Book review: Phase Transitions
Phase Transitions by Ricard Solé was one of those books that nurtured my curiosity and motivated me to carry on with my PhD. Ana, my girlfriend at the time (2011), always suggested me to bring nice books for holidays that would distract me from work, books with stories or authors from the places we were visiting . But with Solé it was difficult to leave it at home. Most of the book was read in 2012-13 on the beaches and bars of Barcelona, Solé’s home; and believe or not, it did distracted me from work by making me looking it from a different perspective.
Phase Transitions is the concept that physicist like Solé use to describe changes in dynamic systems with bifurcations – changes between different states of organisation in complex systems. It’s the same as ‘critical transitions’ or critical phenomena, as other authors like Marten Scheffer prefer to use; or ‘regime shifts’ as ecologist often call them. But that’s just jargon. I read the book too long ago to be able to give a fair summary and highlight its most important lessons. However, this review will be more from an emotional perspective, what I like and dislike from that bunch of math.
The book is an amazing resource for teaching. It’s structured in 16 very short chapters, most of them don’t exceed the 10 pages. Yet they cover as many disciplines as you can imagine, it’s like brain candy for an interdisciplinary inclined mind. Chapter 1-5 set up the basics: what are phase transitions, analysis of stability and instability, bifurcations, percolations and random graphs. Solé keeps the mathematics to a minimum, any student without a strong maths background like me follows and enjoy more the story that the mathematical subtleties. He also guide you on how the math or the set of equations that helps you understand something, say percolations, are also useful to understand what looks like unrelated topics such as cancer dynamics or lexical change in a language.
And that is exactly what I like of the book. Chapters 6 – 16 takes you on a journey of where phase transitions have applications in different fields in science: the origins of life (6), virus dynamics (7), and cell structure (8) for the biology inclined. For the medicine inclined: epidemic spreading (9), gene networks (10), and cancer (11). For someone like me: ecological shifts (12), social collapse (16), information and traffic jams (13) and collective intelligence (14). And my absolute favourite: language (15) because it surprised me how phase transitions can be used to understand change in language, and also because it introduced a very peculiar model called the hypercube. Now what I dislike of the book was the incomplete list of references, imagine if the one missing is the one you want to follow up!
I took the book out of the shelf today and look at it with nostalgia. Last week I read a paper that studies depression as a critical transition using models of symptoms networks with thresholds (co-authored by Scheffer, the author of the book that inspired this blog), and today I accidentally ended up watching the video below on how music can also have basins of attraction. That feeling of déjà vu, that two disparate fields can have something fundamental in common, that we can learn music and better understand depression or cancer and viceversa; that’s what makes me in love with science. That’s what I enjoyed the most of Solé’s book, it opened the horizon of what I was actually doing on my PhD and helped me feel less afraid of exploring; otherwise how does one make the nice connections?
What are the main drivers of regime shifts globally?
That was one of the key questions that inspired my PhD work. There is a buzz both in the media and the scientific literature that we are approaching a dangerous zone where the stability of the world ecosystems are at stake. Coral reefs are struggling and under a 2ºC warming scenario they will most likely disappear from many areas of the world. Every summer we hear of new ice free records in the Arctic while last few months there has been a consensus that Antarctica is also warming at a higher rate than previously expected. As today, boreal forest in Canada is burning at remarkably higher rates than usual. This year droughts have impacted strongly California and Brazil, with potential impacts on US food production and carbon storage in the Amazon respectively. Things are happening as ‘we speak’ and yet our knowledge about critical transitions in ecosystems is limited and often confined to well understood case studies (e.g. Jamaican coral reefs) and theoretical models. To the best of my knowledge, comparison of regime shifts exist for a handful of systems such as climate, agricultural landscapes, hydrological regime shifts, coral reefs and marine ecosystems.
