International audienceTree reconciliation methods aim at estimating the evolutionary events that cause discrepancy between gene trees and species trees. We provide a discrete computational model that considers duplications, transfers and losses of genes. The model yields a fast and exact algorithm to infer time consistent and most parsimonious reconciliations. Then we study the conditions under which parsimony is able to accurately infer such events. Overall, it performs well even under realistic rates, transfers being in general less accurately recovered than duplications. An implementation is freely available at http://www.atgc-montpellier.fr/MPR

We present a short proof of the excluded grid theorem of Robertson and Seymour, the fact that a graph has no large grid minor if and only if it has small tree-width. We further propose a very simple obstruction to small tree-width inspired by that proof, showing that a graph has small tree-width if and only if it contains no large highly connected set of vertices. Academic Press

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BackgroundOne of the main aims of phylogenomics is the reconstruction of objects defined in the leaves along the whole phylogenetic tree to minimize the specified functional, which may also include the phylogenetic tree generation. Such objects can include nucleotide and amino acid sequences, chromosomal structures, etc. The structures can have any set of linear and circular chromosomes, variable gene composition and include any number of paralogs, as well as any weights of individual evolutionary operations to transform a chromosome structure. Many heuristic algorithms were proposed for this purpose, but there are just a few exact algorithms with low (linear, cubic or similar) polynomial computational complexity among them to our knowledge. The algorithms naturally start from the calculation of both the distance between two structures and the shortest sequence of operations transforming one structure into another. Such calculation per se is an NP-hard problem.ResultsA general model of chromosomal structure rearrangements is considered. Exact algorithms with almost linear or cubic polynomial complexities have been developed to solve the problems for the case of any chromosomal structure but with certain limitations on operation weights. The computer programs are tested on biological data for the problem of mitochondrial or plastid chromosomal structure reconstruction. To our knowledge, no computer programs are available for this model.ConclusionsExactness of the proposed algorithms and such low polynomial complexities were proved. The reconstructed evolutionary trees of mitochondrial and plastid chromosomal structures as well as the ancestral states of the structures appear to be reasonable.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-016-0878-z) contains supplementary material, which is available to authorized users.