  We study the role of phylogenetic trees on correlations in mutation
processes. Generally, correlations decay exponentially with the generation
number. We find that two distinct regimes of behavior exist. For mutation rates
smaller than a critical rate, the underlying tree morphology is almost
irrelevant, while mutation rates higher than this critical rate lead to strong
tree-dependent correlations. We show analytically that identical critical
behavior underlies all multiple point correlations. This behavior generally
characterizes branching processes undergoing mutation.
