I have found something interesting about persistence hunting by the Kalahari Bushmen. Apparently this was also done by the Tarahumara or Raramuri people of Northern Mexico.
The persistence hunt may well have been the first form of hunting practiced by hominids. It is likely that this method of hunting evolved before humans invented projectile weapons, such as darts, spears, or slings. Since they could not kill their prey from a distance and were not fast enough to catch the animal, one reliable way to kill it would have been to run it down over a long distance.
In this regard one has to bear in mind that, as hominids adapted to bipedalism they would have lost some speed, becoming less able to catch prey with short, fast charges. They would, however, have gained endurance and become better adapted to persistence hunting. Although many mammals sweat, only humans have evolved to use sweating for effective thermoregulation. This coupled with relative hairlessness would have given human hunters an additional advantage by keeping their bodies cool in the midday heat.
During the persistence hunt an antelope, such as a kudu, is not shot or speared from a distance, but simply run down in the midday heat. Depending on the specific conditions, hunters of the central Kalahari will chase a kudu for about two to five hours over 25 to 35 km (16 to 22 mi) in temperatures of about 40 to 42 °C (104 to 108 °F). The hunter chases the kudu, which then runs away out of sight. By tracking it down at a fast running pace the hunter catches up with it before it has had enough time to rest in the shade. The animal is repeatedly chased and tracked down until it is too exhausted to continue running. The hunter then kills it at close range with a spear.
I think this was/is a very sustainable way of hunting. One animal is run down and not a whole herd. It was/is all about endurance and furthermore impossible for a few hunters to hunt down/butcher a whole herd of antelope.