Natural parameter values for generalized gene adjacency

As genomes of related species diverge through rearrangement mutations, groups of genes once tightly clustered on a chromosome will tend to disperse to remote locations on this chromosome or even onto other chromosomes. Even if most rearrangements are local, e.g., small inversions or transpositions, after a long enough period of time their chromosomal locations may reflect little or none of their original proximity. Given the gene orders in two modern genomes, then, it may be difficult to decide if some set of genes are close enough in both genomes to infer some ancestral proximity or some functional relationship. There are a number of formal criteria for gene clustering in two or more organisms, giving rise to cluster detection algorithms and statistical tests for the significance of clusters. These methods all depend on one or more arbitrary parameters as well as n, the number of genes in common in the two genomes. The various parameters control, in different ways, the proximity of the genes on the chromosome in order to be considered a cluster. Change the parameters and the number of clusters may change, as may the content of each cluster. We explore a two-parameter class of gene proximity criteria, and find natural values for these parameters. One has to do with the parameter value where the expected information contained in two genomes about each other is maximized. The other has to do with parameter values beyond which all genes are clustered. We analyse these using combinatorial and probabilistic arguments as well as simulations