When research active, the foci of our systematic studies included: 1) Elucidation of relationships among the major clades and their tribal/generic relationships within the family Cactaceae; 2) Intergeneric relationships in the species-rich tribe Cacteae; 3) Phylogenetic structure and tribal/generic delimitation of the Subfamily Opuntioideae; 4) Determination of relationships between North and South American columnar cactus lineages; and 5) Relationships among related families of the ‘Portulacaceous Alliance’ of families in Order Caryophyllales, in particular Portulacaceae, Cactaceae, Didiereaceae, and segregates.