We present data-analytic and statistical tools for studying rates of rearrangement of whole genomes and to assess the stability of these methods with changes in the level of resolution of the genomic data. We construct datasets on the numbers of conserved syntenies and conserved segments shared by pairs of animal genomes at different levels of resolution. We fit these data to an evolutionary tree and find the rates of rearrangement on various evolutionary lineages. We document the lack of clocklike behavior of rearrangement processes, the independence of translocation and inversion rates, and the level of resolution beyond which translocations rates are lost in noise due to other processes.