  Predicting the ancestral sequences of a group of homologous sequences related
by a phylogenetic tree has been the subject of many studies, and numerous
methods have been proposed to this purpose. Theoretical results are available
that show that when the mutation rate become too large, reconstructing the
ancestral state at the tree root is no longer feasible. Here, we also study the
reconstruction of the ancestral changes that occurred along the tree edges. We
show that, depending on the tree and branch length distribution, reconstructing
these changes (i.e. reconstructing the ancestral state of all internal nodes in
the tree) may be easier or harder than reconstructing the ancestral root state.
However, results from information theory indicate that for the standard Yule
tree, the task of reconstructing internal node states remains feasible, even
for very high substitution rates. Moreover, computer simulations demonstrate
that for more complex trees and scenarios, this result still holds. For a large
variety of counting, parsimony-based and likelihood-based methods, the
predictive accuracy of a randomly selected internal node in the tree is indeed
much higher than the accuracy of the same method when applied to the tree root.
Moreover, parsimony- and likelihood-based methods appear to be remarkably
robust to sampling bias and model mis-specification.
