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62
Haplotyping as Perfect Phylogeny: Conceptual Framework and Efficient Solutions (Extended Abstract)
, 2002
"... The next highpriority phase of human genomics will involve the development of a full Haplotype Map of the human genome [12]. It will be used in largescale screens of populations to associate specific haplotypes with specific complex geneticinfluenced diseases. A prototype Haplotype Mapping strat ..."
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Cited by 109 (10 self)
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The next highpriority phase of human genomics will involve the development of a full Haplotype Map of the human genome [12]. It will be used in largescale screens of populations to associate specific haplotypes with specific complex geneticinfluenced diseases. A prototype Haplotype Mapping strategy is presently being finalized by an NIH workinggroup. The biological key to that strategy is the surprising fact that genomic DNA can be partitioned into long blocks where genetic recombination has been rare, leading to strikingly fewer distinct haplotypes in the population than previously expected [12, 6, 21, 7]. In this paper
Optimal, efficient reconstruction of phylogenetic networks with constrained recombination
 J. Bioinformatics and Computational Biology
, 2003
"... gusfield,eddhu¡ A phylogenetic network is a generalization of a phylogenetic tree, allowing structural properties that are not treelike. With the growth of genomic data, much of which does not fit ideal tree models, there is greater need to understand the algorithmics and combinatorics of phylogenet ..."
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Cited by 94 (13 self)
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gusfield,eddhu¡ A phylogenetic network is a generalization of a phylogenetic tree, allowing structural properties that are not treelike. With the growth of genomic data, much of which does not fit ideal tree models, there is greater need to understand the algorithmics and combinatorics of phylogenetic networks [10, 11]. However, to date, very little has been published on this, with the notable exception of the paper by Wang et al.[12]. Other related papers include [4, 5, 7] We consider the problem introduced in [12], of determining whether the sequences can be derived on a phylogenetic network where the recombination cycles are node disjoint. In this paper, we call such a phylogenetic network a “galledtree”. By more deeply analysing the combinatorial constraints on cycledisjoint phylogenetic networks, we obtain an efficient algorithm that is guaranteed to be both a necessary and sufficient test for the existence of a galledtree for the data. If there is a galledtree, the algorithm constructs one and obtains an implicit representation of all the galled trees for the data, and can create these in linear time for each one. We also note two additional results related to galled trees: first, any set of sequences that can be derived on a galled tree can be derived on a true tree (without recombination cycles), where at most one back mutation is allowed per site; second, the site compatibility problem (which is NPhard in general) can be solved in linear time for any set of sequences that can be derived on a galled tree. The combinatorial constraints we develop apply (for the most part) to nodedisjoint cycles in any phylogenetic network (not just galledtrees), and can be used for example to prove that a given site cannot be on a nodedisjoint cycle in any phylogenetic network. Perhaps more important than the specific results about galledtrees, we introduce an approach that can be used to study recombination in phylogenetic networks that go beyond galledtrees.
Reconstructing reticulate evolution in species  theory and practice
 In Proc. of 8’th Annual International Conference on Computational Molecular Biology
, 2004
"... We present new methods for reconstructing reticulate evolution of species due to events such as horizontal transfer or hybrid speciation; both methods are based upon extensions of Wayne Maddison’s approach in his seminal 1997 paper. Our first method is a polynomial time algorithm for constructing ph ..."
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Cited by 46 (7 self)
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We present new methods for reconstructing reticulate evolution of species due to events such as horizontal transfer or hybrid speciation; both methods are based upon extensions of Wayne Maddison’s approach in his seminal 1997 paper. Our first method is a polynomial time algorithm for constructing phylogenetic networks from two gene trees contained inside the network. We allow the network to have an arbitrary number of reticulations, but we limit the reticulation in the network so that the cycles in network are nodedisjoint (“galled”). Our second method is a polynomial time algorithm for constructing networks with one reticulation, where we allow for errors in the estimated gene trees. Using simulations, we demonstrate improved performance of this method over both NeighborNet and Maddison’s method. 1
A Fundamental Decomposition Theory for Phylogenetic Networks and Incompatible Characters
 In proc Research in Computational Molecular Biology
, 2005
"... ..."
Reconstruction of reticulate networks from gene trees
 In Proceedings of the Ninth International Conference on Research in Computational Molecular Biology (RECOMB
, 2005
"... Abstract. One of the simplest evolutionary models has molecular sequences evolving from a common ancestor down a bifurcating phylogenetic tree, experiencing pointmutations along the way. However, empirical analyses of different genes indicate that the evolution of genomes is often more complex than ..."
