Many complex dynamical systems have critical thresholds—so-called tipping points—at which the system shifts abruptly from one state to another. In medicine, we have spontaneous systemic failures such as epileptic seizures or depressive disorders; in global finance, there is concern about systemic market crashes; in the Earth system, abrupt shifts in ocean circulation or climate may occur; and catastrophic shifts in rangelands, fish populations or wildlife populations may threaten ecosystem services.
Such transitions are notoriously difficult to predict, because the state of a system may show little change before the tipping point is reached. Also, models of complex systems are usually not good enough to predict reliably where critical thresholds may occur. Interestingly, though, it now appears that certain universal early-warning signals may occur in a wide class of systems as they approach a critical point.
Professor Marten Scheffer, a Dutch mathematical biologist who has been studying critical transitions for years, explains that “If you recognize the early warning signals, you might be able to avoid the transition, or in some cases, promote it. Take for example a depression, or the poverty trap. You want to leave those behind as quickly as possible. But tipping into a much warmer climate without ice caps and with much higher sea levels is something you’d want to avoid.”
At first sight, it may seem surprising that disparate phenomena such as the collapse of an overharvested population and ancient climatic transitions could be indicated by similar signals. However, the dynamics of systems near a critical point share common characteristics, regardless of differences in the details of each system.
Therefore, sharp transitions in a range of complex systems are in fact related. In models, critical thresholds for such transitions correspond to bifurcations. Particularly relevant are ‘catastrophic bifurcations’, where, once a threshold is exceeded, a positive feedback propels the system through a phase of directional change towards a contrasting state.
Another important class of bifurcations are those that mark the transition from a stable equilibrium to a cyclic or chaotic system. The most important clues that have been suggested as indicators of whether a system is getting close to a critical threshold are related to a phenomenon known as critical slowing down. The idea here is to directly measure the recovery time (or rate) of a system back to its initial equilibrium state following a perturbation. In case the system is close to a tipping point the recovery time increases (or the recovery rate decreases).
So is it possible to predict those changes? More and more so, according to Dr. Scheffers: “What we often find is that the resilience of a system decreases in the run-up to a tipping point. We see that in ecosystems, financial markets, health, etc.”
“The ecological systems that I study are in a certain state of equilibrium. A lake is clear, your mood is good. But there’s always something happening. You get a speeding ticket, a volcano erupts, you name it. The system therefore fluctuates, but does have a tendency to return to its equilibrium. If it does so quickly, its resilience is high. But if the recovery is slow, it’s a sign that the system is drifting. You might be close to a tipping point, and the system could turn into a different state just like that, without being able to easily return to its former state.”
“Tropical forests, for instance, can die from drought and heat and turn into a persistent savanna. Forests that are sensitive to such a change recover their canopy after heavy times slower than more resilient forests do. In depressive disorders we’ve shown something similar, along with psychologists and psychiatrists. If you get an unpleasant phone call, or a bird poops on your head, but soon after you’re walking around whistling again, you’re mood is probably very stable. But if it still bothers you the next day, or maybe even a week later, than the recovery time is slower. That’s a bad sign.”
There’s been some criticism of the use of early warning signals, which may be too unreliable to accurately predict a tipping point.
“Ever since we published our first article about this we’ve been saying that you can never predict exactly when a system goes haywire, because there’s always an element of chance. Today we prefer to speak of indicators of resilience. If you have the right indicators, try to increase or decrease the resilience to affect the chances of a turnaround,” Marten Scheffer clarifies.
The question is: are we experiencing a big change now? In the Arctic, the signs of change are everywhere: Temperatures nearly 20°C above the seasonal average, summer sea-ice cover hitting new record lows. But only time can tell how those changes will unfold.
Video: James White, Institute of Arctic and Alpine Research – 2014