Food Chains and Ecosystems
Grass, rabbit, fox: the mathematics of a balance
Summary
An ecosystem is balanced by the predator-prey relationship. If prey increase, predators increase; if predators multiply, prey decrease → the predators decline too → the prey come back. This cycle is modelled mathematically with the Lotka-Volterra equations. Change the parameters with the sliders and watch the ecosystem begin to oscillate.
In depth
In the early 20th century Alfred Lotka and Vito Volterra independently proposed a simple model: the prey population grows naturally but is reduced by predators; the predator population grows by eating prey but dies off naturally when there is no prey. This simple interaction results in periodic oscillations. Although real ecosystems do not follow the model exactly, the Hudson's Bay Company's fur records of lynx and snowshoe hares from the 19th and early 20th centuries show strikingly regular cycles. In the three-level model (grass → rabbit → fox), a carrying capacity K is added because grass cannot grow without limit; the results are more complex but still visually clear. Remove the predator (a high death rate) and the prey explode, the grass runs out and the prey crash: when the balance is broken, the chain breaks.
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