods. FastTree is available at http://microbesonline.org/fasttree.

/pdf/fast-tree-computing-large-minimum-evolution-trees-with-4grq0gwfpy.pdf

Fast Tree: Computing Large Minimum-Evolution Trees with Profiles instead of a Distance Matrix

Reconstructing the evolutionary tree for a set of n species based on pairwise distances between the species is a fundamental problem in bioinformatics. Neighbor joining is a popular distance based tree reconstruction method. It always proposes fully resolved binary trees despite missing evidence in the underlying distance data. Distance based methods based on the theory of Buneman trees and refined Buneman trees avoid this problem by only proposing evolutionary trees whose edges satisfy a number of constraints. These trees might not be fully resolved but there is strong combinatorial evidence for each proposed edge. The currently best algorithm for computing the refined Buneman tree from a given distance measure has a running time of O(n 5) and a space consumption of O(n 4). In this paper, we present an algorithm with running time O(n 3) and space consumption O(n 2). The improved complexity of our algorithm makes the method of refined Buneman trees computational competitive to methods based on neighbor joining.

Computing Refined Buneman Trees in Cubic Time

For a set of points in the plane and a fixed integer k > 0, the Yao graph Yk partitions the space around each point into k equiangular cones of angle θ = 2π/k, and connects each point to a nearest neighbor in each cone. It is known for all Yao graphs, with the sole exception of Y5, whether or not they are geometric spanners. In this paper we close this gap by showing that for odd k ≥ 5, the spanning ratio of Yk is at most 1/(1−2sin(3θ/8)), which gives the first constant upper bound for Y5, and is an improvement over the previous bound of 1/(1−2sin(θ/2)) for odd k ≥ 7. We further reduce the upper bound on the spanning ratio for Y5 from 10.9 to 2 + √3 a 3.74, which falls slightly below the lower bound of 3.79 established for the spanning ratio of o5 (o-graphs differ from Yao graphs only in the way they select the closest neighbor in each cone). This is the first such separation between a Yao and o-graph with the same number of cones. We also give a lower bound of 2.87 on the spanning ratio of Y5. Finally, we revisit the Y6 graph, which plays a particularly important role as the transition between the graphs (k > 6) for which simple inductive proofs are known, and the graphs (k ≤ 6) whose best spanning ratios have been established by complex arguments. Here we reduce the known spanning ratio of Y6 from 17.6 to 5.8, getting closer to the spanning ratio of 2 established for o6.

https://cglab.ca/~lfbarba/publications/NeyYaoSpanningSoCG.pdf

New and Improved Spanning Ratios for Yao Graphs

We give a randomized algorithm for sorting strings in external memory. For K binary strings comprising N words in total, our algorithm finds the sorted order and the longest common prefix sequence of the strings using $O(\frac{K}{B}log_{M/B}(\frac{K}{M})log(\frac{N}{K}) + \frac{N}{B})$ I/Os. This bound is never worse than $O(\frac{K}{B}log_{M/B}(\frac{K}{M})log log_{M/B}(\frac{K}{M}) + \frac{N}{B})$ I/Os, and improves on the (deterministic) algorithm of Arge et al. (On sorting strings in external memory, STOC '97). The error probability of the algorithm can be chosen as O(N$^{\rm -{\it c}}$) for any positive constant c. The algorithm even works in the cache-oblivious model under the tall cache assumption, i.e,, assuming M > B1+e for some e > 0. An implication of our result is improved construction algorithms for external memory string dictionaries.

http://www.it-c.dk/people/pagh/papers/string.pdf

External string sorting: faster and cache-oblivious

The triplet distance is a distance measure that compares two rooted trees on the same set of leaves by enumerating all sub-sets of three leaves and counting how often the induced topologies of the tree are equal or different. We present an algorithm that computes the triplet distance between two rooted binary trees in time O (n log2 n). The algorithm is related to an algorithm for computing the quartet distance between two unrooted binary trees in time O (n log n). While the quartet distance algorithm has a very severe overhead in the asymptotic time complexity that makes it impractical compared to O (n2) time algorithms, we show through experiments that the triplet distance algorithm can be implemented to give a competitive wall-time running time.

http://www.cs.au.dk/~gerth/papers/apbc13.pdf

A practical O(n log2 n) time algorithm for computing the triplet distance on binary trees.

1Department of Mathematics and Computer Science, University of Southern Denmark, Odense M DK-5230, Denmark 2Institute for Theoretical Chemistry, University of Vienna, Wien A-1090, Austria 3Bioinformatics Group, Department of Computer Science, University of Leipzig, Leipzig D-04107, Germany 4Max Planck Institute for Mathematics in the Sciences, Leipzig D-04103, Germany 5Interdisciplinary Center for Bioinformatics, and German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig and Competence Center for Scalable Data Services and Solutions Dresden-Leipzig and Leipzig Research Center for Civilization Diseases, University of Leipzig, Leipzig D-04107, Germany 6Fraunhofer Institute for Cell Therapy and Immunology, Leipzig D-04103, Germany 7Center for non-coding RNA in Technology and Health, University of Copenhagen, Frederiksberg C DK-1870, Denmark 8Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe NM 87501, USA 9Vienna Metabolomics Center (VIME), University of Vienna, Wien A-1090, Austria 10Earth-Life Science Institute, Tokyo Institute of Technology, Tokyo 152-8550, Japan 11Research group Bioinformatics and Computational Biology, Faculty of Computer Science, University of Vienna, Wien A-1090, Austria

https://findresearcher.sdu.dk:8443/ws/files/148769282/Towards_mechanistic_prediction_of_mass_spectra_using_graph_transformation.pdf

Rolf Fagerberg

Papers

Computing Refined Buneman Trees in Cubic Time

New and Improved Spanning Ratios for Yao Graphs

External string sorting: faster and cache-oblivious

A practical O(n log2 n) time algorithm for computing the triplet distance on binary trees.

Towards mechanistic prediction of mass spectra using graph transformation