Rapid environmental change can threaten even a peaceful Daisyworld

WASHINGTON, Feb. 18, 2025 – Imagine a world filled only with daisies. Light-colored daisies reflect sunlight, cooling down the planet, while darker daisies absorb sunlight, warming it up. Together, these two types of daisies work to regulate the planet’s temperature, making the world more habitable for all of them.

And yet, even in this flowery paradise, a simple change can cause the entire ecosystem to collapse.

In Chaos, by AIP Publishing, researchers from the University of Cambridge and University College Cork found that this simple daisy-filled ecological model was vulnerable to collapse after experiencing relatively small, but rapid, changes to the environment.

The hypothetical planet full of daisies is more than an idle curiosity. It has a name — Daisyworld — and was invented in the 1980s as a model to help scientists understand how organisms could help regulate their environment. Since then, researchers have used it to explore topics like biodiversity and climate change.

“The Daisyworld model is a classic thought experiment regarding the co-evolution of life and the environment and has been widely used in the teaching of Earth system science,” said author Constantin Arnscheidt.

Because of its basic and fundamental nature, the authors wanted to use it to study the idea of ecological tipping points, points of no return beyond which an ecosystem is doomed to collapse. This can occur if the environment gets too extreme, but it can also happen if the environment changes too fast. This second type of tipping point is what they were interested in.

“Essentially, if you push the system quickly enough, you can trigger a collapse even if you don’t push it that hard,” said Arnscheidt. “This is called rate-induced tipping: The rate of change is the key factor in determining whether the system tips.”

Using mathematical modeling, the authors discovered that rate-induced tipping can happen even in Daisyworld. If the planet heats up or cools down too quickly, all the daisies will go extinct, even if they would otherwise have been able to survive just fine under those conditions.

This discovery mirrors similar observations found in other models and observed in real-life ecosystems.

“Rate-induced tipping has been shown to be relevant in more and more systems, especially complex ones like those in Earth science and ecology,” said Arnscheidt. “It’s also a phenomenon that will likely be quite relevant for humanity as we continue to navigate an era marked by rapid human-driven rates of change.”

Understanding rate-induced tipping is crucial because these collapse conditions are less obvious, but just as deadly. Without a clear picture of how these ecosystems respond to rapid environmental changes, we could unwittingly doom far more than a planet of hypothetical daisies.

“The fact that we can find rate-induced tipping in a model as classic and well-studied as Daisyworld, more than four decades since its inception, suggests that rate-induced tipping might be present in many other classic models if we only look for it,” said Arnscheidt.

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The article “Rate-induced biosphere collapse in the Daisyworld model” is authored by Constantin W Arnscheidt and Hassan Alkhayuon. It will appear in Chaos on Feb. 18, 2025 (DOI: 10.1063/5.0240983). After that date, it can be accessed at https://doi.org/10.1063/5.0240983.

ABOUT THE JOURNAL

Chaos is devoted to increasing the understanding of nonlinear phenomena in all areas of science and engineering and describing their manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines. See https://pubs.aip.org/aip/cha.

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