Resilience Science » Regime Shifts

Systems theorist Vladimir Arnold has died

Garry Peterson — Sat, 12 Jun 2010 12:39:25 +0000

Vladimir I. Arnold one of the major creators of dynamical systems theory used to represent ecological regime shifts died June 3rd this year.

He was one of the creators of the mathematics behind what is known as catastrophe theory and singularity theory which are used to represent regime shifts. The New York Times writes:

Singularity theory predicts that under certain circumstances slow, smooth changes in a system can lead to an abrupt major change, in the way that the slipping of a few small rocks can set off an avalanche. The theory has applications in physics, chemistry and biology.

“He was a genius and one of the greatest and most influential mathematicians of our time,” said Boris A. Khesin, a former student of Dr. Arnold’s and now a professor of mathematics at the University of Toronto.

One of Dr. Arnold’s biggest contributions was applying the methods of geometry and symmetry to the motion of particles. Dr. Arnold work on how fluids flow was applied to the dynamics of weather, providing a mathematical explanation for why it is not possible to make forecasts months in advance. Infinitesimal gaps or errors in information cause forecasts to diverge completely from reality.

A similar approach can also be applied to the motion of planets. If Earth were the only planet to circle the Sun, its orbit would follow a precise elliptical path, but the gravity of the other planets disturbs the motion. Scientists found that it impossible to calculate the precise motion of the planets over very long periods of time or even prove that Earth will not one day be flung out of the solar system.

Understanding the subtle and difficult-to-predict boundary between stability and instability is important not only in the study of planetary dynamics but also in other endeavors, like designing a nuclear fusion reactor.

In 1954, the Russian mathematician Andrey Kolmogorov figured out a key insight to calculating whether such systems are stable. Dr. Arnold provided a rigorous proof in 1963 for one set of circumstances. Another mathematician, Jürgen Moser, provided the proof for another. The work is now collectively know at the KAM theory.

Jeremy Jackson describes “How we wrecked the ocean”

Garry Peterson — Wed, 19 May 2010 08:33:54 +0000

Eminent coral reef ecologist Jeremy Jackson recently gave a talk at TED called How we wrecked the ocean, which presents a popular version of his research on the long-term human impact on the ocean.

Johan Röckstrom talks about Planetary Boundaries

Garry Peterson — Tue, 06 Apr 2010 08:28:29 +0000

Johan Röckstrom recently gave a talk on Planetary Boundaries based on the papers Nature (doi:10.1038/461472a) and Ecology and Society.

In those papers the authors propose propose nine planetary boundaries, beyond which the functioning of the earth system will fundamentally change from the conditions in which human civilization has emerged. They argue that we have crossed the climate, nitrogen and extinction boundaries, and need to change the course of our civilization to move back into conditions which provide a safety for human civilization.

The talk is now up in two parts on YouTube (but the quality is only ok).

Four Short Links

Garry Peterson — Mon, 15 Feb 2010 21:45:03 +0000

1) A new paper in Ecology Letters, Regime shifts in ecological systems can occur with no warning, by Alan Hastings and Derin B. Wysham shows that in models certain types of regime shifts do not exhibit any signs of early warning. In their abstract they write:

… we show that the class of ecological systems that will exhibit leading indicators of regime shifts is limited, and that there is a set of ecological models and, therefore, also likely to be a class of natural systems for which there will be no forewarning of a regime change … We then illustrate the impact of these general arguments by numerically examining the dynamics of several model ecological systems under slowly changing conditions. Our results offer a cautionary note about the generality of forecasting sudden changes in ecosystems.

2) Climate charts and graphs is a useful blog about using R to download and analyze publically available climate data.

3) Tom Fiddaman makes a simple systems management game in Processing.

4) Alex Steffen on World Changing claims that Bill Gates gave the Most Important Climate Speech of the Year:

On Friday, the world’s most successful businessperson and most powerful philanthropist did something outstandingly bold, that went almost unremarked: Bill Gates announced that his top priority is getting the world to zero climate emissions.

Computer trading producing new financial dynamics?

