We consider two algorithmic questions related to the evolution of gene families. First, given a gene tree for a gene family, can the evolutionary history of this family be explained with only speciation and duplication events? Such gene trees are called DS-trees. We show that this question can be answered in linear time, and that a DS-tree induces a single species tree. We then study a natural extension of this problem: what is the minimum number of gene losses involved in an evolutionary history leading to an observed gene tree or set of gene trees? Based on our characterization of DS-trees, we propose a heuristic for this problem, and evaluate it on a dataset of plants gene families and on simulated data.

Tandemly arrayed genes (TAG) constitute a large fraction of most genomes and play important biological roles. They evolve through unequal recombination, which places duplicated genes next to the original ones (tandem duplications). Many algorithms have been proposed to infer a tandem duplication history for a TAG cluster. However, the presence of different transcriptional orientations in many clusters highlights the fact that processes such as inversions also contribute to their evolution. Moreover, existing algorithms are restricted to the study of TAGs evolution in a single species (only paralogous genes are considered). To circumvent these limitations, we consider an evolutionary model for TAGs involving duplication, gene loss, inversion and speciation events. A general framework to infer ancestral gene orders that minimize the number of inversions in the whole evolutionary history is presented. At the methodological level, this paper integrates three approaches to genome evolution: the duplication tree reconstruction, the gene tree/species tree reconciliation theory, and the concept of inversion median used in order-based phylogeny reconstruction. An application on a cluster of olfactory receptor genes in 4 mammals is presented.

Abstract. Tandemly arrayed genes (TAG) constitute a large fraction of most genomes and play important biological roles. They evolve through unequal recombination, which places duplicated genes next to the original ones (tandem duplications). Many algorithms have been proposed to infer a tandem duplication history for a TAGs cluster in a single species. However, the presence of different transcriptional orientations in most TAGs clusters highlight the fact that processes such as inversion also contribute to their evolution. This makes those algorithms inapplicable in many cases. To circumvent this limitation, we proposed an extended evolutionary model which includes inversions and presented a branch-and-bound algorithm allowing to infer a most parsimonious scenario of evolution for a given TAGs cluster. Here, we generalize this model to multiple species and present a general framework to infer ancestral gene orders that minimize the number of inversions in the whole evolutionary history. An application on a pair of human-rat TAGs clusters is presented. 1

We consider two algorithmical questions related to the evolution of gene families. First, given a gene tree for a gene family, can the evolutionary history of this family be explained with only speciation and duplication events? Such gene trees are called DS-trees. We show that this question can be answered in linear time, and that a DS-tree induces a single species tree. We then study a natural extension of this problem: what is the minimum number of gene losses involved in an evolutionary history leading to an observed gene tree or set of gene trees? Based on our characterization of DS-trees, we propose a heuristic for this problem, and Background. Genes are the major building blocks of genomic sequences, containing the information necessary to produce all the proteins and non-coding RNAs of a cell. Genes, in a genome or across genomes, that are related by sequence or function similarity are called homologs and grouped into a gene family. The completed sequencing of a variety of genomes

Gene families are composed of homologous genes that share a common ancestor. Each is the result of an (unknown) evolution scenario involving gene duplication, speciation and gene loss. Importance of knowing the evolutionary scenario of each gene family

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