In theory, there should be an equilibrium between predators and prey. Thus, when predators are scarce, the numbers of prey should rise. Predators would respond by reproducing more and, possibly, by changing their hunting habits. As the population of predators rises, more prey is killed and their numbers fall. Many of the predators then die; thus numbers of predators and prey oscillate between two extremes. See Gilpin and Rosenzweig (1972) Science 177, 1358 for the classic model. Gilg et al. (2003) Science 302, 866 should be useful.

The keystone predator effect predicts that prey that are strong resource competitors are expected to dominate at low levels of potential productivity; augmenting prey resources permits less efficient competitors but more predator-resistant prey to invade and dominate. The underlying trade-off among prey can be termed the ‘keystone trade-off’ (Leibold (1996) Am. Nat. 147). See Steiner (2003) Oikos 101, 3.