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from QuantaMagazine Website
photography by Todd
Pearsons/Engbretson Underwater Photography
Scientists are homing in on a warning signal that arises in complex systems like ecological food webs, the brain and the Earth's climate.
Could it help prevent future
catastrophes?
Nestled in the northern Wisconsin woods, Peter Lake once brimmed with golden shiners, fatheads and other minnows, which plucked algae-eating fleas from the murky water.
Then, seven years ago, a crew of ecologists began stepping up the lake's population of predatory largemouth bass.
To the 39 bass already present, they added 12, then 15 more a year later, and another 15 a month after that. The bass hunted down the minnows and drove survivors to the rocky shoreline, which gave fleas free rein to multiply and pick the water clean.
Meanwhile, bass hatchlings - formerly gobbled up by the minnows - flourished, and in 2010, the bass population exploded to more than 1,000. The original algae-laced, minnow-dominated ecosystem was gone, and the reign of bass in clear water began.
Today, largemouth bass still swim rampant.
The Peter Lake experiment demonstrated a well-known problem with complex systems:
But systems that exhibit such "critical transitions" tend to be so complicated and riddled with feedback loops that experts cannot hope to calculate in advance where their tipping points lie - or how much additional tampering they can withstand before snapping irrevocably into a new state.
Courtesy of Steve Carpenter Peter Lake (bottom), a six-acre body of water at the University of Notre Dame Environmental Research Center that has been used in ecosystem experiments since 1951, is separated by an earthen dike from Paul Lake, which serves as a reference during experiments.
At Peter Lake, though, Stephen Carpenter and his team saw the critical transition coming.
Rowing from trap to trap counting wriggling minnows and harvesting other data every day for three summers, the researchers captured the first field evidence of an early-warning signal that is theorized to arise in many complex systems as they drift toward their unknown points of no return.
The signal, a phenomenon called "critical slowing down," is a lengthening of the time that a system takes to recover from small disturbances, such as a disease that reduces the minnow population, in the vicinity of a critical transition.
It occurs because a system's internal stabilizing forces - whatever they might be - become weaker near the point at which they suddenly propel the system toward a different state.
Since the Peter Lake study, interest in critical slowing down has spread across disciplines, bringing with it the hope of foreseeing and preventing a plethora of catastrophic failures.
As theoreticians refine their understanding of the phenomenon, experimentalists are gathering further evidence of it in a mix of real-world systems.
Experts stress that the study of critical slowing down is in its early stages, and not yet ready to serve as a call to action in the management of real systems.
In some cases, responding to the signal might save an endangered species, a patient's mental health, or an industry. But in other types of complex systems that have been studied mathematically - such as food webs that, unlike Peter Lake's, are so chaotic that they do not exhibit critical transitions at all - the same signal might be a false alarm.
Carpenter, who has returned to Peter Lake for a new experiment, says much more research is needed to sort out these different cases.
In the meantime, he said,
One Fish Two Fish
An outdoorsman who enjoys fishing, hunting and training a flamethrower on nonnative plants around his cottage in southwestern Wisconsin, Carpenter,
Carpenter has worked on and off for 35 years at the experimental reserve where Peter Lake is located, making use of the relatively closed systems that lakes provide to test big ideas in complexity theory.
Critical slowing down, as an idea, can be traced back at least as far as the 1950s, when physicists theorized that it would arise in certain properties of matter near a phase change.
But as Carpenter tells it, the potential usefulness of critical slowing down went unrecognized until a boozy conversation in 2003 at a restaurant-bar in Tobago, where he and several colleagues had gathered for a conference.
Jeff Miller/University of Wisconsin, Madison Stephen Carpenter, professor of zoology and director of the Center for Limnology at the University of Wisconsin, Madison, standing in Lake Mendota near the campus shoreline.
Crawford "Buzz" Holling, an eminent Canadian theoretical ecologist, had begun reminiscing about a celebrated explanation of insect outbreaks that he and two collaborators had developed in 1978.
They showed that in a mathematical model of an evolving forest ecosystem, when conditions were just right, it was possible for a small change in these conditions to touch off a sudden explosion of tree-killing insects, as happens every few decades in eastern Canadian and American spruce and fir forests.
But there was one aspect of the model that Holling said he had never understood:
Sitting across the table was William "Buz" Brock, a mathematical economist specializing in dynamical systems at Madison.
Brock knew right away why the variance in the insect population had increased near the brink of an outbreak. He whipped out a yellow legal pad, and, over a couple of bottles of wine, explained critical slowing down to his ecologist companions.
Carpenter said he realized "immediately" that the phenomenon could serve as an ecological warning signal.
It turned out the German ecologist Christian Wissel had made the same point 20 years earlier, but hardly anyone had noticed.
Peter Lake's food web has two stable states, known in math lingo as "attractors."
Once again, the ecosystem is driven by a self-reinforcing feedback loop.
Andrew Silver for Quanta Magazine, with design by Olena Shmahalo and photography by Todd Pearsons/Engbretson Underwater Photography
In a simplified diagram of the ecosystem's possible states, the two stable states form the upper and lower sections of an S-shaped curve.
If the ecosystem drifts away from this curve, it quickly returns to it, staying anchored to either the upper or the lower state depending on which feedback loop dominates its dynamics.
Over time the ecosystem may wander horizontally along the curve, swept by a current of outside influences, toward one of the hairpin bends - a tipping point.
