The use of molecular phylogenies to examine evolutionary questions has become commonplace with the automation of DNA sequencing and the availability of efficient computer programs to perform phylogenetic analyses. The application of computer simulation and likelihood ratio tests to evolutionary hypotheses represents a recent methodological development in this field. Likelihood ratio tests have enabled biologists to address many questions in evolutionary biology that have been difficult to resolve in the past, such as whether host-parasite systems are cospeciating and whether models of DNA substitution adequately explain observed sequences.