This is they way it happens in a purely wild state. However, we now have domesticated herds of food walking around for predators to eat when their natural prey goes through the slump cycle. This keeps the predators at an unnaturally high population rate, and they keep killing wild animals and domesticated which makes the herds of wild prey animals stay very small and might actually cause the extinction of some of them over time.
This is the reason that we need predator control over wolves, lions, coyotes and some bears. There was a reason our forefathers killed off most of the predators. Granted we need some predators but don't cry over the death of a lion, there are plenty of them out there, regardless of what the greenies try to tell us, and they need to be kept down to a decent number along with wolves which should never have been introduced into the USA again without a decent hunting season set up to control them.
without predators of some type prey animals will eat themselves out of existence. The Kaibab national forest is a prime example of that happening back in the early days of the 20th century.