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)

We show that the problem of computing all contiguous k-ary compositions of a sequence of n values under an associative and commutative operator requires 3(k−1)/ (k+1)n − O(k) operations. For the operator max we show in contrast that in the decision tree model the complexity is (1+ Theta(1/sqrt(k)) n − O(k). Finally we show that the complexity of the corresponding on-line problem for the operator max is (2 − 1/(k−1)) n − O(k).

/pdf/the-complexity-of-computing-the-k-ary-composition-of-a-28toowu3ts.pdf

The Complexity of Computing the k-ary Composition of a Binary Associative Operator

We present time and work optimal priority queues for the CREW PRAM, supporting FindMin in constant time with one processor and MakeQueue, Insert, Meld, Findmin, Extractmin, Delete and DecreaseKey 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 and k elements can be inserted into a priority queue in time O(log k) with O((log n + k)/log k) processors. With a slowdown of O(log log n) in time the priority queues adopt to the EREW PRAM by only increasing the required work by a constant factor. A pipelined version of the priority queues adopt to a processor array of size O(log n), supporting the operations MakeQueue, Insert, Meld, FindMin, Extractmin, Delete and DecreaseKey in constant time.

Priority Queues on Parallel Machines

We present a new overlay, called the Deterministic Decentralized tree (D 2-tree). The D 2-tree compares favourably to other overlays for the following reasons: (a) it provides matching and better complexities, which are deterministic for the supported operations; (b) the management of nodes (peers) and elements are completely decoupled from each other; and (c) an efficient deterministic load-balancing mechanism is presented for the uniform distribution of elements into nodes, while at the same time probabilistic optimal bounds are provided for the congestion of operations at the nodes.

D 2 -Tree: A New Overlay with Deterministic Bounds

We study the design of efficient data structures. In particular we focus on the design of data structures where each operation has a worst case efficient implementations. The concrete problems we consider are partial persistence, implementation of priority queues, and implementation of dictionaries. The first problem we consider is how to make bounded in-degree and out-degree data structures partially persistent, i.e., how to remember old versions of a data structure for later access. A node copying technique of Driscoll et al. supports update steps in amortized constant time and access steps in worst case constant time. The worst case time for an update step can be linear in the size of the structure. We show how to extend the technique of Driscoll et al. such that update steps can be performed in worst case constant time on the pointer machine model. We present two new comparison based priority queue implementations, with the following properties. The first implementation supports the operations FindMin, Insert and Meld in worst case constant time and Delete and DeleteMin in worst case time O(log n). The priority queues can be implemented on the pointer machine and require linear space. The second implementation achieves the same worst case performance, but furthermore supports DecreaseKey in worst case constant time. The space requirement is again linear, but the implementation requires auxiliary arrays of size O(log n). Our bounds match the best known amortized bounds (achieved by respectively binomial queues and Fibonacci heaps). The data structures presented are the first achieving these worst case bounds, in particular supporting Meld in worst case constant time. We show that these time bounds are optimal for all implementations supporting Meld in worst case time o(n). We also present a tradeoff between the update time and the query time of comparison based priority queue implementations. Finally we show that any randomized implementation with expected amortized cost t comparisons per Insert and Delete operation has expected cost at least n/2O(t) comparisons for FindMin. Next we consider how to implement priority queues on parallel (comparison based) models. We present time and work optimal priority queues for the CREW PRAM, supporting FindMin, Insert, Meld, DeleteMin, Delete and DecreaseKey in constant time with O(log n) processors. Our implementation is the first supporting all of the listed operations in constant time. To be able to speed up Dijkstra’s algorithm for the single-source shortest path problem we present a different parallel priority data structure. With this specialized data structure we give a parallel implementation of Dijkstra’s algorithm which runs in O(n) time and performs O(m log n) work on a CREW PRAM. This represents a logarithmic factor improvement for the running time compared with previous approaches. We also consider priority queues on a RAM model which is stronger than the comparison model. The specific problem is the maintenance of a set of n integers in the range 0..2 − 1 under the operations Insert, Delete, FindMin, FindMax and Pred (predecessor query) on a unit cost RAM with word size w bits. The RAM operations used are addition, left and right bit shifts,

/pdf/worst-case-efficient-data-structures-2nlur1y3tj.pdf

Worst Case Efficient Data Structures

Point location is an extremely well-studied problem both in internal memory models and recently also in the external memory model. In this paper, we present an I/O-efficient dynamic data structure for point location in general planar subdivisions. Our structure uses linear space to store a subdivision with N segments. Insertions and deletions of segments can be performed in amortized O(log  B N) I/Os and queries can be answered in $O(\log_{B}^{2} N)$ I/Os in the worst-case. The previous best known linear space dynamic structure also answers queries in $O(\log_{B}^{2} N)$ I/Os, but only supports insertions in amortized $O(\log_{B}^{2} N)$ I/Os. Our structure is also considerably simpler than previous structures.

Gerth Stølting Brodal

Papers

The Complexity of Computing the k-ary Composition of a Binary Associative Operator

Priority Queues on Parallel Machines

D 2 -Tree: A New Overlay with Deterministic Bounds

Worst Case Efficient Data Structures

External Memory Planar Point Location with Logarithmic Updates