What is happening

The island

Grass grows. Rabbits eat grass. Foxes eat rabbits. Nothing arrives and nothing leaves.

Why the numbers swing

Plenty of grass, so the rabbits do well and there get to be more of them. More rabbits, so more food for foxes, so more foxes. More foxes and less grass, so fewer rabbits. Fewer rabbits, so the foxes go hungry. Then the grass grows back and it starts again.

Neither number ever sits still. A living island is a swing, not a balance.

Why a good year becomes a bad one

Rabbits eat faster than the grass grows. Ground with its roots left comes back quickly. Ground eaten down bare takes far longer. A very good year strips what they need for the next one, so they cause their own crash.

The foxes are always late

Watch the two lines. The foxes rise after the rabbits and fall after them. When the rabbits start running out there are still enough to feed foxes for a while, so the fox crash comes weeks later.

Lotka and Volterra worked this out on paper a century ago. It is the oldest result about predators and prey. Nobody told this island about it. When there is enough to go on, the notebook measures the gap and gives you the number in weeks.

It measures from week one hundred, not from the start. The animals begin knowing nothing, and the first ninety weeks are one clumsy boom and the crash after it. That is a species learning to be a species. Mixing it in with the rest answers neither question.

Feed them and see who gets fatter

Almost nobody guesses this one right. How many rabbits the island settles at depends only on how the foxes are doing. How many foxes depends only on how the rabbits are doing. So richer grass does not buy you rabbits. It buys you foxes, and about as many rabbits as before.

There is a button for it under DO SOMETHING. Press it and the notebook writes the prediction down first, waits sixty weeks, then writes what actually happened, including when the two disagree.

Nobody taught the animals anything

Each animal picks one of six things to do. The rabbits pick from graze, wander, run, sit, breed and seek grass. The foxes pick from hunt, wander, roam, sit, breed and follow.

No rule anywhere tells a rabbit to run from a fox. At the start they pick almost at random and plenty of them die stupidly. All they get back is one number, near enough to "you are still alive". Over thousands of small decisions each species builds a memory of what tends to work, and starts picking it more often.

Being straight about it: they learn which of the six. The six themselves are written into the page. And the memory belongs to the species, not the animal, since no rabbit lives long enough to learn much alone.

What the measurements say

Over five hundred weeks, animals that learn live about five per cent longer than animals that never do. Over the first hundred and sixty they live shorter lives. Exploring costs you, and the bill comes before the benefit.

An earlier version of this page said a fifth longer. That was wrong. The memory was carrying between runs, so six hundred and forty weeks of practice were being credited to a hundred and sixty. Left here rather than quietly corrected.

The foxes barely improve, and the reason matters: there are so few of them that they get far less practice. Being rare is its own disadvantage, and not only because of the hunting.

The equations, if you want them

Two lines. Alfred Lotka wrote them down in 1925 and Vito Volterra in 1926, working separately. Volterra got into it because his daughter's suitor was a marine biologist who could not explain why the share of predatory fish in the Adriatic catch went UP during the First World War, when there was less fishing.

The prey: they multiply by themselves, and they get eaten in proportion to how often the two species run into each other.

The hunters: they die off at a steady rate, and they multiply in proportion to those same meetings.

All of the hunting is that one term, prey times hunters. It says a hunt is a chance meeting. That is why filter feeding, where the hunter just swims through whatever is there, is the version of this island closest to the original.

Four things follow, and three of them are on this page.

It never settles. The answers are closed loops, not resting points.

The hunters trail by a quarter of a cycle. The notebook measures the gap and gives you it in weeks.

Feeding the prey feeds the hunters. The settled prey number has nothing but hunter terms in it, and the settled hunter number nothing but prey terms. Faster plants means more hunters. This is also Volterra's answer about the fish: stop fishing, life gets better for the prey, and that turns into more predators.

And the fourth is where this island leaves the paper behind. On paper the prey can fall to a millionth of an animal and come back, because the equations deal in smooth quantities. This island is made of whole animals. When the last one dies it stays dead, and that is why some seeds end quiet.

And the other equations

The same pair with the signs changed is the competition model: two species eating the same food instead of eating each other. It usually ends with one of them gone. A rival is more dangerous than a predator.

Change them again and you get Lanchester's laws, written in 1916 about air combat, which is why there is a gorilla in the list. Two sides, each removing the other in proportion to how many are fighting. If everyone can reach at once, strength goes as numbers squared and a hundred is worth ten thousand. If only a few can reach, it goes as numbers plainly and quality decides it. So the hundred against one has an answer, and the answer is that it depends on the doorway.

The same two lines have been used for firms taking market share off each other, and by Richard Goodwin in 1967 for wages against employment, with the workers as the prey. None of that makes them true. It makes them a shape that turns up whenever two things feed on each other, which is reason enough to spend an hour watching rabbits.

You

You are on the shore, not on the island. Every twenty weeks you may do one thing. Doing nothing is a real choice and most of the time it is the right one.

CLOSE

Who lives here

Fifteen places to start, and every line under a name is something that was measured rather than something hoped for. Underneath them, if you want it, is the box of parts they were all built out of.

Changing anything restarts the island on the same seed, so the coastline and the lakes stay put and the animals are the only thing that moved.

What actually changes what

The creature is a body. It brings a name, an outline, a size, and five numbers of its own: appetite, metabolism, how fast it breeds, how long it lives, how much it starts with. Those apply whichever job it is doing, because a krill is small whether it is eating or being eaten.

The plant sets the pace. Plankton blooms, grass is ordinary, ferns are slow and lichen barely grows at all. That is the one number the whole feeding-them-more result turns on, so a lichen island and a plankton island are different places to be an animal.

And plankton is water. A creature that does not belong where you put it burns energy nearly twice as fast and lives about half as long. Nothing stops you putting cats in the open ocean. They will not be there long, and that is the answer rather than an error message.

The extra rule is the physics. It is the row that changes how the island works, and what each one changes is written down under WHAT IS HAPPENING, measured against the plain version on the same twelve islands. Two of them came out the opposite way from the prediction, and the wrong predictions are still there beside the answers.

CLOSE

You are standing on the shore

You are not on this island. You get to do one thing, now, and then nothing for another twenty weeks. Doing nothing is a real answer and most of the time it is the right one.

DO NOTHING close this and keep watching, and you keep your turn for later

TAKE SOME RABBITS OFF removes a fifth of them

PUT TWO FOXES ON from somewhere else

PUT TEN RABBITS ON from somewhere else

FENCE THE EAST OFF nothing feeds there for twenty weeks

MAKE THE FOOD RICHER doubles how fast the plants grow, for good. The notebook will write down what the equations say happens next, before it happens, and then what actually did.