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 specie s and their common ancestor can be made by comparing map positions of marke r loci. Statistical methods for doing so are based on a random-breakage mod el of chromosomal rearrangement. The model treats all modes of chromosome r earrangement alike, and it assumes that chromosome boundaries and breakpoin ts are distributed randomly along a single genomic interval. Here we use si mulation and numerical analysis to test the validity of these model assumpt ions. 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 trans location alone. But when marker density is low relative to the number of ch romosomes, and when rearrangements occur by both translocation and inversio n, the number of breakpoints is underestimated. The underestimate arises be cause rearranged segments may contain markers, vet the rearranged segments may, nevertheless, be undetected. Variances of the estimate of numbers of b reakpoints decrease rapidly as markers are added to the comparative maps, b ut are less influenced by the number or type of chromosomal rearrangement s eparating 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 hete rogeneity in the rate of chromosomal rearrangement is also investigated. Re sults are interpreted with respect to the amount of marker information requ ired to make accurate inferences about chromosomal evolution.