How to use this population growth simulation
This page loads the Population growth lab using meadow code d4: three pairs of rabbits, no hunters and no deer, on a small meadow 80 tiles by 50, so the limit arrives within a couple of in-game months. The lab keeps it summer the whole time, which leaves food as the only brake. Press Start, keep the Graphs tab on Animals, tap Bees to hide that line, and speed up to 8× or 16×. A doe breeds whenever she is well fed, has three to six kits after three days, and her young are grown after ten.
What the curve shows
Run it and the line bends through three stages. Early on, six rabbits can only add a few young at a time, so the count creeps. Then every new adult breeds too and the count multiplies by a similar factor every few days: exponential growth. Finally the grass near the warrens is cropped to stubble, fewer does are fed well enough to breed, and hungry rabbits begin to die. Our own run of this exact meadow (September 2026) counted 15 rabbits after 12 days, 46 after 24, 90 after 36, 194 after 48 and 275 after 60, then 303 and 336 as the climb flattened. After that it stopped climbing: checked every 12 days for the rest of three game years, it stood somewhere between 175 and 398, and 659 of the 725 deaths in those three years were from hunger. That band is the meadow’s carrying capacity. Open the Plants chart as well: grass cover fell from 97% to between a quarter and a half as the rabbits filled up the space.
Where the idea comes from
The S-shaped curve is the logistic function, introduced by the Belgian mathematician Pierre François Verhulst in a brief note in 1838 and named in a longer paper he presented in 1844 (published 1845), as a model of population growth that starts out geometric, slows as the population grows, and approaches a limit. Its fastest growth comes at half that limit. Real populations, and this one, follow the shape loosely: patchy food, weather and chance add wobbles the smooth curve leaves out.
Things to try
- Paint extra ponds and grass before you press Start, and see whether the band the rabbits settle in moves up.
- Bring a drought once the count levels off: the grass stops regrowing and the rabbits crash below their old level.
- Add a beehive and flowers. Rabbits don’t live on flowers, so the curve should hardly change: a quick control experiment.