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Cladistic mechanics and ramifications of various species concepts rooted in phylogenetic theory are explored. Published discussions of the phylogenetic species concept (PSC) have been hampered by persistent misconceptions surrounding its ontology and applicability, and by confusion of various incompatible versions of species concepts claiming to follow from Hennig's (1966), Phylogenetic Systematics, Univ. of Illinois Press, Urbana work. Especially problematic are topology- or tree-based versions of species diagnosis, which render diagnoses dependent on relationships depicted as hierarchically structured regardless of any lack of underlying hierarchy. Because the applicability of concepts such as monophyly, paraphyly, and polyphyly rests ultimately on the underlying hierarchical distribution of characters, representations of tokogenetic or reticulating systems as nested hierarchies are necessarily inaccurate. And since hierarchical representations—even if accurate—of nonrecombining genetic elements need not coincide with the organisms that bear them, tree-based diagnoses are further hampered, except potentially as retrospective tools. The relationship between tree-based species delineations and the criterion of character fixation is explored. Fixation of characters by which one identifies phylogenetic species is further distinguished from the fixation of character state differences, and the implications of that distinction are explored with reference to the interpretation of speciation events. It is demonstrated that character fixation in alternative species need not coincide with the achievement of reciprocal monophyly. While the PSC retains shortcomings, some of the more frequently criticized aspects of the PSC are functions of sampling that are no more problematic than for any basic systematic endeavor.