Likelihood and Inconsistency

Parsimony can be inconsistent, but not maximum likelihood—likelihood advocates often say. This difference and conclusions drawn from it have provided the main reasons advanced by likelihoodists against the use of parsimony. Recent statistical research, however, shows that maximum likelihood estimation of phylogenetic trees can become inconsistent in all but the simplest cases, so that under realistic conditions the consistency of maximum likelihood cannot be assured. If likelihoodists wish to dispose of parsimony, they will have to find another argument.