  Maximum likelihood estimation (MLE) methods are widely used for evolutionary
tree. As evolutionary tree is not a smooth parameter, the consistency of its
MLE has been a topic of debate. It has been noted without proof that the
classical proof of consistency by Wald holds for the MLE of evolutionary tree.
Other proofs of consistency under various models were also proposed. Here we
will discuss some shortcomings in some of these proofs and comment on the
applicability of Wald's proof.
