Practice question

Predator and prey time series are often represented by approximately sinusoidal waves because both populations rise and fall repeatedly, with the predator peak lagging behind the prey peak. When predators are scarce, prey increase; abundant prey then supports predator reproduction. The enlarged predator population depresses prey, after which food shortage causes predator decline and allows prey recovery. This negative feedback generates coupled cycles in the classical Lotka–Volterra model. A sine wave is only a visual approximation: actual trajectories need not be mathematically sinusoidal, and cycle amplitude and period can vary through seasonality, density dependence, refuges, stochasticity, or delayed responses. A linear increase cannot represent repeated reversals, a constant decline lacks recovery, and random scatter lacks the temporal coupling expected from consumer–resource feedback. Phase-plane plots provide another representation, showing orbits around an equilibrium rather than abundance through time. The important feature is regular, lagged oscillation, not perfect adherence to a particular trigonometric function.