When Carpenter and his crew increased the lake's bass population, the ecosystem drifted from the bottom left part of the S-curve toward the first bend. As it approached this tipping point, the feedback loop that favored minnows started to lose its dominance over the competing feedback loop that favored bass. The effects nearly canceled each other out.
Consequently, when disease and other random disturbances pushed the species' populations away from the curve, the ecosystem took much longer to restabilize than before. This is critical slowing down.
The slowdown allows disturbances to the ecosystem to accumulate, which is why, in Holling's model, the variance in insect numbers increases near the brink of an outbreak. And when Carpenter and his team counted minnows in 60 traps each day, the variance in the minnow counts also increased as the tipping point of the critical transition approached.
Peter Lake's food web is now anchored to the top of the S curve.
Removing enough bass to propel the system to its left tipping point and restore it to its minnow-dominated state would probably only be possible using a ruthless and indiscriminate fish poison.
Anyway, it isn't necessary.
For the new Peter Lake experiment, the dominance of bass or minnows is irrelevant.
Critical Slowings
Critical slowing down has to be actionable to be useful in preventing real-world catastrophes.
Two years ago, Carpenter and his crew began gradually enriching Peter Lake with nutrients to drive it to the brink of a different critical transition: the onset of an algae bloom.
When they became statistically confident that they had measured critical slowing down in pH and algae levels, they stopped enriching the lake, and waited to see whether the algae bloom would happen anyway or if the researchers' response to the signal allowed the lake to return to normal.
Eventually, he said, ecosystem managers with limited resources might use measurements of critical slowing down to compare the relative well-being of different lakes, triaging them into healthy, deteriorating and doomed categories and concentrating their efforts where they can make the most difference.
Courtesy of Lisandro Benedetti-Cecchi The intertidal waters off of Capraia, an Italian island, are dominated by either species-diverse miniature forests (top) or less environmentally favorable turf (bottom). The forest exhibits early warning indicators before collapsing to the turf state.
Lisandro Benedetti-Cecchi, an ecologist at the University of Pisa in Italy, has found strong signals of critical slowing down in response to the deterioration of an intertidal marine ecosystem in the Mediterranean.
There, the intertidal zone can be dominated either by species-diverse miniature forests, or by environmentally unfavorable turf.
As Benedetti-Cecchi and his team deteriorated small patches of forest, driving them toward the tipping point at which turf takes over (with care taken to avoid harming non-experimental areas), they measured critical slowing down in the forest's recovery time.
In a separate study that has not yet been published, they found that the recovery length, or the distance needed for a turf-dominated region to transition back to a healthy forest-dominated region, also increased near the tipping point.
Benedetti-Cecchi hopes measurements of recovery time and length will eventually become part of every coastal wildlife manager's tool kit.
Marten Scheffer and his collaborators have found that critical slowing down in mood variations can serve as an indicator of impending depressive episodes.
They're now looking for the signal in neuronal activity before migraine attacks, which affect 12 percent of adults and are believed to be triggered by critical transitions in the cerebral cortex.
Other researchers have begun using critical slowing down as a tool for predicting the future of Earth's climate.
Back in 2008, Vasilis Dakos of ETH Zurich in Switzerland and collaborators found evidence in paleo-climate data that critical slowing down preceded many abrupt climatic shifts in Earth's history, such as,
...suggesting that many major climate systems undergo critical transitions.
In a study of current observational data (Slowing down of North Pacific Climate Variability and Its Implications for Abrupt Ecosystem Change) published in September, Tim Lenton and Chris Boulton, Earth system scientists at the University of Exeter in the United Kingdom, measured a slowing down of sea-surface temperature fluctuations in an ocean circulation pattern called the Pacific Decadal Oscillation (PDO).
The PDO itself doesn't seem to undergo critical transitions, but a weakening of its internal stabilizing forces could be bad news for related marine ecosystems that do have tipping points.
Currently, Lenton said, climate scientists tend to treat critical transitions in Earth's climate as high-impact but low-probability events.
However, a,
But with no window into the intricate internal workings of most complex systems, we can often only guess whether they have multiple stable states and critical transitions.
Many real-world systems appear to follow the Peter Lake blueprint. But others are so chaotic that their variables evolve unpredictably and do not exhibit critical transitions at all.
This could be true of some climate systems, and even some lakes.
In 2010, theoretical ecologists at the University of California, Davis, showed that in a particular model of a three-species lake food web, one of the species can get knocked off balance and go extinct without ever showing signs of critical slowing down.
Unlike the S curve representing Peter Lake's stable states, Hastings said, for these ecosystems,
In other cases, critical slowing down might be present in a system, but too weak to be easily measured.
Jeff Gore, a biophysicist at the Massachusetts Institute of Technology and a co-investigator on the Mediterranean shoreline study, has also led a series of detailed studies (Generic Indicators for Loss of Resilience Before a Tipping Point Leading to Population Collapse) of critical slowing down in laboratory yeast cultures - ecosystems that Gore admits to caring nothing about, but which exhibit unambiguous critical transitions.
In yeast cultures that are stabilized by multiple environmental influences at the same time, Gore's team recently reported that signals of critical slowing down can (for certain combinations of influences) become washed out and difficult to detect.
A recent review paper by Scheffer, Carpenter, Dakos and Egbert van Nes of Wageningen University summarizes what is currently known about the scope of critical slowing down, including its limitations.
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