Comparative genomics, marker density and statistical analysis of chromosome rearrangements.

Estimates of the number of chromosomal breakpoints that have arisen (e.g., by translocation and inversion) in the evolutionary past between two species and their common ancestor can be made by comparing map positions of marker loci. Statistical methods for doing so are based on a random-breakage model of chromosomal rearrangement. The model treats all modes of chromosome rearrangement alike, and it assumes that chromosome boundaries and breakpoints are distributed randomly along a single genomic interval. Here we use simulation and numerical analysis to test the validity of these model assumptions. Mean estimates of numbers of breakpoints are close to those expected under the random-breakage model when marker density is high relative to the amount of chromosomal rearrangement and when rearrangements occur by translocation alone. But when marker density is low relative to the number of chromosomes, and when rearrangements occur by both translocation and inversion, the number of breakpoints is underestimated. The underestimate arises because rearranged segments may contain markers, yet the rearranged segments may, nevertheless, be undetected. Variances of the estimate of numbers of breakpoints decrease rapidly as markers are added to the comparative maps, but are less influenced by the number or type of chromosomal rearrangement separating the species. Variances obtained with simulated genomes comprised of chromosomes of equal length are substantially lower than those obtained when chromosome size is unconstrained. Statistical power for detecting heterogeneity in the rate of chromosomal rearrangement is also investigated. Results are interpreted with respect to the amount of marker information required to make accurate inferences about chromosomal evolution.