Yesterday our paper Regime Shifts in the Anthropocene: Drivers, Risks, and Resilience was published in PlosONE. It address the question ‘What are the main drivers of regime shifts?’ by studying co-occurrence patterns of drivers reported by the regime shift database. It is the first large comparison of regime shift and their drivers, in fact we analysed 25 regime shifts types in marine (blue), terrestrial (green) and polar/subcontinental (orange) ecosystems. The figure below shows a network of drivers (57) on the left and regime shifts (25) on the right. The bigger the dot, the higher is the number of connections, which is is a proxy of the number of drivers a regime shifts has reported, or the number of regime shifts a driver is reported to cause. While nodes in the bottom show idiosyncratic drivers and regime shifts, the ones on the top are generalist, this is the most common drivers and the regime shifts with higher drivers diversity.
The main results of our work is that drivers related to climate change (e.g. droughts, floods, green house emissions) and food production (e.g. fishing, crops, use of fertilisers) are the main responsible for regime shifts globally. They co-occur together in patterns that one wouldn’t expect by pure chance, and this associations help us envisage management opportunities and challenges. The opportunities center around the knowledge base. We found that if two regime shifts share certain attributes such as occurring on the same ecosystem type, similar space and temporal scales, and impact similar ecosystem services; we can assume that they are caused by similar sets of drivers and therefore transfer successful management strategies from well-understood regime shifts to less understood ones. The challenge is to embrace drivers diversity. Addressing only well understood variables won’t preclude regime shifts from happening. Our work shows that these phenomena are often caused by a diversity of drivers and addressing them imply co-ordinated actions across scales, especially at the international level.
If you want to know more about our work, just follow the link above. The paper is on a open access journal and the data is also publicly available both in the regime shifts database and the public scientific repository Figshare. I happy to reply to questions or comments here or on the journal’s website.
One third of Earth’s largest groundwater basins are being rapidly depleted by human consumption
NASA and CalTech report two studies that quantify the depletion rate of major aquifers in the planet. Here are the links to the papers, both open access:
- Quantifying renewable groundwater stress with GRACE
- Uncertainty in global groundwater storage estimates in a Total Groundwater Stress framework
This means that significant segments of Earth’s population are consuming groundwater quickly without knowing when it might run out, the researchers conclude […]
The studies are the first to comprehensively characterize global groundwater losses with data from space, using readings generated by NASA’s twin GRACE satellites. GRACE measures dips and bumps in Earth’s gravity, which are affected by the mass of water. In the first paper, researchers found that 13 of the planet’s 37 largest aquifers studied between 2003 and 2013 were being depleted while receiving little to no recharge.
Eight were classified as “overstressed,” with nearly no natural replenishment to offset usage. Another five were found to be “extremely” or “highly” stressed, depending upon the level of replenishment in each. Those aquifers were still being depleted but had some water flowing back into them.
The most overburdened aquifers are in the world’s driest areas, where populations draw heavily on underground water. Climate change and population growth are expected to intensify the problem.
“What happens when a highly stressed aquifer is located in a region with socioeconomic or political tensions that can’t supplement declining water supplies fast enough?” asked Alexandra Richey, the lead author on both studies, who conducted the research as a UCI doctoral student. “We’re trying to raise red flags now to pinpoint where active management today could protect future lives and livelihoods.”
The research team — which included co-authors from NASA, the National Center for Atmospheric Research, National Taiwan University and UC Santa Barbara — found that the Arabian Aquifer System, an important water source for more than 60 million people, is the most overstressed in the world.
The Indus Basin aquifer of northwestern India and Pakistan is the second-most overstressed, and the Murzuk-Djado Basin in northern Africa is third. […]
In a companion paper published today in the same journal, the scientists conclude that the total remaining volume of the world’s usable groundwater is poorly known, with estimates that often vary widely. The total groundwater volume is likely far less than rudimentary estimates made decades ago. By comparing their satellite-derived groundwater loss rates to what little data exist on groundwater availability, the researchers found major discrepancies in projected “time to depletion.” In the overstressed Northwest Sahara Aquifer System, for example, time to depletion estimates varied between 10 years and 21,000 years.
“We don’t actually know how much is stored in each of these aquifers. Estimates of remaining storage might vary from decades to millennia,” said Richey. “In a water-scarce society, we can no longer tolerate this level of uncertainty, especially since groundwater is disappearing so rapidly.”
