1. Tipping Points or Critical Transitions

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

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

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

6. Also transitions in other complex systems
...
Marine ecosystems

7. h

8. How to predict critical transitions ?

9. Extrapolation ?
Claussen, et al (1999) Geophysical Research Letters 26,
Scheffer, et al. (2001). Nature 413:

10. Extrapolation ? Terrigenuous Sediment (%)
Claussen, et al (1999) Geophysical Research Letters 26,
Scheffer, et al. (2001). Nature 413:

11. Statistics for many cases ?
Adler (2001) Nature 414:

12. Experiments !

13. Experiments ?

14. Past behaviour

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

17. Universal Laws Rule at Critical Points

18. Generic Early Warning Signals

19. 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 Nature

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

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

22. High Resilience

23. Low Resilience

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

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

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

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

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

29. 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)

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

31. 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
William Brock

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

33. 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

36. 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

37. 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

38. 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?

39. 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?

40. 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