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Early warning signals for critical transitions

Press release issued: 7 February 2012

Researchers from the University of Bristol and Max-Planck-Institute for the Physics of Complex Systems have presented a methodology that uses mathematics to exploit easily obtainable information to a greater effect and as a result can reduce the amount of additional data that needs to be collected.

A new method developed by Dr Thilo Gross, Senior Lecturer in Engineering Mathematics at the University of Bristol and Dr Steven Lade from the Max-Planck-Institute for the Physics of Complex Systems in Germany promises to change this.

In a paper published in PLoS Computational Biology, the researchers present a methodology that uses mathematics to exploit easily obtainable information to a greater effect and thus can reduce the amount of additional data that needs to be collected.  

The newly proposed method adds a new twist to an old idea. Predicting the behaviour of a system is easy if the system is well understood. For instance the behaviour of a simple pendulum can be well captured by a simple mathematical model that then predicts the dynamics of the pendulum for a long time. However, systems at risk of severe transitions, such as fisheries, are generally complex and not understood in great detail. To warn of critical transitions, scientists therefore use mostly model-free approaches that require close and continuous monitoring of the system under consideration. The present situation thus presents a fundamental dilemma: Predicting transitions without a credible mathematical model needs large amounts of data, but building such a model would entail gathering even larger amounts of information. 

“How can we improve our chances of seeing crashes coming? The number-crunching methods used by economists and others require massive amounts of data, and all too frequently collapse under their own weight,” explains Len Fisher, author of Crashes, Crisis, and Calamities and other top-selling popular science books. “In their ground-breaking new paper, Thilo Gross and Steven Lade show how we can use traditional intuition and understanding in a surprising and mathematically rigorous new way to reduce the amount of data that we need while actually enhancing our chances of 'seeing it coming'.”

The key insight on which the new approach builds is that some bits of information are easier to obtain than others. For instance in fisheries it is easier to find out what fish are eaten by a specific species of predator then to precisely quantify this relationship. The researchers have found a way to use easily obtainable information without requiring the difficult information. "Our approach combines the best of both worlds: we make use of specific knowledge that is available, while not requiring full knowledge of the system," says Dr Lade. “Our main contribution is how partial information is utilized,” adds Dr Gross. “We don’t try to build any single full-fledged model. Instead, we use a mathematical trick to study all models in parallel that are not excluded by what we know.”

In fisheries simulations Lade and Gross have already demonstrated that their method can use available expert knowledge to reduce the need for stock monitoring data that is costly to collect. "We have shown our method to be effective for a simulated collapse, with some level of a prior knowledge about the fishery," confirms Dr Lade. "We now plan to test our method with observational data, refine the approach to incorporate shades of gray in the expert knowledge, and develop a framework to readily apply it to any system."

Paper: Early warning signals for critical transitions: a generalized modeling approach, Steven J. Lade and Thilo Gross, PLoS Computational Biology, 02 February 2012.

Further information

Please contact joanne.fryer@bristol.ac.uk for further information.