Researchers are developing equations to prevent the collapse of our planet’s most threatened ecosystems

Scientists can now predict and compare tipping points so resources can be directed where they are needed most

Headlines about extreme weather, melting ice caps and endangered species remind us daily of how our environment is changing. The profound scale and intensity of these challenges can lead to the question: “What should we do first? Researchers have recently developed formulas that help answer this question, effectively creating a method to sort ecosystems in decline by measuring and comparing their distance from tipping points.

In research just published in Nature Ecology & Evolution, a team led by Jianxi Gao, Assistant Professor of Computer Science at Rensselaer Polytechnic Institute, developed equations that compare distances to tipping points in various mutualistic systems. . In other words, for the first time, various environments can be analyzed for their degree of complete and, perhaps, irreversible change, and they can be compared to others to determine the areas most in need of intervention. .

Previously, scientists could detect early warning signals that a system was approaching its tipping point, but they were unable to assign an exact value to the distance between a system and its tipping point. The value could define the likelihood of a system going from the desired state to the undesired state, or how easily a tipping point could be reached.

Gao’s team developed a general dimension reduction approach to simplify data in complex systems, allowing precise measurements of distances to tipping points in various ecosystems. The team also developed a scale factor that places the resilience of different systems on the same scale so they can be compared.

“With so many ecosystems grappling with the impacts of climate change, it’s critical to be able to express how little time we have left to intervene before a tipping point is reached,” said Curt Breneman, Dean from the Rensselaer School of Science. “Mobilization will not happen without a sense of urgency.”

Gao’s team studied 54 different environments from around the world and analyzed the many factors that control their resilience. Species loss, invasions, human activities, and environmental change all cause “disturbance” in an ecosystem, but its likelihood of collapse is determined by the structural properties of the ecosystem. For example, if a few trees are felled in a thick forest, the impact on the ecosystem will be minimal as new trees will grow and the system will return to its previous state. However, in an area where trees are lacking, the loss of a few can have a deeper impact and the system can slip into an undesirable state from which recovery is difficult. In mathematical terms, resilience is the distance to the edge of the basin of attraction.

“For example, if one pull element is forest and the other is savannah, the system may or may not transfer to savannah due to many factors,” Gao said. “The base of attraction refers to the region of these factors inside high-dimensional space. Where is the region of forest where if you cross the boundary it turns into savannah? If a system stays in the limit, it will always recover.Only when it crosses a certain value, it goes to another state and cannot recover.

Gao’s team believes that the method cannot only be used to determine the resilience of ecological systems, but also of biological, technical and social systems.

“The dimension reduction approach is very general and can be applied to different types of systems,” Gao said. “It’s universal.”

The team also measured the tipping point within a supply chain network.

On an optimistic note, the team’s research does not conclude with tipping points. They are also pursuing a restoration algorithm in the event of systems failure.

Gao was joined in the research by Huixin Zhang and Weidong Zhang from Shanghai Jiao Tong University, Qi “Ryan” Wang from Northeastern University, and Shlomo Havlin from Bar-Ilan University. Their work was supported by the NSF CAREER Award.

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