Modeling Chaos, Forecasting Collapse

Evidence is accumulating that ecological systems—rangelands, coral reefs, forests, and lakes among them—face tipping points, after which an additional small change can cause large, rapid disruptions. Once a system is sent into sharp decline, it can take a long time to recover.

Are there early warning signs that the tipping point is near? And if so, can these signs be detected in complex and dynamic situations such as financial markets, political conflict, or medical conditions like heart attacks or epilepsy?

Becker Friedman Institute Visiting Scholar William “Buz” Brock explored these questions at a talk Oct. 25. After reviewing the evidence, his answer was a definite maybe, with some skepticism, especially when it comes to predicting sudden changes in asset markets.

Brock, a former faculty member at the University of Chicago, is known for applying mathematical principles of chaos theory to study dynamic systems and nonlinearities in economics and econometrics. In his current role at the University of Wisconsin, he has been collaborating with others to study variations in the ecology of lake systems. Studies suggest increased fluctuations in the state of such systems may be the early warning sign of sudden changes that tip the system into crisis, he said.

Brock illustrated the point with the example of rangelands, showing how heavy grazing disrupts the natural balance that allows wildfires to spread on grass and control the growth of woody shrubbery. Increasing the density of sheep per acre beyond a healthy level tips this balance.

Variation in the measured vegetation starts to rise as the system approaches this critical point; “When you see the standard deviation of vegetative biomass start rising, you’d better back off and not add more sheep or you will lose your rangeland,” Brock said. Once this happens, it takes a long time for the system to bounce back.

Researchers are testing systems at differing scales to see if this heightened variation can be an early warning signal. At the microbial level, laboratory experiments with yeast cell systems have documented increased variation in populations as food was removed to stress the system to a critical point.

Brock and colleagues are interested in finding an early warning signal for ecological damage to lakes. In Wisconsin lakes, the threat comes from both ends of the food chain. Increased phosphorus flowing into lakes from fertilizers in farm waste and runoff adds to algae growth at the bottom of the food chain. At the top, sports fishermen are removing the large fish that eat smaller fish, that in turn eat the zooplankton, which eat the algae.  This also allows the algae to multiply, resulting in fish dying off and cloudy, slimy, smelly lakes.

Researchers are simulating models of the mean and standard deviation of phosphorus to mimic observed lake conditions and outcomes. “We want an early warning signal to tell you to back off because if the lake flips [to this state], it’s going to take a long time to bring it back,” Brock said. “Once a lake passes to a bad state, we have to reduce [phosphorus] to a much lower than where it was at a clean level to get the lake back to a healthy state,

Moving out of the models, researchers have conducted an experiment with side-by-side lakes in Wisconsin, manipulating the food chain in one and using the other as a control. This is the largest scale that the early warning theory has been tested on. Researchers argued that the variation in the system indeed increased; Brock, however, found that the results were very messy. “I would bet 70/30 that some future study would overturn this,” he said.

“People have been trying to apply this to the climate system,” Brock noted. “I’m skeptical. Lars (Hansen) and I have been working on modeling climate systems and there is just too much uncertainty.

Brock said he is more optimistic about research that is looking for increases in variability in biometric measures leading up to a seizure or heart attack. “That might go somewhere.”

“Where I’m really skeptical is stock market breakdowns,” he continued. He has collaborated on others with work on trading models where investors tried to extract meaningful signals from the noise of volatile trading. His colleagues are arguing about the results. “I took the Chicago economics position that if you actually picked up an early warning signal, if you have competitive trading people will trade on it and the signal will be traded away.” Noting that he was just restating the Efficient Markets Hypothesis, Brock acknowledged there were exceptions to it, “but in general the signals would be brief and transitory.”