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

We consider the problem of performing predecessor searches in a bounded universe while achieving query times that depend on the distribution of queries. We obtain several data structures with various properties: in particular, we give data structures that achieve expected query times logarithmic in the entropy of the distribution of queries but with space bounded in terms of universe size, as well as data structures that use only linear space but with query times that are higher (but still sublinear) functions of the entropy. For these structures, the distribution is assumed to be known. We also consider individual query times on universe elements with general weights, as well as the case when the distribution is not known in advance.

Biased Predecessor Search

We study the approximate string matching and regular expression matching problem for the case when the text to be searched is compressed with the Ziv-Lempel adaptive dictionary compression schemes. We present a time-space trade-off that leads to algorithms improving the previously known complexities for both problems. In particular, we significantly improve the space bounds, which in practical applications are likely to be a bottleneck.

Improved Approximate String Matching and Regular Expression Matching on Ziv-Lempel Compressed Texts

We consider the problem of performing predecessor searches in a bounded universe while achieving query times that depend on the distribution of queries. We obtain several data structures with various properties: in particular, we give data structures that achieve expected query times logarithmic in the entropy of the distribution of queries but with space bounded in terms of universe size, as well as data structures that use only linear space but with query times that are higher (but still sublinear) functions of the entropy. For these structures, the distribution is assumed known. We also consider data structures with general weights on universe elements, as well as the case when the distribution is not known in advance.

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(K/B log M/B (K/M) log(N/K) + N/B) I/Os. This bound is never worse than O(K/B log M/B (K/B) log log M/B (K/M) + 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 -c ) for any positive constant c. The algorithm even works in the cache-oblivious model under the tall cache assumption, i.e,, assuming M > B 1+ ∈ for some e > 0. An implication of our result is improved construction algorithms for external memory string dictionaries.

External string sorting : Faster and cache-oblivious

. Graph transformation formalisms have proven to be suitable tools for the modeling of chemical reactions. They are well established in theoretical studies [15] and increasingly also in practical applications in chemistry [11, 28]. The latter is made feasible via the development of programming frameworks which make the formalisms executable [5, 19, 12]. The application of such frameworks to large networks of chemical reactions poses unique computational challenges due to the nature of the involved graphs, since these often consist of many individual connected components. While the existing methods for implementing graph transformations can be applied to such graphs, the combinatorics of constructing the graph matches involved in the application of graph transformation rules quickly becomes a computational bottleneck when the size of the chemical reaction network grows. In this contribution, we develop a new method of enumerating graph matches during graph transformation rule application. The method is designed to improve performance in such scenarios and is based on constructing graph matches in an iterative, component-wise fashion which allows redundant applications to be detected early and pruned. We further extend the algorithm with an eﬃcient heuristic based on local symmetries of the graphs, which allow us to detect and discard isomorphic applications early. Finally, we conduct chemical network generation experiments on real-life as well as synthetic data and compare against the state-of-the-art algorithm in the ﬁeld.

Rolf Fagerberg

Papers

Biased Predecessor Search

Improved Approximate String Matching and Regular Expression Matching on Ziv-Lempel Compressed Texts

Biased Predecessor Search

External string sorting : Faster and cache-oblivious

Efficient Modular Graph Transformation Rule Application