Tipping Points or Critical Transitions

Relationship between conditions or drivers and system state Scheffer et al 2009

Relationship between conditions or drivers and system state Scheffer et al 2009

Grasslands Holmgren & Scheffer (2001) Ecosystems 4: 151-159; Holmgren et al. (2001) TREE 16:89-94

Also transitions in other complex systems ... Marine ecosystems

h

How to predict critical transitions ?

Extrapolation ? Claussen, et al (1999) Geophysical Research Letters 26, 2037-2040. Scheffer, et al. (2001). Nature 413: 591-596

Extrapolation ? Terrigenuous Sediment (%) Claussen, et al (1999) Geophysical Research Letters 26, 2037-2040. Scheffer, et al. (2001). Nature 413: 591-596

Statistics for many cases ? Adler (2001) Nature 414: 480-481

Experiments !

Experiments ?

Past behaviour

Can Critical Transitions be predicted ? Even if we do not understand the system ?

Universal Laws Rule at Critical Points

Generic Early Warning Signals

Scheffer, Carpenter, Walker, Foley and Folke 2001. Nature I guess most here will know this idea… In brief… However, thinking of real systems, this is a charicature of one aspect… Scheffer, Carpenter, Walker, Foley and Folke 2001. Nature

“Slow recovery from perturbations” Critical Slowing Down Van Nes & Scheffer “Slow recovery from perturbations” American Naturalist 2007

“Generic Early Warning Signals” in stochastic environments close to tipping point increased variance increased autocorrelation + skewness... + flickering....

High Resilience

Low Resilience

Such early warning signals have been shown in models Sharp shifts are common in palaeo climate on all scales

Slowing down precedes ancient climate shifts but also in the lab Drake & Griffen Nature 2010 Vasilis Dakos

Slowing down precedes ancient climate shifts but also in the lab Vasilis Dakos

And in real climate dynamics Sharp shifts are common in palaeo climate on all scales Vasilis Dakos Dakos et al PNAS 2008

Critical slowing down announced 8 abrupt climate shifts Slowing down precedes ancient climate shifts Dakos et al PNAS 2008

Spatial patterns may warn earlier Dakos et al Theoretical Ecology 2010 Fig. 4 An example of the evolution of spatial and temporal correlation between neighboring cells in the vegetation turbidity model (Scheffer, 1998). Panels a, c show the spatial mean of the system’s state variable following the slow change in the control parameter. The gray-shaded area indicates the period before the system starts flipping. c Note the shift in the case of low connectivity is gradual, as each cell shifts almost independently from its neighbor. a The shift is abrupt when connectivity is high and the system reaches the transition globally. b Spatial correlation signals well in advance the shift of the lake to turbid conditions, outperforming the increase in temporal autocorrelation. d At low connectivity, spatial correlation hardly changes before the onset of transition, but the trend in temporal autocorrelation is stronger. Top panels are snapshots of the spatial distribution of vegetation cover far from the transition (high resilience), and just before the transition (low resilience; parameter values as in Table 1 for high heterogeneity in hE)

So far Critical Slowing Down ...... Subtle signs close to equilibrium What about more Stochastic Systems ?

No Critical Slowing Down but Hints of Alternative States ‘Flickering’ No Critical Slowing Down George Sugihara but Hints of Alternative States Livina et al Clim. Past. 2010 William Brock

Spatial Information may also reveal such Stability Properties George Sugihara William Brock

Hirota, Holmgren, VanNes & Scheffer 2011 Australia Africa Tree cover (untransformed) in 1-km2 grid cells as a function of the mean annual precipitation for (A) Africa, (B) Australia, (C) South America, and (D) intercontinental data sets [between 35°S and 15°N (12)]. Although the precipitation distribution and forest abundance vary between continents, the statistical relationships of tree cover to precipitation are quite similar (fig. S2). South America Hirota, Holmgren, VanNes & Scheffer 2011

Hirota, Holmgren, VanNes & Scheffer Science 2011 Relationship between the resilience of tropical forest, savanna, and treeless states and mean annual precipitation (in millimeters per year). (A) The tree cover data (percent, bottom plane) suggest a double catastrophe-fold. Stable states correspond to solid parts of the curve on the bottom plane and to minima in the stability landscapes. Unstable equilibria correspond to the dashed parts of the curve and to hilltops in the stability landscapes. At bifurcation points (B), stable equilibria disappear through collision with unstable equilibria. Resilience measured as the width of the basin of attraction around a stable state diminishes toward such bifurcation points. (B) Potential landscapes as computed directly from the data. Stable states (solid dots) are minima and the unstable equilibria (open dots) are maxima at a given precipitation level. A three-dimensional animation is available at (12). Hirota, Holmgren, VanNes & Scheffer Science 2011 Published by AAAS

Hirota, Holmgren, VanNes & Scheffer Science 2011 Resilience Maps Forest resilience for South America. (A) Resilience of remaining forest expressed as the probability of finding forest at the local mean annual precipitation level, computed with the global logistic regression model depicted in Fig. 2B. Forest with low resilience (yellow dots) is predicted to be most likely to turn into a savanna or treeless state. (B) Current distribution of tree density obtained from remote sensing (12). Resilience maps of forest, savanna, and treeless states for South America, Africa, and Australia can be found in (12). Hirota, Holmgren, VanNes & Scheffer Science 2011 Published by AAAS

Questions 1. Could Bayesian models help to reduce the uncertainty and limitations identified in the papers? 2. What are some barriers that challenge the adaptation of resilience modeling to social sciences?

Questions 3. How do these models deal with the nested and hierarchical characteristics of the underlying complex systems, specially where human beings are involved as conscious actors? 4. In designing “desirable” systems, how do you choose among homogeneity vs. heterogeneity?

Questions 5. What other examples of socio-ecological systems (particularly those in which conscious processes are involved) could we think of in terms of the two types of early-warning signals? 6. How do you scale for autocorrelations?- How do you know what time of time scale to consider