The Distribution of Inversion Lengths in Bacteria

The distribution of the lengths of genomic segments inverted during the evolutionary divergence of two species cannot be inferred directly from the output of genome rearrangement algorithms, due to the rapid loss of signal from all but the shortest inversions. The number of short inversions produced by these algorithms, however, particularly those involving a single gene, is relatively reliable. To gain some insight into the shape of the inversion-length distribution we first apply a genome rearrangement algorithm to each of 32 pairs of bacterial genomes. For each pair we then simulate their divergence using a test distribution to generate the inversions and use the simulated genomes as input to the reconstruction algorithm. It is the comparison between the algorithm output for the real pair of genomes and the simulated pair which is used to assess the test distribution. We find that simulations based on the exponential distribution cannot provide a good fit, but that simulations based on a gamma distribution can account for both single-gene inversions and short inversions involving at most 20 genes, and we conclude that the shape of latter distribution corresponds well to the true distribution at least for small inversion lengths.