Garry Peterson — Fri, 29 Jan 2010 19:32:07 +0000

In October 1987, stock markets around the world crashed, with the Dow Jones droping 22%. The causes of this crash are still unclear, but one of the suspected causes was computer automated trading. This concern lead attempts to design mechanisms to break potential viscous cycles by creating ‘circuit breakers‘, rules that halt trading if the Dow rapidly . However, as financial engineers innovate, new risks are emerging. The Financial Times writes Computer-driven trading raises meltdown fears:

An explosion in trading propelled by computers is raising fears that trading platforms could be knocked out by rogue trades triggered by systems running out of control.

Trading in equities and derivatives is being driven increasingly by mathematical algorithms used in computer programs. They allow trading to take place automatically in response to market data and news, deciding when and how much to trade similar to the autopilot function in aircraft.

Analysts estimate that up to 60 per cent of trading in equity markets is driven in this way.

… Frederic Ponzo, managing partner at GreySpark Partners, a consultancy, said: “It is absolutely possible to bring an exchange to breaking point by having an ‘algo’ entering into a loop so that by sending them at such a rate the exchange can’t cope.”

Regulators say it is unclear who is monitoring traders to ensure they do not take undue risks with their algorithms.

The Securities and Exchange Commission has proposed new rules that would require brokers to establish procedures to prevent erroneous orders.

Mark van Vugt, global head of sales at RTS Realtime Systems, a trading technology company, said: “If a position is blowing up so fast without the exchange or clearing firm able to react or reverse positions, the firm itself could be in danger as well.”

For more details on current problems see the Financial Times article Credit Suisse fined over algo failures

NYSE Euronext revealed on Wednesday it had for the first time fined a trading firm for failing to control its trading algorithms in a case that highlights the pitfalls of the rapid-fire electronic trading that has come to dominate many markets.

The group, which operates the New York Stock Exchange, said it had fined Credit Suisse $150,000 after a case in 2007 when hundreds of thousands of “erroneous messages” bombarded the exchange’s trading system.

The messages, generated by the Credit Suisse proprietary trading algorithm, caused the trading system to slow down, affecting 900 share issues, according to Ray Pellechia, a NYSE Euronext spokesman.

Asked if the exchange’s systems could have been knocked out, he said: “If you had multiplied this many times you’d have had a problem on your hands.”

Fire, climate change, and the reorganization of Arctic ecosystems

Garry Peterson — Mon, 18 Jan 2010 09:43:00 +0000

Alaskan nature writer Bill Sherwonit reports on Yale Environment 360 about the complex response of Arctic ecosystems to climate change in how Arctic Tundra is Being Lost As Far North Quickly Warms:

Researchers have known for years that the Arctic landscape is being transformed by rising temperatures. Now, scientists are amassing growing evidence that major events precipitated by warming — such as fires and the collapse of slopes caused by melting permafrost — are leading to the loss of tundra in the Arctic. The cold, dry, and treeless ecosystem — characterized by an extremely short growing season; underlying layers of frozen soil, or permafrost; and grasses, sedges, mosses, lichens, and berry plants — will eventually be replaced by shrub lands and even boreal forest, scientists forecast.

Much of the Arctic has experienced temperature increases of 3 to 5 degrees F in the past half-century and could see temperatures soar 10 degrees F above pre-industrial levels by 2100. University of Vermont professor Breck Bowden, a watershed specialist participating in a long-term study of the Alaskan tundra, said that such rapidly rising temperatures will mean that the “tundra as we imagine it today will largely be gone throughout the Arctic. It may take longer than 50 or even 100 years, but the inevitable direction is toward boreal forest or something like it.”

… In the course of studying caribou, Joly has also learned a great deal about the role of fire in “low,” or sub-Arctic, tundra, where for several decades at least it has been a much more significant factor than on the North Slope’s “high Arctic” landscape. About 9 percent of Alaska’s lower latitude tundra burned between 1950 and 2007, whereas only 7 percent of the North Slope caught fire during that period. That could change as the region warms and fires become more frequent farther north.

Joly’s and Jandt’s overlapping interests and study areas have prompted them to jointly analyze several interrelated factors — fires, caribou foraging, global warming, and shrub expansion — that appear to be acting “unidirectionally” to reduce lichen cover in northwest Alaska, a change likely to have substantial ripple effects.

