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. “Once that top predator is dominant, it’s very hard to dislodge,” said Stephen Carpenter, an ecologist at the University of Wisconsin, Madison, who led the experiment. “You could do it, but it’s gonna cost you.”
The Peter Lake experiment demonstrated a well-known problem with complex systems: They are sensitive beasts. Just as when the Earth periodically plunges into an ice age, or when grasslands turn to desert, fisheries suddenly collapse, or a person slumps into a deep depression, systems can drift toward an invisible edge, where only a small change is needed to touch off a dramatic and often disastrous transformation. 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.
At Peter Lake, though, 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.
“We have all these complex systems like the brain, the climate, ecosystems, the financial market, that are really difficult to understand, and we will probably never fully understand them,” said Marten Scheffer, a complex systems theorist at Wageningen University in the Netherlands. “So it’s really kind of a small miracle that across these very different systems, we could find these universal indicators of how close they are to a threshold.”
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, “don’t try this at home.”
One Fish Two Fish
An outdoorsman who enjoys fishing, hunting and training a flamethrower on nonnative plants around his cottage in southwestern Wisconsin, Carpenter “sees the big picture faster and better than most scientists,” said Michael Pace, an ecologist at the University of Virginia and a collaborator. 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.
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: Before an outbreak, when insects were still scarce but the model forest was drifting toward its tipping point, the insect population would start to vary more and more erratically from one place to another across the forest.
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. “The work that we started doing after that 2003 conversation has really spawned a growth industry in ecology,” Carpenter said.
Peter Lake’s food web has two stable states, known in math lingo as “attractors.” In one possible state, the lake is laced with algae, and largemouth bass are scarce. This gives minnows the run of the place. They devour the water fleas (enabling the algae to flourish) as well as most newly hatched bass. The feedback loop reinforces the state of the lake, correcting for small fluctuations away from equilibrium. When, for instance, disease afflicts the minnows, the resulting flea surplus allows their numbers to quickly bounce back.
But Peter Lake is also stable when it is clear and full of bass. In this alternative state, predation is high, so minnow numbers are curbed; this allows water fleas to thrive (which suppresses algae) and bass hatchlings to reach maturity. Once again, the ecosystem is driven by a self-reinforcing feedback loop.
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. “No one likes that approach,” Pace said. Anyway, it isn’t necessary. For the new Peter Lake experiment, the dominance of bass or minnows is irrelevant.
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. “I can definitely say that you get very strong critical-slowing-down indicators from algae blooms, and I can also say we had some success in halting them,” Carpenter said, stressing that the findings have not yet been peer-reviewed.
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.
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 nonexperimental 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. “My vision is to have an alarm system over the coast of the civilized world where you can measure the environmental conditions of the system,” he said. “Any change in conditions would provide indication where something is going wrong.”
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. “All kinds of other factors make people move closer and further from the tipping point [of a migraine], but so far we have no way of measuring that,” Scheffer said. “If we can measure objectively how close the brain is to this tipping point, we can do much more powerful research on what are potential causal factors.”
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 paleoclimate data that critical slowing down preceded many abrupt climatic shifts in Earth’s history, such as the ends of ice ages and the desertification of North Africa, suggesting that many major climate systems undergo critical transitions. In a study of current observational data 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 “really good risk assessment” based on critical slowing down would show, he said, that “if we carry on climate-change business as usual, these become high-impact, high-probability events.”
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. “These are systems which are just a bit more complicated in the underlying dynamics,” said Alan Hastings, who led the study. Unlike the S curve representing Peter Lake’s stable states, Hastings said, for these ecosystems, “you can’t draw a picture. Not only is the picture impossibly more complicated but the picture doesn’t even exist.”
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 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.
“You can look at the glass being half-empty and say, oh yeah, there’s all those situations where we cannot really expect” critical slowing down, Scheffer said. “But I think it’s a miracle that the glass is actually half-full.”