Eventually, the environment will be unable to support the production of wildebeests, this will cause there to be a loss of vegitation that then causes a food shortage, and then the wildebeests will starve.
Explanation:
It's a very unhappy process, but those herds who don't migrate to another pasture will starve and die. The death will depopulate the savanna and give the fields some time for regrowth and the cycle will begin again.
