My research focuses on methods for essential data analyses in phylogenetics. I have been principally been interested in two broad topics. First, I am interested in the relationship between molecular sequence alignment and the traditional concept of character homology, and how we might implement this relationship in a computer program. To date, no computer algorithm exists for producing a DNA or RNA sequence alignment based on homology, because the conceptual issues behind this problem have not yet been fully elucidated. Second, I have also investigated the need for network representations of complex relationships among organisms, rather than the traditional use of phylogenetic trees. Evolutionary history consists of both vertical descent (parent to offspring) and horizontal gene flow among contemporaries (as created by processes like hybridization and horizontal gene transfer). Trees represent only the vertical inheritance whereas networks can represent both components. To date, there are few computer algorithms for constructing these networks.