Tipping PointsMathematics, Metaphors and Meanings
How to predict tipping points Posted on April 11, 2011 by brettcherry
Are tipping points inherently unpredictable? Some physical and social scientists tend to think so and say that even if people were able to predict the point before a tip it would be too late. But others are a little more optimistic. Mark Buchanan, a member of the Tipping Points project’s advisory council who is a physicist, freelance science writer and author of popular books such as Ubiquity and The Social Atom wrote a fascinating piece for New Scientist not long ago that focuses on this very question. Mark gives a number of interesting examples of tipping point systems from economics to ecology and physics. I highlight some of them below.
Researchers writing a computer program to simulate outbreaks of the Spruce Budworm in North America led them to using ‘bifurcation theory’ –‘…the branch of applied mathematics used to characterise how a system’s internal dynamics change, often abruptly, in response to mainly gradual changes around it.’ They found that ‘critical slowing down’ or ‘jagged fluctuations’ in the numbers of budworms could be used to predict tipping points in budworm populations that destroy North American forests. According to the article, one of the most influential outside changes on budworms is foliage density of forests:
For example, over many years the foliage harbouring the budworms would grow thicker as trees grew and matured, making it progressively more difficult for birds to find the grubs. That gradual change, outwardly almost imperceptible, would first make itself known in how a budworm population fluctuated: each time the number of grubs was higher than average, it would take longer to sink back to its equilibrium value. Eventually, the long-term increase in foliage density, coupled with a natural short-term rise in the bug population, would be enough to render the birds’ foraging strategy ineffective. Budworm numbers would start increasing exponentially and the system would tip abruptly into a radically different state, with catastrophic consequences for the forest. ‘Prophets of doom: The secret of soothsaying’. New Scientist.
Other examples of tipping points include abrupt changes in the Earth’s past climate:
Vasilis Dakos and Marten Scheffer of the University of Wageningen in the Netherlands and their colleagues, meanwhile, were looking into eight cases of abrupt changes in Earth’s past climate. These ranged from the transition from a balmy tropical state to a colder climate with ice caps 34 million years ago to an event 5000 years ago when the north African landscape switched abruptly from a savannah dotted with lakes to desert. In each case, the researchers identified a sudden increase in the autocorrelation of the temperature record in the time leading up to the transition. Autocorrelation is a mathematical sign of critical slowing: it reflects the predictability of a time series, or how closely its behaviour correlates with what it did in the recent past. As a system approaches a tipping point and its responses to natural perturbations grow slower, that autocorrelation grows larger. ‘Prophets of doom: The secret of soothsaying’. New Scientist.
Could auto-correlations be understood as an indicator of ‘tipping points’? If mapping these patterns of behaviour within a system is an accurate method for predicting disaster then maybe.
Foreseeing tipping points could also play an important role in ecology such as the relationship between coastline development and fish stocks. Developing shorelines eliminates valuable marine environments that fish depend on for survival and can have a devastating effect on fish stocks overall.
… Stephen Carpenter, Buz Brock and ecologist Reinette Biggs of Stockholm University in Sweden developed a computer model of a fishing ground in which they varied fishing and shoreline development policies and watched for their effects on the virtual fish stocks. Shoreline development can have a profound effect on fish numbers by depriving fish of natural habitats and increasing harmful run-offs. But once developed, a shore is not easy to undevelop, at least quickly. In this case, the warning signs of critical slowing and increased autocorrelation did indeed show up, but too late for any change in development policy to feed through and avert a collapse. “If you wait for clear evidence of negative environmental impacts, you may well be too late to do anything about it,” says Brock. In the case of simple overfishing, however, the outcome was more positive. If policies such as fishing moratoriums were implemented immediately after an early warning was received, the collapse of fish populations could be prevented. (Proceedings of the National Academy of Sciences, vol 106, p 826). This suggests that with the right high-precision data to hand we can recognise and avert impending catastrophes. “With the rapid growth in high-frequency environmental monitoring equipment, this may be more possible in the future,” says Biggs. ‘Prophets of doom: The secret of soothsaying’. New Scientist.
Obviously, this article is about understanding or predicting the negative consequences of some tipping points, but tipping points need not only apply to forthcoming disasters. How about a tipping point that leads to a social revolution that topples over a corrupt or ineffective government? Or perhaps a tipping point that leads to equality or intelligent uses of energy resources? Indeed, these are theoretical examples of tipping points that the world could look forward to, but the time of disaster is certainly upon us and therefore research on tipping points for providing some kind of foresight into how people might prepare for disaster whether it’s an earthquake, climate change or a financial crisis could not come at a better time. There is also the question of how to define ‘tipping point’ in relation to complex systems, as it seems to imply more than simply unexpected rapid or exponential change.
Πηγή:
http://tippingpointsproject.org/
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