A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.
The Lotka-Volterra predator-prey model describes reciprocal oscillations in predator and prey population sizes: prey grows when predators are rare; predators increase when prey is abundant; overhunting then crashes prey, followed by predator decline. The model predicts neutrally stable cycles around equilibrium. Real systems (e.g., snowshoe hares and lynx) show similar but more complex dynamics influenced by vegetation, refuges, and multiple prey species. Predators can regulate prey populations and have strong community-level effects.
Graph the predator and prey population cycles and identify the phase lag between them. Modify model parameters (predation efficiency, prey reproduction rate) to see how cycle amplitude and period change. Compare model predictions to empirical time series.
When you studied population growth models, you learned how a single population grows in isolation — exponential when resources are unlimited, logistic when they are constrained by carrying capacity. Predator-prey dynamics extend this framework to two interacting populations whose fortunes are linked: one species is the resource, the other is the consumer. The result is a model that predicts something qualitatively new — oscillations — arising from feedback between the populations rather than from any external forcing.
The Lotka-Volterra equations capture this with two differential equations. Prey grows exponentially when predators are absent but is depressed by predation at a rate proportional to both prey and predator density. Predators starve (decline) when prey is absent but grow at a rate proportional to how much prey they consume. When you analyze this system, you find a single unstable equilibrium point — a combination of predator and prey densities where both populations are momentarily stable — surrounded by closed orbits. Any starting condition near the equilibrium produces cycles that go around the equilibrium forever, neither spiraling in nor spiraling out. This is called neutral stability.
The mechanism of the cycle follows a clear logical sequence. When prey is abundant, predators have plentiful food and reproduce rapidly. The growing predator population consumes prey faster than prey can reproduce, driving prey numbers down. Now food-scarce predators begin to starve, and predator numbers decline. With predator pressure reduced, prey recovers. The recovered prey population allows predators to recover, and the cycle repeats. Crucially, the predator peak *lags behind* the prey peak because it takes time for the predator population to respond to abundant food. This phase lag is visible in famous empirical data sets like the Canadian lynx and snowshoe hare fur-trade records.
The basic model makes simplifying assumptions that real systems violate. Prey is assumed to grow exponentially without a carrying capacity; predators are assumed to convert prey into offspring with perfect efficiency; there is no refuge, no alternative prey, no territorial behavior. Real systems show more complex dynamics — shorter cycles, dampened oscillations, or even stable equilibria — because of these added factors. The model's value is not predictive precision but conceptual clarity: it shows that oscillations are an *emergent property* of the predator-prey feedback structure, requiring no external forcing and no intentional behavior on the part of either species.
One common misinterpretation is that predators "regulate" prey or "manage" the ecosystem. This is teleological thinking. Predators eat prey because they are hungry, not to keep ecosystems in balance. Any regulatory effect is an unintended consequence of individual-level behavior interacting through population-level feedback. Keeping the mechanism and the outcome separate is essential for clear ecological reasoning.