The Statistical Significance of Max-Gap Clusters

Identifying gene clusters, genomic regions that share local similarities in gene organization, is a prerequisite for many different types of genomic analyses, including operon prediction, reconstruction of chromosomal rearrangements, and detection of whole-genome duplications. A number of formal definitions of gene clusters have been proposed, as well as methods for finding such clusters and/or statistical tests for determining their significance. Unfortunately, there is very little overlap between previously published rigorous analytical statistical tests and the definitions used in practice. In this paper, we consider the max-gap cluster: a contiguous region containing a maximal set of homologs, where the number of non-homologous genes between pairs of adjacent homologs is never greater than a predefined, fixed parameter, g. Although this is one of the models most widely used in practice, currently the statistical significance of max-gap clusters can only be evaluated using Monte Carlo simulations because no analytical statistical tests have been developed for it. We give exact expressions for the probability of observing such a cluster by chance, assuming a simple reference-region scenario and random gene order, as well as more efficient methods for approximating this probability. We use these methods to identify which regions of the parameter space yield clusters that are statistically significant. Finally, we discuss some of the challenges in extending this model to whole-genome comparison.