INTERACTIVE COMPANION · REPLICATION · CLIMATE MODELLING

The Daisy Bench

A live model accompanying “A Planet of Daisies That Regulates Its Own Temperature”

Two kinds of daisy, one star, no atmosphere. Black daisies absorb sunlight and warm the ground they stand on. White daisies reflect it and cool theirs. Both grow best at 22.35 °C and neither can grow below 4.85 °C or above 39.85 °C. Nothing in the model wants anything. What follows is the whole argument, running in your browser.

The two panels below are the same code the club ran in Python, transcribed to JavaScript. At the default settings they reproduce the article’s headline numbers exactly: a regulated interval of L = 0.704 to 1.556, a residual drift of 10.421 °C, a suppression factor of 5.78, and a planet sitting at 21.841 °C when L = 1.000.

Model 1. Drive the star

Move the luminosity slider and the crosshair moves along a curve that was computed by integrating the population equations to steady state at every one of 501 luminosities, carrying the daisies forward from each step to the next. The upper panel is temperature, with the bare-planet control drawn beside it. The lower panel is who owns the ground.

The three quantities that do the work are the two daisy albedos and the heat transport coefficient q, which decides how much warmer a black patch is than the planetary average. Set both albedos to 0.50 and the daisies become radiatively invisible: the biosphere is still there, still large, and the temperature curve lies exactly on top of the bare control. That is the control the whole argument needs, and it is one drag away.

Solar luminosity L 1.000 Start at 1.000 and walk it slowly upward. Watch the black daisies hand the planet over to the white ones while the temperature barely moves. Then push past 1.556 and watch the whole biosphere vanish in a single step of 0.002, taking 32 °C of regulation with it. Black daisy albedo 0.25 0.25 is the published value. Drag it up to 0.50 and the black daisies stop being black; the cold end of the regulated range walks inward because nothing can warm the planet enough to get started. White daisy albedo 0.75 Set this to 0.50 as well, so both daisies match bare ground. The populations carry on growing and dying and the temperature curve collapses onto the control. Nothing else in the model changes. Heat transport q 2.06e9 K⁴ q = 0 is a perfectly conducting planet: every patch sits at the planetary mean, so a daisy cannot feel its own colour and the two species become one. Try it, then come back through 2.06e9 to 6e9 and watch regulation get wider and sloppier at the same time.

planet: – bare control: – albedo: – black / white / bare: – regulated L: – drift: – suppression: –

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Model 2. Find the breaking point

The published daisy tolerates a 35 K range of temperature and dies at a rate of 0.3 per unit time. Neither number was measured. Neither could be. So the question worth asking is how much of the result survives a different choice.

Narrow the growth window and the regulated range shrinks from both ends, but slowly, and the regulation that remains gets tighter, because a fussier daisy that survives at all has pinned the planet closer to its optimum. Raise the death rate and something different happens: the range shrinks, the regulation gets worse, and at γ = 1 it stops entirely, because β ≤ 1 and bare ground ≤ 1 make growth incapable of matching death at any temperature.

Growth window half-width h 17.5 K 17.5 K is the published value, giving a daisy that grows between 4.85 and 39.85 °C. Pull it down to 4 and the regulated range falls to about half, while the suppression factor roughly triples. Fussier daisies regulate a narrower band, harder. Death rate γ 0.30 Walk it up from 0.30 in steps. The regulated width falls roughly linearly and the suppression factor falls with it. Somewhere past 0.95 the population cannot balance its own losses anywhere in the sweep and the curve snaps onto the bare control. Seeding rule This one is not a parameter, it is a modelling assumption, and it is worth more than either slider. Switch to a fresh start and the hot end of the regulated range falls from 1.556 to 1.212, because a bare planet at high luminosity is already too hot for a white daisy to germinate. Regulation up there is inherited, not achieved.

regulated L: – width: – drift: – suppression: – peak cover: –

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Published settings: regulated L = 0.704 to 1.556, width 0.852
Residual drift: 10.421 °C against a bare span of 60.236 °C
Suppression: 5.78×, rising to 8.30× over the middle 90 per cent
Coexistence band: bare ground pinned at 0.326531 for every L from 0.744 to 1.340
Collapse: +32.294 °C in one step of dL = 0.002 at L = 1.558

What to try, and what it will tell you

Set both albedos to 0.50 in Model 1. The temperature curve lands on the control and the readout says the difference is zero. This is the experiment that turns the parable into an argument: the daisies were not regulating because they were alive, they were regulating because they were coloured.

Then set q to zero. Black and white patches now feel identical temperatures, so the two species are the same species wearing different paint, and whichever one is slightly ahead takes everything. Regulation does not vanish, which surprised us, but it narrows sharply and the suppression factor falls to 1.00. The remaining range is the part of the story that owes nothing to having two colours.

Finally, in Model 2, switch the seeding rule. Nothing about the daisies changes. A third of the regulated range disappears. That number is not a result about planets. It is a result about the convention we chose, and a model whose headline answer moves by 40 per cent when you change a bookkeeping rule should be quoted with that fact attached.