  We present a method to quantify spatial fluctuations of the substitution rate
on different length scales throughout genomes of eukaryotes. The fluctuations
on large length scales are found to be predominantly a consequence of a
coarse-graining effect of fluctuations on shorter length scales. This is
verified for both the mouse and the human genome. We also found that both
species show similar standard deviation of fluctuations even though their mean
substitution rate differs by a factor of two. Our method furthermore allows to
determine time-resolved substitution rate maps from which we can compute
auto-correlation functions in order to quantify how fast the spatial
fluctuations in substitution rate change in time.
