Predation
A predator's effect on its prey species is hard to see in the short-term. However, if observed over a longer period of time, it is seen that the population of a predator will correlationally rise and fall with the population of its prey in a cycle similar to the boom and bust cycle of economics. If a predator overhunts its prey, the prey population will lower to numbers that are too scarce for the predators to find. This will cause the predator population to dip, decreasing the predation pressure on the prey population. The decrease in predators will allow the small number of prey left to slowly increase their population to somewhere around their previous abundance, which will allow the predator population to increase in response to the greater availability of resources. If a predator hunts its prey species to numbers too low to sustain the population in the short term, they can cause not only the extinction or extirpation of the prey but also the extinction of their own species, a phenomenon known as coextinction. This is a risk that wildlife conservationists encounter when introducing predators to prey that have not coevolved with the same or similar predators. This possibility depends largely on how well and how fast the prey species is able to adapt to the introduced predator. One way that this risk can be avoided is if the predator finds an alternative prey species or if an alternative prey species is introduced (something that ecologists and environmentalists try to avoid whenever possible). An alternative prey species would help to lift some of the predation pressure from the initial prey species, giving the population a chance to recover, however it does not guarantee that the initial prey species will be able to recover as the initial prey population may have been hunted to below sustainable numbers or to complete extinction.

Q: The rise and fall of predator and prey populations are similar to what, in the US economy?
boom and bust cycle of economics