Same as foxes. Their numbers follow the fortunes of their prey animals, so as the predators get more successful, they take more prey, as the amount of prey falls, the predator numbers fall since there's not enough prey to support the enlarged population. As the predators' numbers decline due to starvation, the prey population recovers and as those numbers rise, so do the predators'.
They also do fall to other raptors. A friend has a series of shots of a Peregrine taking a buzzard out over Exeter a couple of years ago.
"Only" 5 in the stack on Thursday morning.