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Cited by 33 (14 self)
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Abstract. One of the simplest evolutionary models has molecular sequences evolving from a common ancestor down a bifurcating phylogenetic tree, experiencing pointmutations along the way. However, empirical analyses of different genes indicate that the evolution of genomes is often more complex than can be represented by such a model. Thus, the following problem is of significant interest in molecular evolution: Given a set of molecular sequences, compute a reticulate network that explains the data using a minimal number of reticulations. This paper makes four contributions toward solving this problem. First, it shows that there exists a onetoone correspondence between the tangles in a reticulate network, the connected components of the associated incompatibility graph and the netted components of the associated splits graph. Second, it provides an algorithm that computes a most parsimonious reticulate network in polynomial time, if the reticulations contained in any tangle have a certain overlapping property, and if the number of reticulations contained in any given tangle is bounded by a constant. Third, an algorithm for drawing reticulate networks is described and a robust and flexible implementation of the algorithms is provided. Fourth, the paper presents a statistical test for distinguishing between reticulations due to hybridization, and ones due to other events such as lineage sorting or treeestimation error. 1
A survey of computational methods for determining haplotypes
 Lecture Notes in Computer Science (2983): Computational Methods for SNPs and Haplotype Inference
, 2004
"... Abstract. It is widely anticipated that the study of variation in the human genome will provide a means of predicting risk of a variety of complex diseases. Single nucleotide polymorphisms (SNPs) are the most common form of genomic variation. Haplotypes have been suggested as one means for reducing ..."
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Cited by 33 (4 self)
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Abstract. It is widely anticipated that the study of variation in the human genome will provide a means of predicting risk of a variety of complex diseases. Single nucleotide polymorphisms (SNPs) are the most common form of genomic variation. Haplotypes have been suggested as one means for reducing the complexity of studying SNPs. In this paper we review some of the computational approaches that have been taking for determining haplotypes and suggest new approaches. 1
Computing the minimum number of hybridization events for a consistent evolutionary history
, 2007
"... ..."
Comparison of TreeChild Phylogenetic Networks
, 708
"... Abstract. Phylogenetic networks are a generalization of phylogenetic trees that allow for the representation of nontreelike evolutionary events, like recombination, hybridization, or lateral gene transfer. While much progress has been made to find practical algorithms for reconstructing a phylogene ..."
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Cited by 24 (5 self)
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Abstract. Phylogenetic networks are a generalization of phylogenetic trees that allow for the representation of nontreelike evolutionary events, like recombination, hybridization, or lateral gene transfer. While much progress has been made to find practical algorithms for reconstructing a phylogenetic network from a set of sequences, all attempts to endorse a class of phylogenetic networks (strictly extending the class of phylogenetic trees) with a wellfounded distance measure have, to the best of our knowledge, failed so far. In this paper, we present and study a new meaningful class of phylogenetic networks, called treechild phylogenetic networks, and we provide an injective representation of these networks as multisets of vectors of natural numbers, their path multiplicity vectors. We then use this representation to define a distance on this class that extends the wellknown RobinsonFoulds distance for phylogenetic trees, and to give an alignment method for pairs of networks in this class. Simple, polynomial algorithms for reconstructing a treechild phylogenetic network from its path multiplicity vectors, for computing the distance between two treechild phylogenetic networks, and for aligning a pair of treechild phylogenetic networks, are provided. They have been implemented as a Perl package and a Java applet, and they are available at the Supplementary Material web page. 1
The Number of Recombination Events in a Sample History: Conflict Graph and Lower Bounds
, 2004
"... We consider the following problem: Given a set of binary sequences, determine lower bounds on the minimum number of recombinations required to explain the history of the sample, under the infinitesites model of mutation. The problem has implications for finding recombination hotspots and for the A ..."
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Cited by 23 (1 self)
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We consider the following problem: Given a set of binary sequences, determine lower bounds on the minimum number of recombinations required to explain the history of the sample, under the infinitesites model of mutation. The problem has implications for finding recombination hotspots and for the Ancestral Recombination Graph reconstruction problem [29]. Hudson and Kaplan [15] gave a lower bound based on the fourgamete test. In practice, their bound Rm often greatly underestimates the minimum number of recombinations. The problem was recently revisited by Myers and Griffiths [22], who introduced two new lower bounds Rh and Rs which are provably better, and also yield good bounds in practice. However, the worstcase complexities of their procedures for computing Rh and Rs are exponential and superexponential, respectively. In this paper, we show that the number of nontrivial connected components, Rc, in the conflict graph [4] for a given set of sequences, computable in time Oðnm 2 Þ, is also a lower bound on the minimum number of recombination events. We show that in many cases, Rc is a better bound than Rh. The conflict graph was used by Gusfield et al. [4] to obtain a polynomial time algorithm for the galled tree problem, which is a special case of the Ancestral Recombination Graph (ARG) reconstruction problem. Our results also offer some insight into the structural properties of this graph and are of interest for the general Ancestral Recombination Graph reconstruction problem.
Efficient computation of close lower and upper bounds on the minimum number of needed recombinations in the evolution of biological sequences
 Bioinformatics
, 2005
"... or population genetics ..."