Hierarchical expansions of the theory of natural selection exist in two distinct bodies of thought in evolutionary biology, the group selection and the species selection traditions. Both traditions share the point of view that the principles of natural selection apply at levels of biological organization above the level of the individual organism. This leads them both to considermultilevel selection situations, where selection is occurring simultaneously at more than one level. Impeding unification of the theoretical approaches of the multilevel selection traditions (...) are the different goals of investigators in the different subdisciplines and the different types of data potentially available for analysis. We identify two alternative approaches to multilevel situations, which we termmultilevel selection [1] andmultilevel selection [2]. Of interest in the former case are the effects of group membership onindividual fitnesses, and in the latter the tendencies for the groups themselves to go extinct or to found new groups (i.e., group fitnesses). We argue that: neither represents the entire multilevel selection process; both are aspects of any multilevel selection situation; and both are legitimate approaches, suitable for answering different questions. Using this formalism, we show that: multilevel selection [2] does not require emergent group properties in order to provide an explanatory mechanism of evolutionary change; multilevel selection [1] is usually more appropriate for neontological group selection studies; and species selection is most fruitfully considered from the point of view of multilevel selection [2]. Finally we argue that the effect hypothesis of macroevolution, requiring, in selection among species, both the absence of group effects on organismic fitness (multilevel selection [1]), and the direct determination of species fitnesses by those of organisms, is untestable with paleontological data. Furthermore, the conditions for the effect hypothesis to hold are extremely restrictive and unlikely to apply to the vast majority of situations encountered in nature. (shrink)