Estimating Phylogenies with Invariant Functions of Data

Estimating phylogenies, or evolutionary trees, is a complex task even under the best of circumstances, and it encounters particular difficulties when using molecular data to investigate distantly related species. In recent years researchers have studied how methods to infer phylogenetic relations, such as those based on parsimony, behave for simple models of nucleic acid evolution. The results are not entirely encouraging: HENDY AND PENNY (1989), for example, illustrated simple cases under which parsimony will converge to an incorrect phylogenetic tree, even for equal rates of evolution. What is encouraging, however, is that researchers are beginning to develop methods of estimating phylogenies which may be robust under conditions where parsimony is not. A strategy shared by some of these methods (CAVENDER AND FELSENSTEIN (1987), LAKE (1987a)) is to use invariant functions of the data to identify the correct topology of the corresponding phylogeny. But which invariants, and how? What assumptions underlie these approaches? I discuss these issues and indicate the direction this research seems to be taking.