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How do predator-prey relationships produce cycles in population size?

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Line graph showing world population growth from 1700 to 2000 with a steep rise after 1950, followed by three projection scenarios for 2000 to 2100: high, medium, and low, reaching between 7 and 14 billion. — population Graph of the world's estimated human population from 1700 until 2000, with population projections extending until 2100.

Predator-prey relationships produce cycles in population size through reciprocal, density-dependent interactions where the abundance of one species directly influences the growth rate of the other.12

These dynamics are often modeled using the Lotka-Volterra equations. In this framework, the prey population grows based on its own resources, but its growth rate is reduced by the presence of predators. Conversely, the predator population’s growth rate increases as it consumes prey.1

When prey populations are high, predators have more food, leading to an increase in the predator population. As the number of predators rises, the rate of prey consumption increases, eventually causing the prey population to decline. With less food available, the predator population subsequently decreases, which allows the prey population to recover, restarting the cycle. While these cycles are marked by distinct periods and amplitudes, they are influenced by various factors, including the availability of food and the presence of spatial refugia that protect prey from predation.21