Reading Barry Lopez’s book “Of Wolves and Men”:
[…] disadvantage. The important thing to bear in mind is that generally wolves do not overrun the prey population and kill it out, although they have been known to do so, just as they have, extraordinary as it seems, practiced a kind of fallow-field farming by not killing deer in certain parts of their territories for four or five years, letting the prey population recover there.



Also it’s dumber than crop rotation with nitrogen fixers.
And that’s dumber than just companion planting deep rooted perennials with poly cultures that include nitrogen fixers.