Cope's rule--the generalization that animal taxa tend to evolve toward larger body size--suggests that there are widespread net selective advantages to being large. Size-abundance relationships within bird and desert rodent guilds show that larger species usually do control more energy locally, and thus maintain larger populations than expected for their body size, implying that larger individuals are relatively better at obtaining and using local resources. But we report here results that show that this is not generally the case among mammal species. Within dietary groups containing only small species, larger species usually do better, but within those that contain the largest mammals, small species tend to control more energy. This suggests that in mammals there is an optimum body size for energy acquisition at about 1 kg. Thus, net adaptive advantages of large individuals for resource control cannot be used as a general explanation for evolutionary size increase in mammals, although other proposed explanations for Cope's rule are unaffected. Instead, these results suggest a partial explanation for another widespread ecotypic pattern, the 'island rule': that on islands, small mammal species evolve to larger size and large species to smaller size. If on an island a species' usual competitors and predators are absent, it should often tend to evolve toward the optimum body size, and the adaptive advantages of doing so would be greatest for populations starting at body-size extremes.