On necessary and sufficient conditions for group selection efficacy

The statement “group selection predominates over individual selection” is formulated within a class of patch-structured models. Conditions involving both “selfish” and “altruistic” predator characteristics are then shown to be necessary and sufficient for group selection predominance in this class of models. Maynard Smith's criterion M < 1 (Group selection, Quart. Rev. Biol., June 1976, pp. 277–283) is shown to be sufficient but not necessary for group selection predominance.