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.