How to use this predator–prey simulation
This page opens the free sandbox on meadow g7: about 90 rabbits, 8 foxes, a herd of deer, a small wolf pack and three beehives, with no goal and no limits. Press Free sandbox, open Graphs and run at 8× or faster. Rabbits graze, drink and dig burrows, and have litters as long as they are eating well; foxes stalk them, pounce from close range and raise their cubs in dens. With few rabbits left, foxes chase them on fewer days and eat voles instead: enough to see a handful through, never enough for cubs. The lines on the graph are just the sum of what those animals do.
What you should see
We let this meadow run with no help for eight game years (September 2026) and averaged the counts over a year to take out the seasons. The rabbits shot up to about 1,230 by day 60. The foxes followed weeks behind and peaked at about 53 around day 108, by which time the rabbits were already falling; they bottomed out near 380 around day 180, the foxes went hungry and shrank to under 30, and the rabbits came back to about 780 by day 264. The foxes answered again, peaking near 39 around day 288, and the rabbits dropped to about 350 by day 324 before starting a third climb. Every species was still there after eight years.
Where the idea comes from
Mathematically, the rise and fall of predators and prey was first described by Alfred J. Lotka, who applied his equations to predators and prey in a 1925 book, and by Vito Volterra, who published the same equations independently in 1926. Volterra’s short account in Nature, “Fluctuations in the Abundance of a Species considered Mathematically” (volume 118, pages 558–560, 16 October 1926), grew out of a puzzle from the biologist Umberto D’Ancona: the share of predatory fish in Adriatic catches had risen during the First World War, when fishing was reduced. The best-known real example is the snowshoe hare and the lynx, whose ups and downs show in the fur-trade records of the Hudson’s Bay Company.
In the idealised equations, the two populations circle for ever, with the predator peak trailing the prey peak. Real animals, and the ones here, are noisier: seasons, burrows, other food and small numbers make each swing a different size.
Things to try
- Release a disease among the foxes as they near their peak and see how much sooner the rabbits recover.
- Trigger a harsh winter at a rabbit high and watch the foxes follow them down.
- Turn on Log scale to compare the shapes of the two lines despite the very different numbers.
- For a harder game, try the Balance scenario: a valley with no voles, where the foxes live or die by the rabbits alone.