U. Stege. Gene Trees and Species Trees: The Gene-Duplication Problem is FixedParameter Tractable. In Proceedings of Workshop on Algorithms And Data Structures 1999 (WADS'99), pages 288-293, 1999  Home/Search   Document Details and Download   Summary   Related Articles   Check

....arising from the exemplar analysis of multigene genomes [2] is NP hard even when the number of copies of a given label is at most two. Finally we introduce two novel formulations for the problem of recombining evolutionary trees, extending the notion of the gene duplication problem studied in [8, 11, 9, 10, 6], and we give an exact algorithm (via dynamic programming) for one of the formulations given. 1 Introduction The reconstruction and comparison of evolutionary trees is a main topic of computational biology that poses several new challenging problems to the computer science research community. ....

U. Stege. Gene Trees and Species Trees: The Gene-Duplication Problem is FixedParameter Tractable. In Proceedings of Workshop on Algorithms And Data Structures 1999 (WADS'99), pages 288-293, 1999

....contain paralogies. They introduced the notion of a map between a gene tree and a species tree and suggested a cost function for evaluating a species tree with respect to a gene tree based on edit distance, gene duplication and gene loss. These concepts were further developed and formal ized in [7, 15, 19, 20, 26]. Formally, given a rooted gene tree, G, the problem is to find the species tree, T, that optimizes an evaluation criterion. Several op timality criteria have been proposed (see [3, 4] for a comparative survey) all of which attempt to capture the notion that gene duplication and subsequent loss ....

....tree is unknown. The problem of finding an optimal species tree is NP hard [29] for the optimality criteria considered so far. In contrast, we assume that the true species tree is known and use it to infer the duplication history of a gene tree. While we share some mathemat ical structure with [7, 15, 19, 26], most notably the mapping M, we consider the problem of dating duplication events and generating and evaluating alternate hypotheses. Dating duplication events in rooted and unrooted trees is a computationally tractible problem, which is crucial if we hope to apply this to large data sets. The ....

U. Stege. Gene trees and species trees: The gene- duplication problem is fixed-parameter tractable. In Proceedings of the 6th International Workshop on Algorithms and Data Structures (WADS'99), 1999.

....give a heuristic derived from their approximation algorithm. Further heuristics based upon local search operations are also given in [13] as part of the GeneTree package. It is also known that the Duplication problem is fixed parameter tractable when parameterized by the number of duplications [15]. Here we study, among other things, the Width k Duplication Loss problem. A gene tree has width k with respect to a species tree, if the species tree can explain the gene tree using at most k simultaneously active copies of the gene along any of its branches. The Width k Duplication Loss problem ....

....5 gives a tree we found using our algorithm from Section 5 that scores better under the Duplication Loss model. In total, the tree scores 159 (36 duplications and 123 losses) The overall width is 4 and 26 of the gene trees agreed with the species tree. The [duplications, losses] 0,2] 0,0] [0,15] [0,2] 10,10] 4,18] 7,12] 0,2] 9,12] 0,0] 0,6] 0,2] 3,19] 1,9] 2,14] PROTOZOA FUNGI ARTHROPODA CHLOROPHYCEA EMBRYOPHITA ACOELEMATES ANNELIDA CHONDRICHTHYES ECHINODERMATA OSTEICHTHYES AVES REPTILIA AGNATHA MOLLUSCA AMPHIBIA MAMMALIA Figure 5: One of the best ....

Stege, U. (1999) Gene trees and species trees: The gene-duplication problem is fixed-parameter tractable. Proceedings of the 6th International Workshop on Algorithms and Data Structures (WADS'99), Vancouver, Canada, LNCS 1663.

.... problem: Given a set of species and a set of trees (the gene trees) with their leaves labeled from the species set, the question is, intuitively speaking, to nd a tree (the species tree) that requires a minimum number of gene duplications in order to explain the given gene trees (refer to [41,88] for further details) Note that in this model we count duplication events copying only one gene at a time. Stege [88] gives a xed parameter algorithm for gene duplication, with the allowed number of duplications as the parameter. As a duplication event in evolutionary history copies a piece of ....

....the question is, intuitively speaking, to nd a tree (the species tree) that requires a minimum number of gene duplications in order to explain the given gene trees (refer to [41,88] for further details) Note that in this model we count duplication events copying only one gene at a time. Stege [88] gives a xed parameter algorithm for gene duplication, with the allowed number of duplications as the parameter. As a duplication event in evolutionary history copies a piece of DNA with possibly many genes on it, Fellows et al. 41] study the multiple gene duplication problem. In contrast to ....

U. Stege. Gene trees and species trees: The gene-duplication problem is xedparameter tractable. In Proceedings of the 6th Workshop on Algorithms and Data Structures, number 1663 in Lecture Notes in Computer Science, pages 288-293. Springer-Verlag, 1999.

....contain paralogies. They introduced the notion of a map between a gene tree and a species tree and suggested a cost function for evaluating a species tree with respect to a gene tree based on edit distance, gene duplication and gene loss. These concepts were further developed and formalized in [7, 15, 19, 20, 26]. Formally, given a rooted gene tree, G, the problem is to find the species tree, T , that optimizes an evaluation criterion. Several optimality criteria have been proposed (see [3, 4] for a comparative survey) all of which attempt to capture the notion that gene duplication and subsequent loss ....

....tree is unknown. The problem of finding an optimal species tree is NP hard [29] for the optimality criteria considered so far. In contrast, we assume that the true species tree is known and use it to infer the duplication history of a gene tree. While we share some mathematical structure with [7, 15, 19, 26], most notably the mapping M , we consider the problem of dating duplication events and generating and evaluating alternate hypotheses. Dating duplication events in rooted and unrooted trees is a computationally tractible problem, which is crucial if we hope to apply this to large data sets. The ....

U. Stege. Gene trees and species trees: The geneduplication problem is fixed-parameter tractable. In Proceedings of the 6th International Workshop on Algorithms and Data Structures (WADS'99), 1999.

....problem is known to be approximable to within a factor of 2 in polynomial time [MLZ98] here the authors also give a heuristic derived from their approximation algorithm. It is also known that the Duplication problem is fixed parameter tractable when parameterized by the number of duplications [S99]. Here we study, among other things, the Width k Duplication Loss problem. A gene tree has width k with respect to a species tree, if the species tree can explain the gene tree using at most k simultaneously active copies of the gene along any of its branches. The Width k Duplication Loss problem ....

Stege, U. (1999) Gene trees and species trees: The gene-duplication problem is fixed-parameter tractable. Proceedings of the 6th International Workshop on Algorithms and Data Structures (WADS'99), Vancouver, Canada, LNCS 1663.

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