Rabbits and Foxes

0rabbits

0foxes

–ticks from one rabbit boom to the next

–ticks the fox boom comes after the rabbit boom

rabbit fox grass eaten, growing back

Over time

rabbits foxes (× 4, to fit) grass (share, right) something you did

Rabbits against foxes

Each point is one moment: how many rabbits (across) and foxes (up). The waves draw loops, always the same way round: rabbits boom → foxes boom → rabbits crash → foxes crash → again.

Run

Speed

ticks

–

of the field has grass

rabbits born

rabbits eaten by foxes

Try this

No foxes

Rabbits fill the field until the grass can feed no more, then stay there. No waves at all: it takes two to make them.

Grass grows back fast

More food should help everyone, right? Watch the waves get wilder until they crash. In 20 worlds, none keeps both. This is the paradox of enrichment.

A small island

Same rules, smaller world. Few foxes at the bottom of a wave, and bad luck finishes them.

Super foxes

Foxes that always chase a rabbit they see. Too good at hunting: they eat their own future.

Shoot rabbits

Hunters shoot 1% of the rabbits each tick. Guess: fewer rabbits? On average there are more, because the foxes go hungry.

People

Fox hunting Rabbit hunting

Hunting is the chance per tick that each animal is shot. Click the field to drop in animals.

Animals and grass

Grass grows in Rabbit babies Fox cubs Fox food Fox skill World Start rabbits Start foxes

Babies / cubs: chance per tick to have one, sharing half the parent's energy. Fox food: energy from one rabbit (a rabbit gets 4 from grass; every animal burns 1 a tick). Fox skill: chance a fox steps toward a rabbit next door instead of wandering. World and start numbers make a new world.

Many worlds

One run can be luck. Run 20 worlds with your settings for 3,000 ticks each, without drawing, and count how they end.

both surviveonly rabbits leftall gone

Why it happens

Many rabbits feed many foxes, so foxes multiply. Many foxes eat the rabbits faster than they breed, so rabbits crash. Then the foxes starve, and with few foxes left the rabbits boom again. Each side always reacts to the other late, so they overshoot, like the drivers on the ring road. Alfred Lotka and Vito Volterra wrote this down as two equations in the 1920s; Volterra wanted to know why fishermen in the Adriatic caught more sharks and other hunting fish while fishing slowed down during the First World War. The Hudson's Bay Company's records of lynx and hare furs show the same waves, about every 10 years.