Biodiversity sciences witness a double dynamic. Whereas the need for interdisciplinary approaches is increasingly appreciated, most disciplinary studies are still confined to developing operational, discipline-specific indices. We show that a reassessment of the general notion of biodiversity is needed to clarify this situation. We advocate a new approach, according to which the main usefulness of this notion is not to capture quantitatively biological objects or processes, but to organize meaningful and coherent interdisciplinary interactions by constructively criticizing disciplinary studies. We apply this approach to ecological-economic models, in the hope of launching more fruitful critical dialogs between economists and biologists.