Genomic Divergence through Gene Rearrangement 429

Measures of similarities and distances among nucleotide or amino acid sequences have been used to find related regions in long sequences, to test for homology, to assess phylogenetic and functional relationships, and to estimate divergence time between pairs of evolutionarily related sequences. This last use especially invokes a model, possibly implicit and including a random component, of sequence change through nucleotide (or amino acid) replacement and insertion or deletion of single nucleotides or small blocks of contiguous nucleotides. Modeling genetic events by these mechanisms, however, cannot reflect the more macroscopic processes of evolutionary divergence of organisms, such as duplication, inversion, and transposition (shuffling) of parts of the genome. Although little comprehensive data are available as yet to study evolution at the level of entire genomes, the megasequencing projects now being set up will be producing genomic sequences in the near future. In this chapter we discuss simple probabilistic models for genome shuffling introduced by Sankoff and Goldstein’ and apply them to the assessment of relationships among a number of bacterial genomes. Lacking complete nucleotide sequences at this level, we assess our methodology on genetic map data. See Nadeau and Tayloti and Sakharov and Valeev3 for comparable approaches.