This simulator models a three-level food web of plants, herbivores and carnivores using a coupled set of Lotka-Volterra ordinary differential equations. Plant growth follows logistic dynamics capped by a carrying capacity, herbivores graze the plants, and carnivores prey on the herbivores. The equations are integrated in the browser with a fourth-order Runge-Kutta scheme. By toggling off the apex predator you can watch a trophic cascade unfold: herbivores boom, then overgraze and crash the plant base.
A 3-level Lotka-Volterra system: dP/dt = rP·P(1 − P/K) − a·P·H, dH/dt = eH·a·P·H − mH·H − b·H·C, and dC/dt = eC·b·H·C − mC·C. The three population time series are integrated with RK4 and plotted against time in years, revealing oscillations and equilibria.
Five sliders set plant growth rate r, herbivore predation a, herbivore mortality mH, carnivore predation b and carnivore mortality mC. The "Remove Apex Predator" button zeroes the carnivore's prey term to trigger a cascade, and Forest, Ocean and Grassland buttons load preset parameter sets and starting populations.
The classic real-world example is the reintroduction of grey wolves to Yellowstone in 1995, which reduced elk overbrowsing and allowed willow and aspen to recover along rivers, illustrating how an apex predator can shape entire landscapes.
A trophic cascade is an indirect effect that ripples down a food web when a predator at one level changes the abundance of organisms two or more levels below it. Here, removing carnivores releases herbivores from control, which then overgraze the plants, so a top-level change propagates all the way to the vegetation base.
It solves three coupled differential equations for plants (P), herbivores (H) and carnivores (C). Plant growth is logistic with carrying capacity K = 200, while predation and mortality terms link the levels. The solver advances the system with a fourth-order Runge-Kutta method using a time step of 0.05 over 2000 steps.
The r slider sets the plant intrinsic growth rate, a sets how efficiently herbivores consume plants, and mH is the herbivore death rate. The b slider sets the carnivore predation rate on herbivores, and mC is the carnivore death rate. Adjusting them shifts the equilibrium populations and the period of the predator-prey oscillations.
It is a faithful implementation of textbook Lotka-Volterra ecology with logistic plant growth and fixed conversion efficiencies, so the qualitative behaviour is sound. Real ecosystems, however, involve many more species, spatial structure, time lags and environmental noise, so the model is best read as an illustrative idealisation rather than a precise forecast.
Predator-prey systems naturally produce cycles: abundant prey lets predators grow, the rising predators then suppress the prey, which in turn starves the predators, and the cycle repeats. The simulator estimates the cycle period in years from the herbivore curve's crossings of its mean value, and you can see how parameter changes lengthen or shorten that period.