The study notes that the dearth of groundwater is already leading to significant ecological damage, including depleted rivers, declining water quality and subsiding land.
Both papers draw the attention to yet another driver of ecological regime shifts that might be occurring unnoticed by the challenges of data gathering. The recharging of aquifers could be thought of as a regime shift where the dominant feedbacks relate to the recharging rate but also through the coupling of vegetation and rain patterns produced by moisturising recycling. Far fetched idea that worth keep an eye on. For the time being, both papers go to the ‘potential regime shifts’ folder.
Cascading & domino effects
In my master thesis (2010) started exploring the ideas of domino effects across regime shifts. Although the idea is cool, attractive and hard to avoid, it’s hard to break down to formal theory and even worst to test empirically. This post from Scientific American (March 15, 2013) best summarises the state of the art in the debate. It only focus on climate tipping points, but the reader can easily extend it to non-climatic ones, such as the global collapse scenario proposed by the HANDY model recently developed with NASA support (news from the Guardian), where the tipping points rest on inequality.
From here down is copied from Scientific American website, I just find it inspiring:
Quick-Change Planet: Do Global Climate Tipping Points Exist?
Is there a chance that human intervention—rising temperatures, massive land-use changes, biodiversity loss and so on—could “tip” the entire world into a new climatic state? And if so, does that change what we should do about it?
As far back as 2008 NASA’s James Hansen argued that we had crossed a “tipping point” in the Arctic with regard to summer sea ice. The diminishing ice cover had moved past a critical threshold, and from then on levels would drop precipitously toward zero, with little hope of recovery. Other experts now say that recent years have confirmed that particular cliff-fall, and the September 2012 record minimum—an astonishing 18 percent lower than 2007’s previous record—was likely no fluke.
Sea ice represents a big system, but it is generally thought to be self-contained enough to follow such a tipping-point pattern. The question that has started to pop up increasingly in the last year, however, is whether that sort of phase transition, where a system shifts rapidly—in nonlinear fashion, as scientists say—from one state to another without recovery in a timescale meaningful to humanity, is possible on a truly global scale.
“You’re pushing an egg toward the end of the table,” says Tony Barnosky, a professor at the University of California, Berkeley. At first, he says, “not much happens. Then it goes off the edge and it breaks. That egg is now in a fundamentally different state, you can’t get it back to what it was.” Barnosky was the lead author on a much-discussed paper in Nature[DL1] last summer that suggested the world’s biosphere was nearing a “state shift”—a planetary-scale tipping point where seemingly disconnected systems all shifted simultaneously into a “new normal.” (Scientific American is part of Nature Publishing Group.)
Claims of catastrophic temperature shifts are unlikely to go down without an argument. A new paper published recently in Trends in Ecology & Evolution by Barry Brook of the University of Adelaide in Australia and colleagues argues that there is no real grounding to the idea that the world could display true tipping-point characteristics. The only way such a massive shift could occur, Brook says, is if ecosystems around the world respond to human forcings in essentially identical ways. Generally, there would need to be “strong connections between continents that allow for rapid diffusion of impacts across the planet.”
This sort of connection is unlikely to exist, he says. Oceans and mountain ranges cut off different ecosystems from each other, and the response of a given region is likely to be strongly influenced by local circumstances. For example, burning trees in the Amazon can increase CO2 in the atmosphere and help raise temperatures worldwide, but the fate of similar rainforests in Malaysia probably depend more on what’s happening locally than by those global effects of Amazonian deforestation. Brook and colleagues looked at four major drivers of terrestrial ecosystem change: climate change, land-use change, habitat fragmentation and biodiversity loss; they found that truly global nonlinear responses basically won’t happen. Instead, global-scale transitions are likely to be smooth.
“To be honest, when others have said that a planetary critical transition is possible [or] likely, they’ve done so without any underlying model,” Brook says. “It’s just speculation…. No one has found the opposite of what we suggested—they’ve just proposed it.” In their analysis Brook’s group concluded that the diversity of local responses to global forcings like increasing temperature means we cannot identify any particular point of no return.
