Measures for the exceptionality of gene order in conserved genomic regions

We propose in this article three measures for quantifying the exceptionality of gene order in conserved genomic regions found by the reference region approach. The three measures are based on the transposition distance in the permutation group. We obtain analytic expressions for their distribution in the case of a random uniform permutation, i.e. under the null hypothesis of random gene order. Our results can be used to increase the power of the significance tests for gene clusters which take into account only the proximity of the orthologous genes and not their order.