Jandt’s fascination with tundra wildfires has now led her northeast, to the Anaktuvuk River burn, where in 2008 she and several research partners established transects to study burn severity, plant community shifts, and the effects of fire on permafrost and active soil layers. Among the team’s observations so far: virtually no lichen cover remains in the burn area; willows have begun re-sprouting, and by 2009 some were already more than a foot tall; and tundra slumping and collapse has occurred.

Many other scientists have also begun studies in the Anaktuvuk burn, which has become part of the Arctic Long Term Ecological Research (LTER) program. Based at the Toolik Field Station, in the Brooks Range’s northern foothills, the LTER study is funded by the National Science Foundation. Among the many researchers working out of Toolik is Mack, who characterized the tundra as “a very resilient plant community.” But for all its resilience, Mack wonders if North Slope tundra is headed for substantial and perhaps irrevocable change, particularly if “fire starts the ecosystem on a new trajectory,” as has happened on the Seward Peninsula.

…Other scientists are looking at a different, but related, extreme Arctic event: the development of “thermokarst failures” within the burn area and in other parts of the North Slope. … A thermokarst is uneven terrain produced by thawing permafrost, and recent studies have revealed many more thermokarst features than anyone expected. On flat ground, that may mean bumps and hollows. But on sloping ground, it can create huge slumps in which tons of soil move downhill. Such thermokarst failures can lead to high carbon dioxide and methane emissions from newly exposed and thawing soils, thus contributing to atmospheric warming. The thermokarsts provide niches for new plants and shrubs, which add to the “greening” of the tundra and warming of the soil, which in turn favors even more shrub growth. And in moving huge amounts of sediments and nutrients, thermokarsts can have “enormous impacts” on tundra streams and lakes, Bowden says.

Anything that warms tundra and thaws permafrost — from fires to milder annual temperatures and increased rainfall, particularly in winter — can contribute to thermokarst failures. Because climate change models predict a warmer and wetter Arctic with increased summer thunderstorms and lightning, thermokarsts are likely to occur on an ever-larger scale.

Modelling a social-ecological poverty trap due to infectious disease

Garry Peterson — Thu, 31 Dec 2009 05:51:37 +0000

In an interesting article Poverty trap formed by the ecology of infectious diseases (Proc Royal Soc B 2009) Mathew Bonds and others, describes how they couple a simple infectious disease model with an simple economic development model to produce model of a infectious disease induced poverty trap. They write:

The combined causal effects of health on poverty and poverty on health implies a positive feedback system. Despite the importance of understanding such critical and systematic ecological interactions between humans and their most important natural enemies, and the anecdotal evidence that such poverty traps may indeed exist, we lack mechanistic frameworks of poverty traps that are rooted in the dynamics of disease. Here, we propose such a model. We find that a prototypical host–pathogen system, coupled with simple economic models, induces a poverty trap. More broadly, this model serves to illustrate how feedbacks between people and their environment can potentially give rise to major differences in human survival and economic welfare (Diamond 1997).

… we illustrate our underlying concept using a general one-disease SIS (susceptible–infected–susceptible) model, where individuals can be serially reinfected over the course of their lifetime. This model is meant to serve as the simplest general way of representing the kind of repeated threats of infection faced by poor tropical communities. More specifically, the general model also resembles a typical malaria system (Gandon et al. 2001), which has high prevalence rates among the poor and has been especially implicated in hindering economic growth (Gallup & Sachs 2001).

Their model produces two alternative regimes, a high productivity/low disease regime and a low productivity/high disease regime.

Feedback between economics and the ecology of infectious diseases forms a poverty trap. The prevalence of infectious diseases, I*(M) (black line), falls as per capita income rises, while per capita income, M*(I) (grey line), falls as disease prevalence, I, rises. The disease and income functions are in equilibrium where these two curves intersect at (I*(M*), M*(I*)). Two of these equilibria (I*(M*1), M*(I*1) and I*(M*3), M*(I*3)) are stable, and one (I*(M*2), M*(I*2)) is unstable. The poverty trap is the basin of attraction around (I*(M*3), M*(I*3)). α = 0.06; β̄ = 40; μ̄ = 0.01; ν = 0.02; h̄ = 90; δ = 5; ϱ = 0.003; τ = 0.15; ϕ = 15; κ = 30.

