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Abstract— A tension has arisen over the primacy of interbreeding versus monophyly in defining the species category. Manifestations of this tension include unnecessary restriction of the concept of monophyly as well as inappropriate attribution of “species” properties, to “higher taxa”, and vice versa. Distinctions between systems (wholes) deriving their existence from different underlying. processes have been obscured by failure to acknowledge different interpretations of the concept of individuality. We identify interbreeding (resulting in populations) and evolutionary descent (resulting in monophyletic groups) as two processes of interest to phylogenetic systematists, and explore the relations between the systems resulting from these processes. In the case of sexual reproduction, populations of interbreeding organisms (regardless of whether they are monophyletic) exist as cohesive wholes and play a special role in phylogenetic systematics, being the least inclusive entities appropriate for use as terminal units in phylogenetic analysis of organismal relationships. Both sexual and asexual organisms form monophyletic groups. Accepting the reality and significance of both interbreeding and monophyly emphasizes that a conscious decision must be made regarding which phenomenon should be used to define the species category. Examination of species concepts that focus either on interbreeding or on common descent leads us to conclude that several alternatives are acceptable from the standpoint of phylogenetic systematics but that no one species concept can meet the needs of all comparative biologists.