Tipping points and critical slowing down

Malcolm Gladwell's bestseller The Tipping Point popularized that key concept taken from complex system theory and, in particular, illustrated its significance for social systems. One of the central areas of recent research on tipping points has focused on trying to identify when they are about to occur. In other words, what changes are apparent in the system immediately before it reaches the 'tipping point', changes which could be observed and used to predict the likely onset of a system's transition to another equilibrium state?

One such phenomena has been labeled 'critical slowing down,' the decreasing rate of recovery from small disturbances to a system as it approaches a tipping point. In other words, when a system is close to a tipping point, it can take a long time to recover from even a very small disturbance. John M. Drake & Blaine D. Griffen recently reported the first experimental demonstration of such a process in a biological system "Early warning signals of extinction in deteriorating environments" (doi:10.1038/nature09389). Here is a summary of the key points from ScienceDaily:

The paper, published in the early online edition of the journal Nature, describes a study of the fluctuations in experimental populations of water fleas (Daphnia magna) undergoing environmental stress until they reach a tipping point beyond which they do not remain viable. The study is unique in its careful comparison of these stressed populations with other, healthy populations in the context of new theories about dynamic systems undergoing transitions at a tipping point. ...

The experiment featured populations of water fleas that were assigned to either deteriorating environments (in this case, declining levels of food) or stable environments (the control group). The experiment lasted for 416 days, when the last population in the deteriorating environment group became extinct. Depending upon the amount of food they received, populations in the deteriorating environment group reached the population viability tipping point after approximately 300 days. Populations in the control group never reached it; those populations persisted.

The researchers next looked at a variety of statistical indicators, early warning signals that could detect the onset of CSD and thereby predict the approach to a tipping point. They compared the indicators with the timing of the decrease in food and with the achievement of the tipping point, mathematically referred to as a "transcritical bifurcation." They found that each of the indicators -- some more strongly than others -- showed evidence of the approaching tipping point well before it was reached.

According to Drake, what is even more important is the generality such statistical indicators are expected to exhibit. That is, although precise quantitative models are required to predict most natural phenomena -- in any domain of science -- with any degree of accuracy, the theory of critical slowing down applies qualitatively anytime a bifurcation is in the vicinity. "You don't have to know the underlying equations to use the theory," Drake said, "and this is important in biology, where the dynamics are typically sufficiently complex that we often do not know which equations to use. In fact, we may never come to such a complete understanding, given the range of biodiversity out there and the fact that species are evolving all the time."