In this model, a social-ecological system can be pushed into or out of the poverty trap by changes that effect labour productivity, such as changes in the level of education or infrastructure, or changes in disease prevalence due to the expansion or contraction of public health.

In the paper the authors show that empirical patterns of disease burden and income suggest the existence of disease poverty traps.

They conclude:

While we hope that our model framework can serve as a useful point of departure for exploring more complex relationships, the theoretical analysis we present here has significant implications: simply coupling economics with a well-established model of the ecology of infectious diseases can imply radically different levels of health and economic welfare (i.e. poverty traps) depending on initial conditions. The practical implications are also significant. Because the world’s leading killers of the poor—malaria, HIV/AIDS, tuberculosis, diarrhoea and respiratory infections—are highly preventable and treatable, current global efforts to improve public health in areas of extreme poverty could theoretically pay long-term economic dividends. Furthermore, this analysis underscores that there are dramatic implications if economic activity is coupled with ecological processes that are well-known to behave in nonlinear ways.

Richard Alley explains how CO2 is the climate’s “biggest control knob”

Garry Peterson — Tue, 29 Dec 2009 10:23:50 +0000

Richard Alley gave a well reviewed Bjerknes Lecture at the December AGU meetings in San Francisco, in which clearly and interestingly explains the paleo-climatic evidence of how CO2 is a key part of the Earth’s climate regulatory system. Lots of interesting research, some of it quite recent, is synthesized clearly.

His talk The Biggest Control Knob: Carbon Dioxide in Earth’s Climate History is available on the AGU meeting website.

Richard Alley, is a professor of geosciences, at Penn State University and author of the popular science paeleo-climatology book The Two-Mile Time Machine: Ice Cores, Abrupt Climate Change, and Our Future.

Peatlands as complex adaptive systems

Garry Peterson — Mon, 16 Nov 2009 11:01:00 +0000

Shifting states. (Left) Hummock-hollow pattern at Rygmossen, a small raised bog near Uppsala, Sweden. (Right) "Ladder" system of ridges and pools, Inverewe Bogs, Scotland. Persistent environmental change, such as a long-term increase in climate wetness, can trigger a shift from one such peatland type to another.

In a Perspective in Science, Nancy Dise reviews how the response of peatlands to global change will be complex (doi:10.1126/science.1174268). She writes:

Research from a variety of areas and approaches is converging upon the concept of peatlands as complex adaptive systems: self-regulating to some degree, but capable of rapid change and reorganization in response to internal developmental changes or to external forcing (4). It has long been known, for instance, that the surface of a peatland can rise and fall, sometimes dramatically, in response to rainfall or mild drought, while maintaining a fairly constant water level relative to the surface. This “Mooratmung” (“bog-breathing”) is related to the sponge-like nature of Sphagnum, which can adsorb water and trap gases. Recent studies have shown that the carbon balance of peatlands can in turn be surprisingly resilient to perturbations, even fairly severe ones. For example, subjecting peat cores (5) or a peatland field site (6) to a water table drawdown similar to a prolonged drought initially led to a respiration-driven loss of soil carbon. But both carbon loss and subsidence (6) lowered the peat surface, decreasing its height above the water table, and effectively shifted the system back toward its starting state. Conversely, a rising water table stimulated growth of Sphagnum and other vegetation, which increased carbon accumulation, raised the surface of the peat and, in effect, lowered the local water table (5). Thus, an environmental perturbation may trigger an initial gain or loss of carbon, but recovery in the direction of the initial state can moderate the impact.
…
Long-term global changes—particularly warming, drought, and elevated nitrogen deposition—are likely to ultimately induce shifts in some existing peat-forming areas to new ecosystems such as grassland or shrubland (10, 11), and the increase in biomass from vascular plants could in part compensate for carbon losses from soil oxidation during the transition. However, even if some net carbon accumulation returns, the gains are short-lived: The key peatland quality of slowly removing and storing carbon for hundreds or thousands of years is lost.

