Natural Parameter Values for Generalized Gene Adjacency

Given the gene orders in two modern genomes, it may be difficult to decide if some genes are close enough in both genomes to infer some ancestral proximity or some functional relationship. Current methods all depend on arbitrary parameters. We explore a class of gene proximity criteria and find two kinds of natural values for their parameters. One kind has to do with the parameter value where the expected information contained in two genomes about each other is maximized. The other kind of natural value has to do with parameter values beyond which all genes are clustered. We analyze these using combinatorial and probabilistic arguments as well as simulations.