Recent developments of statistical methods in molecular phylogenetics
are reviewed. It is shown that the mathematical foundations of these m
ethods are not well established, but computer simulations and empirica
l data indicate that currently used methods such as neighbor joining,
minimum evolution, likelihood, and parsimony methods produce reasonabl
y good phylogenetic trees when a sufficiently large number of nucleoti
des or amino acids are used. However, when the rate of evolution varie
s extensively from branch to branch, many methods may fail to recover
the true topology. Solid statistical tests for examining the accuracy
of trees obtained by neighbor joining, minimum evolution, and least-sq
uares method are available, but the methods for likelihood and parsimo
ny trees are yet to be refined. Parsimony, likelihood, and distance me
thods can all be used for inferring amino acid sequences of the protei
ns of ancestral organisms that have become extinct.