Considering peatlands as complex adaptive systems characterized by quasistable equilibrium states—resilient to change at some level of perturbation but shifting to new states at higher levels of disturbance—provides a meaningful framework for understanding and modeling their response to environmental change. Ignoring the strong feedbacks inherent in peatlands may lead to substantial under- or overestimates of their response to global change. The challenge is to forecast both the future environmental conditions that peatlands will experience and the internal feedbacks and state changes that may be triggered by these conditions. To meet this challenge it is vital to continue and expand long-term monitoring networks to characterize the present, paleo-environment research to reconstruct the past, and manipulation experiments in the field and laboratory to build our understanding of these unique and valuable ecosystems.

Reviewing Critical Transitions

Garry Peterson — Sat, 31 Oct 2009 05:03:41 +0000

Environmental historian, John R. McNeill, reviews Marten Scheffer’s new book on resilience – Critical Transitions in Nature and Society. In the American Scientist he writes:

Like many before him, Marten Scheffer is impressed with parallels between social systems and natural systems. Moreover, he is convinced that problems confronting the human race require something more integrated than the fragmentary knowledge of the various academic disciplines. In short, he seeks to span the famous “two cultures” and to take a long stride toward consilience. Coming from a background in limnology and aquatic ecology, Scheffer is inevitably more at home in some arenas of knowledge than others, and his new book, Critical Transitions in Nature and Society, is mainly about the critical transitions in nature that are of interest to society. An example with which he begins the book is typical: the transformation of the Western Sahara into desert about 5,500 years ago as a result of initially small climate change that built on itself because the drier climate reduced vegetation, thereby heightening albedo.

Part of Scheffer’s aim is to contribute to the study of how well the theory of system dynamics corresponds to real life, in the behavior both of nature and of society. “If we are able to pin down the mechanisms at work,” he says, “this may eventually open up the possibility of predicting, preventing, or catalyzing big shifts in nature and society.” To be able to do so is a long-standing human ambition, which has been given fullest rein in political regimes that have seen utopia just over the horizon and have aimed to get there as soon as possible. In the abstract, such ambition seems laudable. In practice, it has led to many regrettable “big shifts” in nature and society, such as those undertaken in the headiest days of the Soviet Union or Mao Zedong’s rule in China. To date, those most keen on provoking “big shifts” have known far too little, and perhaps cared too little as well, about the possible outcomes of their actions. When results did not conform closely enough to their hopes, they used their powers to try to force society and nature into preferred channels, which led to gulags and environmental disasters. When trying to catalyze big shifts in nature and society, one must really know what one is doing—and that is very, very hard to do.

…

So Scheffer seems more cheerful about the future of the Social-Eco-Earth-System at the end of writing his book than I am after reading it. But his premise—that hope lies with integrated eco-social science rather than our traditional isolated silos of knowledge—is surely correct. Perhaps we are on the edge of a happy tipping point after which science enters a state in which depth is not unduly esteemed over breadth, in which integrated study of complex systems becomes the norm, in which our insight into real-world eco-social systems grows and grows to formerly unimaginable levels. If so, Scheffer may be right to be optimistic. But there are some powerful attractors working against it.

Planetary Boundaries

Garry Peterson — Thu, 24 Sep 2009 05:28:41 +0000

A number of resilience researchers, and many others, have proposed the concept of planetary boundaries in a new paper A safe operating space for humanity in Nature (doi:10.1038/461472a).

Johan Rockstrom and others propose nine planetary boundaries, beyond which the functioning of the earth system will fundamentally change. They argue that we have crossed the climate, nitrogen and extinction boundaries, and need to change the course of our civilization to move back into conditions which provide a safety for human civilization.

Nature has a special feature on Planetary Boundaries. It has also published seven independent essays by experts who reflect upon each of the defined boundary (two of the nine were not defined due to a lack of information), and their blog Climate Feedback is also hosting a discussion of the article.

Science journalist, Carl Zimmer has written a good article about the paper and concept on Yale’s Environment 360.

The Stockholm Resilience Centre provides links to the full paper, and supporting information, as well as a number of videos explaining the concept.

