Hunters might need to change their strategy.
Instead, on foot and with only spears, chase down the weakest and sickest animals, culling the heard, leaving only the healthiest and strongest to survive. This is called "Natural Selection."
That was the job of wolves and other predators.
When humans eliminate predators and then hunt for only the best of a species with the advantage of projectile weapons, or "unnatural selection," the species as a whole becomes at risk of extinction from other factors like disease or famine.
Diseases can infect animals who remain just healthy enough to spread the sickness through a herd before becoming unable to walk with the herd. Without predators hanging around, the herd had the luxury of remaining with the sickest members because, well, they stick together.
Famine happens because the herd population becomes too large and they deplete their entire food supply before it has a chance to grow back. Herbivores in areas with no carnivores have been known to graze so much grass away that rain later causes erosion and flooding, or even changes the path of streams away from irrigation of crops.
Predators also keep deer and other herbivores from decimating crops, Keeping livestock may be a little more expensive and require a little more effort.
