  Various approaches to alignment-free sequence comparison are based on the
length of exact or inexact word matches between two input sequences. Haubold
{\em et al.} (2009) showed how the average number of substitutions between two
DNA sequences can be estimated based on the average length of exact common
substrings. In this paper, we study the length distribution of $k$-mismatch
common substrings between two sequences. We show that the number of
substitutions per position that have occurred since two sequences have evolved
from their last common ancestor, can be estimated from the position of a local
maximum in the length distribution of their $k$-mismatch common substrings.
