9628835 ROGERS The recent rapid increase in the use of DNA data for estimating phylogenetic or genealogical relationships of genes and organisms has focused attention on the efficiency of various methods for doing this. Several studies have demonstrated that a method known as "maximum likelihood" is often equal or superior to other methods for finding correct relationships. Maximum likelihood, however, has been hampered by the extreme slowness of the computer programs for its implementation. Other doubts regarding its usefulness have also been raised. Preliminary studies have shown that maximum likelihood computer programs may be speeded up considerably by using fast approximate methods. These studies have also indicated that other supposed problems of maximum likelihood may not be serious. In this study, James S. Rogers, in collaboration with David L. Swofford of the Laboratory of Molecular Systematics, Smithsonian Institution, will evaluate these aspects of maximum likelihood. Useful methods that result from the proposed studies will be incorporated into subsequent revisions of PAUP*, Swofford's widely used software package for phylogenetic analysis.