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Steps Toward Accurate Reconstructions of Phylogenies from GeneOrder Data
 J. COMPUT. SYST. SCI
, 2002
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Approximating the expected number of inversions given the number of breakpoints, Algorithms
 in Bioinformatics, Proceedings of WABI 2002, LNCS 2452
, 2002
"... Abstract We look at a problem with motivation from computational biology: Given the number of breakpoints in a permutation (representing a gene sequence), compute the expected number of inversions that have occured. For this problem, we obtain an analytic approximation that is correct within a perce ..."
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Abstract We look at a problem with motivation from computational biology: Given the number of breakpoints in a permutation (representing a gene sequence), compute the expected number of inversions that have occured. For this problem, we obtain an analytic approximation that is correct within a percent or two. For the inverse problem, computing the expected number of breakpoints after any number of inversions, we obtain an analytic approximation with an error of less than a hundredth of a breakpoint. 1
Expected number of inversions after a sequence of random adjacent transpositions — an exact expression
 Discrete Mathematics
, 2005
"... Abstract. A formula for calculating the expected number of inversions after t random adjacent transpositions has been presented by Eriksson et al. We have improved their result by determining a formula for the unknown integer sequence dr that was used in their formula and also made the formula valid ..."
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Cited by 4 (1 self)
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Abstract. A formula for calculating the expected number of inversions after t random adjacent transpositions has been presented by Eriksson et al. We have improved their result by determining a formula for the unknown integer sequence dr that was used in their formula and also made the formula valid for large t. Résumé. Une formule pour calculer le nombre attendu d’inversions après t transpositions adjacentes aléatoires a été présentée par Eriksson et al. Nous avons amélioré ce résultat en déterminant une formule pour la séquence inconnue d’entiers dr, qui était utilisée dans leur formule et qui rendait la formule valide lorsque t prend une grande valeur. 1.
Estimating
"... Vol. 24 ISMB 2008, pages i114–i122 doi:10.1093/bioinformatics/btn148 ..."
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Vol. 24 ISMB 2008, pages i114–i122 doi:10.1093/bioinformatics/btn148
MAXIMUM LIKELIHOOD PHYLOGENETIC RECONSTRUCTION FROM HIGHRESOLUTION WHOLEGENOME DATA AND A TREE OF 68 EUKARYOTES
"... The rapid accumulation of wholegenome data has renewed interest in the study of the evolution of genomic architecture, under such events as rearrangements, duplications, losses. Comparative genomics, evolutionary biology, and cancer research all require tools to elucidate the mechanisms, history, a ..."
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The rapid accumulation of wholegenome data has renewed interest in the study of the evolution of genomic architecture, under such events as rearrangements, duplications, losses. Comparative genomics, evolutionary biology, and cancer research all require tools to elucidate the mechanisms, history, and consequences of those evolutionary events, while phylogenetics could use wholegenome datatoenhanceitspictureoftheTreeofLife.Currentapproachesintheareaofphylogeneticanalysis are limited to very small collections of closely related genomes using lowresolution data (typically a few hundred syntenic blocks); moreover, these approaches typically do not include duplication and loss events. We describe a maximum likelihood (ML) approach for phylogenetic analysis that takes into account genome rearrangements as well as duplications, insertions, and losses. Our approach can handle highresolution genomes (with 40,000 or more markers) and can use in the same analysis genomes with very different numbers of markers. Because our approach uses a standard ML reconstruction program (RAxML), it scales up to large trees. We present the results of extensive testing on both simulated and real data showing that our approach returns very accurate results very quickly. In particular, we analyze a dataset of 68 highresolution eukaryotic genomes, with from 3,000 to 42,000 genes, from the eGOB database; the analysis, including bootstrapping, takes just 3 hours on a desktop system and returns a tree in agreement with all well supported branches, while also suggesting resolutions for some disputed placements.
EVOLUTIONARY FIXED POINT DISTANCE PROBLEMS
, 2009
"... Sammanfattning. Ett av de grundläggande problemen i jämförande genomik är att beräkna det sanna evolutionära avst˚andet mellan tv˚a genom. Flera olika uppskattningar av s˚adana avst˚and finns. I [2] introducerades en metod som grundar sig p˚a ett avst˚andsm˚att, transpositionssavst˚andet, i den symm ..."
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Sammanfattning. Ett av de grundläggande problemen i jämförande genomik är att beräkna det sanna evolutionära avst˚andet mellan tv˚a genom. Flera olika uppskattningar av s˚adana avst˚and finns. I [2] introducerades en metod som grundar sig p˚a ett avst˚andsm˚att, transpositionssavst˚andet, i den symmetriska gruppen. I korthet används väntevärdet av transpositionsavst˚andet av en permutation bildad av att t slumpmässiga transpositioner appliceras p˚a identiteten i Sn, för att ge en uppskattning av det sanna evolutionära avst˚andet mellan tv˚a genom. I den här uppsatsen betraktar vi ett annat avst˚andsm˚att p˚a den symmetriska gruppen, fixpunktsavst˚andet. Vi beräknar väntevärdet och variansen av fixpunktsavst˚andet av en permutation bildad genom att slumpmässigt utvalda transpositioner har multiplicerats ihop. Vi utför vissa numeriska experiment p˚a distributionen av fixpunktsavst˚and och ger en beskrivning av distributionen. Vi ger även en polynomiell algoritm för problemet att bestämma en permutation som har minimalt totalt avst˚and till en mängd av givna permutationer. Abstract. One of the basic problems in comparative genomics is the computation of the true evolutionary distance between two genomes. Several different estimates of such distances exist. One method, introduced in [2], makes use of a distance measure in the symmetric group called the transposition distance. Briefly, the expected value of the transposition distance of a permutation formed by applying t
Inferring gene order phylogenies by learning ancestral adjacencies
"... Abstract. As genomes evolve over very long times, genes get rearranged which changes their order along the genome. The resulting differing orders for various species provide evidence of their phylogenetic relationships, particularly, from long ago. Indeed, this type of data is increasingly useful in ..."
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Abstract. As genomes evolve over very long times, genes get rearranged which changes their order along the genome. The resulting differing orders for various species provide evidence of their phylogenetic relationships, particularly, from long ago. Indeed, this type of data is increasingly useful in sorting out evolutionary relationships [16, 17, 23]. In this paper, we give the first polynomial time algorithm for inferring phylogenies from logarithmic length geneorder data. We provide an implementation of a version of this algorithm which is effective in the high mutation regimes which are difficult for previous polynomial time approaches [17]. Our method takes advantage of reconstructing internal sequences as does the branch and bound approach in GRAPPA [16, 17]. Our polynomial time runtime versus GRAPPA’s exponential time is dramatic in practice as well as theory. The heart of our contribution is a method for estimating distance between genomes and an associated learning method to infer geneorder data at internal nodes. This leads to a polynomial time algorithm for reconstructing a phylogeny on a set of n taxa from geneorder data consisting of N = O(log n) genes. Our algorithm follows the structure of the algorithm by Mihaescu et al. [15] which applies to character data. We replace the estimators and learning subroutines in the Mihaescu algorithm with methods that work with gene order. We implement and test a version of our method against the best previous polynomial time method on simulated data. Our method does considerably better in high evolution conditions. For low evolution conditions, we don’t do as well as previous methods.