Responses to Early Warning Signals for Critical Transitions paper

Garry Peterson — Tue, 08 Sep 2009 07:23:49 +0000

The recent paper by Marten Scheffer and other resilience researchers paper Early Warning Signals for Critical Transitions (doi:10.1038/nature08227) has been reported in a number of places including Time, USA Today, and Wired. While many newspapers just reprint the press release, several articles add something.

A USA Today article Predicting tipping points before they occur quotes Brian Walker:

“This is a very important paper,” says Brian Walker, a fellow at the Stockholm Resilience Center at the University of Stockholm in Sweden.

“The big question they’re trying to answer is, how the hell do you know when it’s coming? Is there any way you can get an inkling of a looming threshold, something that might be a warning signal that you’re getting to one of the crucial transition points?”

Wired magazine article Scientists Seek Warning Signs for Catastrophic Tipping Points quotes several sceptical scientists:

“It’d be very nice if it were true that there were precursors for tipping points in all these diverse systems. It’d be even nicer if we could find these precursors. I want to believe it, but I’m not sure I do,” said Steven Strogatz, a Cornell University biomathematician who was not involved in the paper.

The difficulty of early detection is especially pronounced with markets. Computer models can replicate their bubble-and-crash behavior, but real markets — buffeted by political and social trends, and inevitably responding to the very act of prediction — are much cloudier.

“It is hard to find clear evidence of bifurcations and transitions, let alone find an early warning system to detect an upcoming crash,” said Cars Homme, an economic theorist at the University of Amsterdam.

The most promising evidence of useful early warning signs comes from grasslands, coral reefs and lakes. Vegetation-pattern-based early warning signs have been documented in several regions, and transition theory is already being used to guide land use in parts of Australia.

The U.S. Geological Survey is currently hunting through satellite imagery for signals of impending desertification at two sites in the Southwest. They’ve studied desertification there by painstakingly measuring local conditions and experimentally setting fires, removing grasses and controlling the fall of water. But so far, the vegetation patterns that indicated tipping points in the Kalahari haven’t shown up here, though this may be due to poor image quality rather than bad theory. The researchers are now looking for signals in on-the-ground measurements of vegetation changes.

“These things aren’t going to be foolproof. There will be false positives and false negatives, and people need to be aware of that,” said Carpenter. “There’s still a great deal of basic research going on to understand the indicators better. We’re still in the early days. But why not try? The alternative is to get repeatedly blindsided. The alternative is not appealing.”

Time magazine in Is There a Climate-Change Tipping Point? quotes co-author Steve Carpenter:

So, how do we know that change is at hand? The Nature researchers noticed one potential signal: the sudden variance between two distinct states within one system, known by the less technical term squealing. In an ecological system like a forest, for example, squealing might look like an alternation between two stable states — barren versus fertile — before a drought takes its final toll on the woodland and transforms it into a desert, at which point even monsoons won’t bring the field back to life. Fish populations seem to collapse suddenly as well — overfishing causes fluctuations in fish stocks until it passes a threshold, at which point there are simply too few fish left to bring back the population, even if fishing completely ceases. And even in financial markets, sudden collapses tend to be preceded by heightened trading volatility — a good sign to pull your money out of the market. “Heart attacks, algae blooms in lakes, epileptic attacks — every one shows this type of change,” says Carpenter. “It’s remarkable.”

In climate terms, squealing may involve increased variability of the weather — sudden shifts from hot temperatures to colder ones and back again. General instability ensues and, at some point, the center ceases to hold. “Before we reached a climate tipping point we’d expect to see lots of record heat and record cold,” says Carpenter. “Every example of sudden climate change we’ve seen in the historical record was preceded by this sort of squealing.”

The hard part will be putting this new knowledge into action. It’s true that we have a sense of where some of the tipping points for climate change might lie — the loss of Arctic sea ice, or the release of methane from the melting permafrost of Siberia. But that knowledge is still incomplete, even as the world comes together to try, finally, to address the threat collectively. “Managing the environment is like driving a foggy road at night by a cliff,” says Carpenter. “You know it’s there, but you don’t know where exactly.” The warning signs give us an idea of where that cliff might be — but we’ll need to pay attention.