Abstract not found

Abstract. Phylogenetic reconstruction from gene-rearrangement data has seen increased attention over the last five years. Existing methods are limited computationally and by the assumption (highly unrealistic in practice) that all genomes have the same gene content. We have recently shown that we can scale our reconstruction tool, GRAPPA, to instances with up to a thousand genomes with no loss of accuracy and at minimal computational cost. Computing genomic distances between two genomes with unequal gene contents has seen much progress recently, but that progress has not yet been reflected in phylogenetic reconstruction methods. In this paper, we present extensions to our GRAPPA approach that can handle limited numbers of duplications (one of the main requirements for analyzing genomic data from organelles) and a few deletions. Although GRAPPA is based on exhaustive search, we show that, in practice, our bounding functions suffice to prune away almost all of the search space (our pruning rates never fall below 99.995%), resulting in high accuracy and fast running times. The range of values within which we have tested our approach encompasses mitochondria and chloroplast organellar genomes, whose phylogenetic analysis is providing new insights on evolution. Keywords computational biology, phylogenetic reconstruction, gene-order data, whole-genome data, signed

The comparison of the gene orders in a set of genomes can be used to infer their phylogenetic relationships and to reconstruct ancestral gene orders. For three genomes this is done by solving the "median problem for breakpoints"; this solution can then be incorporated into a routine for estimating optimal gene orders for all the ancestral genomes in a fixed phylogeny. For the di#cult (and most prevalent) case where the genomes contain partially di#erent sets of genes, we present a general heuristic for the median problem for induced breakpoints. A fixed-phylogeny optimization based on this is applied in a phylogenetic study of a set of completely sequenced protist mitochondrial genomes, confirming some of the recent sequence-based groupings which have been proposed and, conversely, confirming the usefulness of the breakpoint method as a phylogenetic tool even for small genomes.

In this paper, we study the Reversal Median Problem (RMP), which arises in computational biology and is a basic model for the reconstruction of evolutionary trees. Given q genomes, RMP calls for another genome such that the sum of the reversal distances between this genome and the given ones is minimized. So far, the problem was considered too complex to derive mathematical models useful for its analysis and solution. We provide a powerful graph theoretic relaxation of RMP, essentially calling for a perfect matching in a graph that forms the maximum number of cycles jointly with q given perfect matchings.

Evolution operates on whole genomes through... In this paper we present two new methods of character coding for parsimony-based analysis of genomic rearrangements: one called MPBE-2, and a new parsimony-based method which we call MPME (based on an encoding of Bryant), both variants of the MPBE method. We then conduct computer simulations to compare this class of methods to distance-based methods (NJ under various distance measures). Our empirical results show that two of our new methods return highly accurate estimates of the true tree, outperforming the other methods significantly, especially when close to saturation

Abstract. In this paper, we study lower bound techniques for branchand-bound algorithms for maximum parsimony, with a focus on gene order data. We give a simple O(n 3) time dynamic programming algorithm for computing the maximum circular ordering lower bound, where n is the number of leaves. The well-known gene order phylogeny program, GRAPPA, currently implements two heuristic approximations to this lower bounds. Our experiments show a significant improvement over both these methods in practice. Next, we show that the linear programmingbased lower bound of Tang and Moret (Tang and Moret, 2005) can be greatly simplified, allowing us to solve the LP in O ∗ n 3) time in the worst case, and in O ∗ (n 2.5) time amortized over all binary trees. Finally, we formalize the problem of computing the circular ordering lower bound, when the tree topologies are generated bottom-up, as a Path-Constrained Traveling Salesman Problem, and give a polynomial-time 3-approximation algorithm for it. This is a special case of the more general Precedence-Constrained Travelling Salesman Problem and has not previously been studied, to the best of our knowledge. 1

The study of genome rearrangements, the evolutionary events that change the order and strandedness of genes within genomes, presents new opportunities for discoveries about deep evolutionary events. The best software so far, GRAPPA, solves breakpoint and inversion phylogenies by scoring each tree topology through iterative improvements of internal node gene orders. We find that the greedy hill-climbing approach means the accuracy is limited because of multiple local optima. To address this problem, we propose integration GRAPPA with MPME, a string encoding of gene adjacency relationships whose optimal internal node assignments can be determined globally in polynomial time, to provide better initializations for GRAPPA. In simulation studies, the new algorithm yields shorter tree lengths and better accuracy in phylogeny reconstruction. 1