Tim Lenton, an expert on tipping points at the University of Exeter in England, says there is no convincing evidence of global shift yet, but he doesn’t rule out the possibility. “It’s not obvious how you can get a change in Siberia then causing a synchronized change in Canada or Alaska,” he says, referring to a commonly cited climate feedback loop of permafrost melting at northern latitudes. “That doesn’t seem likely. It’s more that different parts of the Arctic are going to reach the thawing threshold at the same time just because they’re getting to the same kind of temperature.” This is a fine distinction: Are we looking at multiple systems tipping as one, or just a coincidental amalgam of unconnected systems falling off a ledge at similar time points?
Lenton says that there is a chance that ice-free Arctic summers could start a cascade effect—for example, elevated temperatures on nearby land that eventually find their way down into the permafrost and cause rapid melting. The carbon released by the permafrost could in turn initiate further warming, and maybe tip another disconnected system and so forth. “It’s a bit like having some dominos lined up,” he says. “I’m not sure yet whether we have a scenario like that for future climate change, but it’s worth consideration.”
Such a domino effect could end up looking more like a “smooth” response than a nonlinear one, but NASA’s Hansen says this doesn’t suggest we should ignore it. “Most tipping points are ‘smoothed out,’ but that does not decrease their importance,” he says. Even Arctic sea ice shows a smoothed response as it rolls past the point of no return. “Once you have passed a certain point, it takes only little additional forcing to lose all the sea ice.” And he echoes Lenton on the idea of dominos and hugely important sub-global systems: “[It’s] hard to see how the Greenland ice sheet would survive if we have sea ice-free summers.” In other words, melted sea ice could beget massive sea level rise, thanks to a supposedly unconnected system.
And further, that non-connectivity is not necessarily a given. Barnosky argues that the fundamental assumption that systems around the world are not strongly connected is no longer true. “What used to be isolated parts of the Earth really are very connected now, and we’re the connectors,” he says. Further, his group’s paper based the possibility of a global tipping point largely on comparisons to planetary history: Earth has exhibited rapid phase shifts in the past, and we are blowing those types of changes out of the water now. For example, the shift from the last glacial period into the current interglacial, which took only a few millennia ending around 11,000 years ago, featured abrupt land-use change: about 30 percent of the land surface went from ice-covered to ice-free over those few thousand years. In just a few hundred years, humans have converted about 43 percent of the world’s land to agricultural or urban landscapes.
Whether such rapid changes portend a new global shift is, to some extent, an esoteric, academic question. The answer depends on whether the world can really follow the classic mathematical definition of tipping points that relies on “bifurcation theory.” That theory holds that a system follows a smooth curve until a certain threshold—the egg rolls at similar speed until it hits the edge of the table—when it jumps to a new state with no obvious change in external pressures. And importantly, once that jump is made there is essentially no going back; you can’t “unbreak” the egg.
And at the bottom of the mathematical debate is a question of utility: Would the existence of a real planetary-scale tipping point change how we should confront our environmental challenges, from energy sources to land use?
A more accurate picture would not just let us prepare for rapid climate change, but might help us predict it as well. Marten Scheffer, of Wageningen University in the Netherlands, has done extensive work on ways we can see tipping points coming. On smaller scales, he says, a system can exhibit “critical slowing down”—a slowed ability to recover from perturbations—before jumping to the irreversible new state. Scheffer says, arguing for tipping points, that past global-scale, quick changes in climate appear to have exhibited a similar effect.
And if we agree a tipping point can exist, maybe we can even try and stave it off. As the world seems to be inching closer to addressing climate change, identifying specific targets for the most effective mitigation grows ever more important. In his recent State of the Union speech, Pres. Barack Obama called for unilateral action to address global warming–related emissions; if we can find a tipping point threshold, is that reason to adjust such action to reflect the possibility of rapid global-scale change?
“If there is plausibility to one of these tipping points, which I think there is, then it’s an even more urgent matter to act to slow all of these individual stressors down,” U.C. Berkeley’s Barnosky says, “because the outcomes could be more surprising and more disruptive to society, and happen faster than we have time to react…. I’d much rather err on the side of precaution then ignore the possibility of tipping points and then be unpleasantly surprised when they happen.”
Critical Transitions 