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Simulation · after Watson & Lovelock, 1983

Daisyworld

A planet that keeps itself at a comfortable temperature, though nothing on it means to.

Two kinds of daisy grow on a grey planet orbiting a sun that keeps getting brighter. Black daisies absorb light and warm their surroundings; white daisies reflect it and cool them. Each grows best near 22.5 °C. Nobody is in charge, yet across a wide range of sunlight the planet's temperature barely moves. Turn the sun up and watch.

  • Black daisy
  • White daisy
  • Bare ground
10 °C35 °C Drag on the planet to sow

Temperature against the sun

Planet temperature, °C · Solar luminosity, L
  • This run
  • Without life
  • Original model
  • Daisies can grow
Without life, temperature climbs with the sun. With daisies it stays flat over a wide range, then breaks away at the edges. Rising and falling paths differ: the planet remembers where it has been.
Temperature over time
  • Planet
  • No life
Cover over time
  • Black
  • White
  • Bare

How it works

James Lovelock and Andrew Watson built Daisyworld in 1983 to answer a criticism of the Gaia hypothesis: that a planet could only regulate itself if its organisms somehow planned to. Their model has no planning at all. Each daisy only grows or dies, depending on how warm it is where it stands.

The sun warms the planet according to how much light it absorbs. Ground reflects half the light, black daisies a quarter, white daisies three quarters. The planet's albedo A is the cover-weighted mix, and its temperature follows from the balance between sunlight in and heat radiated out:

σ Te⁴ = S · L · (1 − A) S = 917 W m⁻², σ = 5.67 × 10⁻⁸ Ti⁴ = q · (A − ai) + Te⁴ local temperature of a daisy with albedo ai β(T) = 1 − 0.003265 · (22.5 − T)² growth rate, zero outside 5–40 °C

Black daisies stand on warmer ground than the planet average and white daisies on cooler ground. When the sun is weak only black daisies are warm enough to spread, and as they spread they warm everything. When the sun is strong, white daisies take over and cool things down. The two feedbacks pull against each other, and temperature settles near where the daisies grow best.

This version puts the daisies on a grid. A bare cell is colonised by a random neighbour with probability β, measured at the temperature that neighbour's species would feel there. Every daisy dies with probability γ. A trickle of seeds drifts in from space, so life can come back after an extinction. The dotted curve on the chart is the original model: two differential equations with no space at all. The grid should track it closely.

Things to try

  1. Sweep the sun. Start cold and brighten slowly. Life appears suddenly at about L = 0.75, holds temperature steady to about 1.5, then collapses.
  2. Hysteresis. Take the sun up and back down. Life survives far longer than it took to start. A bare planet is hotter than a living one, so once the daisies die they cannot come back until the sun dims a long way.
  3. Only white daisies. One kind of daisy can still regulate, but only on one side. White daisies cool a hot planet and do nothing for a cold one.
  4. Grey daisies. Set both albedos to 0.5 so the daisies are the same colour as the ground. They still grow, but they no longer change the climate, and the planet follows the lifeless curve.
  5. Plague. Hold the sun at L = 1.0 and kill nine daisies in ten. Temperature jumps, then the survivors regrow and pull it back.
  6. Local climates. Switch to the temperature view. Daisies spread from their neighbours, so they grow in clumps, and each clump makes its own weather: warm under black patches, cool under white ones. The planet's average is the only number that stays steady.

References

1. Watson, A. J. & Lovelock, J. E. (1983). Biological homeostasis of the global environment: the parable of Daisyworld. Tellus B, 35(4), 284–289.

2. Wood, A. J., Ackland, G. J., Dyke, J. G., Williams, H. T. P. & Lenton, T. M. (2008). Daisyworld: a review. Reviews of Geophysics, 46(1).

3. von Bloh, W., Block, A. & Schellnhuber, H. J. (1997). Self-stabilization of the biosphere under global change: a tutorial geophysiological approach. Tellus B, 49(3), 249–262.