Tipping points – those critical thresholds in a complex system where a small nudge can cause a catastrophic response – are perhaps the most fearsome threats to the Earth’s climate, but they also haunt ecosystems, financial markets, and even sufferers of medical conditions such as epilepsy and asthma. A fascinating review in Nature today (subscription) sketches out the mathematical patterns on which many of these instances seem to be based, and describes giveaway signs that might warn us to change course before the system tips.
One common warning sign, for example, is flickering between the pre-tipping point state and the post-tipping point state. In climatology, abrupt changes traced in records of the Earth’s past suggest the planet has regularly gone through tipping points, such as the sudden warm-ups that change glacial periods into deglaciations. Earlier this year researchers reported in Nature Geoscience that rapid flickering signaled the end of Earth’s most recent cold spell, the so-called Younger Dryas period. The authors of the new review, led by Marten Scheffer of Wageningen University in The Netherlands, say that in a similar way, debilitating epileptic seizures can be preceded by frequent small symptomless seizures – the ‘flickers’ of the epileptic brain.
The diagram above shows a kind of Platonic tipping point that can explain this behaviour. Solid lines represent stable states, and the system usually sticks to these paths like a ball in a track. The areas in between are called ‘basins of attraction’, and the grey arrows show which direction the ball will be attracted if it gets bumped off its track. Depending on the shape of the curve and the amount of random noise affecting the system, in some cases a ‘ball’ approaching a critical threshold is likely to get knocked off its track and into the opposite basin of attraction, ending up on the other track – and then get knocked back again. It can go back and forth until it passes the point where there are two side-by-side tracks (or stable states). Going further into simple models like this one, the authors point out other tell-tale warnings, such as a slowdown in the response to perturbations as a tipping point is approached.
This type of analysis popped up in climate change headlines last November. The report that, if it weren’t for human meddling, the planet would be on its way into another ice age (in a mere 10,000 to 100,000 years) was based on the kind of dynamics that Scheffer et al. are reviewing.
The group says such generic early warning signals are an excellent thing when a system’s mechanisms and feedbacks are too murky to allow confident predictions. And if we want the most reliable heads-up on future catastrophes, they say, we should look at patterns across space as well as time, “as a spatial pattern contains much more information than does a single point in a time series, in principle allowing shorter lead times.” The more robust our Earth monitoring programs, then, the better use we can make of this mathematical weathervane.
Image: Reproduced from Nature 461, 53-59 (2009).