In the now-classic standard Lotka-Volterra model of population regulation by predators, the end dynamic is cyclical for both the consumer and the consumed. In particular, herbivores tend to increase in density until brought under control by a specialized predator whose population is dependent on herbivore density. This model gives us hints as to what forces may be responsible for the cycles we actually observe in nature. In particular, predation by specialists or other trophic interactions such as parasite infection could be important, especially if there is a significant lag between the prey density growth and predator density growth.
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