not-yet-known not-yet-known not-yet-known unknown Ecological theory assumes generally that predators hunt as solitary individuals, an assumption that is violated in social predators. We applied a behaviorally-based group foraging model, predicting that group hunting should depress lion fitness due to reduced searching efficiency. Hence, hunting groups > 4 females should be unsustainable. So how do prides of a dozen or more lions persist? Here we show that females in large prides typically fragment into small hunting groups well approximated by an exponential distribution of group size typical of fission-fusion social systems. As a result, the average size of hunting groups falls well within sustainable limits. Our models suggest that fragmentation into smaller groups has a strongly stabilizing effect on predator-prey interactions, allowing lions to persist even when living in large prides in the highly productive Serengeti ecosystem, despite the substantial fitness cost of social foraging.