Inferring ancestral gene orders for a family of tandemly arrayed genes

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 four mammals is presented.