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

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

The Barcode of Life Data System ( BOLD ) is an informatics workbench aiding the acquisition, storage, analysis and publication of DNA barcode records. By assembling molecular, morphological and distributional data, it bridges a traditional bioinformatics chasm. BOLD is freely available to any researcher with interests in DNA barcoding. By providing specialized services, it aids the assembly of records that meet the standards needed to gain BARCODE designation in the global sequence databases. Because of its web-based delivery and flexible data security model, it is also well positioned to support projects that involve broad research alliances. This paper provides a brief introduction to the key elements of BOLD , discusses their functional capabilities, and concludes by examining computational resources and future prospects.

/pdf/bold-the-barcode-of-life-data-system-www-barcodinglife-org-11xa2bq3ju.pdf

BOLD : The Barcode of Life Data System (www.barcodinglife.org)

Graph orientations with low out-degree are one of several ways to efficiently store sparse graphs. If the graphs allow for insertion and deletion of edges, one may have to flip the orientation of some edges to prevent blowing up the maximum out-degree. We use arboricity as our sparsity measure. With an immensely simple greedy algorithm, we get parametrized trade-off bounds between out-degree and worst case number of flips, which previously only existed for amortized number of flips. We match the previous best worst-case algorithm (in $$\mathcal {O}\left( \log n\right) $$ flips) for almost all values of arboricity and beat it for either constant or super-logarithmic arboricity. We also match a previous best amortized result for at least logarithmic arboricity, and give the first results with worst-case $$\mathcal {O}\left( 1\right) $$ and $$\mathcal {O}\left( \sqrt{\log n}\right) $$ flips nearly matching out-degree bounds to their respective amortized solutions.

/pdf/a-simple-greedy-algorithm-for-dynamic-graph-orientation-3810ic44zl.pdf

A Simple Greedy Algorithm for Dynamic Graph Orientation

We propose a version of cache oblivious search trees which is simpler than the previous proposal of Bender, Demaine and Farach-Colton and has the same complexity bounds. In particular, our data structure avoids the use of weight balanced B-trees, and can be implemented as just a single array of data elements, without the use of pointers. The structure also improves space utilization. For storing n elements, our proposal uses (1+epsilon)n times the element size of memory, and performs searches in worst case O(log_B n) memory transfers, updates in amortized O((log^2 n)/(epsilon B)) memory transfers, and range queries in worst case O(log_B n + k/B) memory transfers, where k is the size of the output. The basic idea of our data structure is to maintain a dynamic binary tree of height log n + O(1) using existing methods, embed this tree in a static binary tree, which in turn is embedded in an array in a cache oblivious fashion, using the van Emde Boas layout of Prokop. We also investigate the practicality of cache obliviousness in the area of search trees, by providing an empirical comparison of different methods for laying out a search tree in memory. The source code of the programs, our scripts and tools, and the data we present here are available online under ftp.brics.dk/RS/01/36/Experiments/.

/pdf/cache-oblivious-search-trees-via-binary-trees-of-small-3vy2skv317.pdf

Cache Oblivious Search Trees via Binary Trees of Small Height

We present time and work optimal priority queues for the CREW PRAM, supporting F ind M in in constant time with one processor and M ake Q ueue , I nsert , M eld , F ind M in , E xtract M in , D elete and D ecrease K ey in constant time with O ( log n) processors. A priority queue can be build in time O ( log n) with O (n/ log n) processors. A pipelined version of the priority queues adopt to a processor array of size O ( log n) , supporting the operations M ake Q ueue , I nsert , M eld , F ind M in , E xtract M in , D elete and D ecrease K ey in constant time. By applying the k-bandwidth technique we get a data structure for the CREW PRAM which supports M ulti I nsert k operations in O ( log k) time and M ulti E xtract M in k in O ( log log k) time.

Priority queues on parallel machines

The dispatching problem for object oriented languages is the problem of determining the most specialized method to invoke for calls at run-time. This can be a critical component of execution performance. A number of recent results, including [Muthukrishnan and Muller SODA'96, Ferragina and Muthukrishnan ESA'96, Alstrup et al. FOCS'98], have studied this problem and in particular provided various efficient data structures for the mono-method dispatching problem. A recent paper of Ferragina, Muthukrishnan and de Berg [STOC'99] addresses the multi-method dispatching problem.Our main result is a linear space data structure for binary dispatching that supports dispatching in logarithmic time. Using the same query time as Ferragina et al., this result improves the space bound with a logarithmic factor.

http://www.cs.au.dk/~gerth/papers/itu-tr-01-8.pdf

Gerth Stølting Brodal

Papers

A Simple Greedy Algorithm for Dynamic Graph Orientation

Cache Oblivious Search Trees via Binary Trees of Small Height

Priority queues on parallel machines

Time and Space Efficient Multi-method Dispatching

Priority queues on parallel machines