Final answer:
The populations of predators and prey cycle through periods of growth and decline due to complex predator-prey dynamics, as described by the Lotka-Volterra model and additional ecological studies, which include density-dependent factors and food availability.
Step-by-step explanation:
According to the Lotka-Volterra model and further ecological studies, the populations of predators and prey, such as foxes and rodents, often exhibit cycles of growth and decline due to predator-prey dynamics. This complex interaction is not solely dependent on predation but also includes density-dependent factors.
For instance, the snowshoe hare may experience lower fecundity due to the stress caused by overpopulation, which in turn can affect lynx populations, their predators. Predation models predict that as the prey population increases, more food is available for predators to consume, which allows the predator population to grow. However, when predators reach a high density, the prey population can sharply decline due to increased predation, triggering a subsequent decline in the predator population due to a reduction in available food.
This cycling generally occurs over a period of approximately ten years, with the predator population typically lagging one to two years behind the prey population. Predator-prey dynamics, therefore, involve a repeating cycle where prey numbers increase, followed by an increase in predator numbers, then a decline in prey, resulting in a decrease in predators, starting the cycle again.