There are some empirical, illustrative case-studies in which catastrophic did happen. The first classical example is the interactive dynamics between the spruce budworm, its predators and the boreal forest  in North America (Holling 1986; Meadows 2008). When the budworm became a ‘pest’ and northern forests were sprayed with the insecticide known as DDT to control it, success in killing the budworm was meagre. The reason was, it turned out, that the forest managers set up a situation of ‘persistent semi-outbreak’ by keeping the budworm food stock (balsam fir) at a high level and killing off the natural predators.

Another well-researched case is Eutrophication of shallow lakes (Scheffer et al. 2001). It has become another archetype of ecosystems under stress of a disturbance such as a pollutant. An influx of nutrients from inflowing fertiliser and wastewater and industrial effluent had caused prolific growth of phytoplankton, which in turn caused bottom plants to disappear as they got less or no light. The lake became turbid, which makes the lake look greenish and turbid and a monotonous community was all that remained. Even the bird populations dropped by an order of magnitude. Hypothesizing a regime shift with nutrient concentration the fast- and turbidity the slow-changing variable, it became clear that the lake had two regimes. A clear lake with bottom vegetation with low turbidity becomes more turbid as nutrient concentration rises, until a certain threshold is reached. At this critical level. the bottom vegetation collapses and the system jumps to a steady-state without vegetation and high turbidity. “Overall, the diversity of animal and plant communities of shallow lakes in the turbid state is strikingly lower than that of lakes in the clear state.” (Scheffer et al. 2001).

A third case-study of nonlinear regime shifts in response to external and associated internal ecosystem variables is when there is a positive feedback between consumers (such as plants) in combination with limiting resources (such as water or nutrients). This is quite common: fine-scale interactions lead to spatial resource concentration and self-organised patchiness because of endogenous causes. If if grazing pressure exceeds a critical threshold, vegetation cover will decrease. If then dryness increases, for instance due to a slow change in climate, a regime shift can happen. The high grazing pressure indicates that an optimal long-term stocking rate should be 10% to 20% below the benchmark model value, instead of the current stocking rates in the order of 50% above the indicated optimal rate. These are clear warnings that sudden ecosystem change might happen in semi-arid regions, with catastrophic results for the inhabitants (§9.7). Models of long-term climate-induced changes in the (semi-)arid regions should incorporate these risks, because only then can these stories and these models prepare for such events and their consequences. Increasingly, ABM are developed to investigate situations like these and suggest strategies for sustainable management.

This phenomenon has been investigated for heterogeneous landscapes using a stochastic cellular automata model and field data from three regions in the Mediterranean (Kefi et al. 2007). It is found that the patch-size distribution of the vegetation follows a power law and can be explained from local feedback interactions amongst plants. When the model is used to simulate the effects of increasing grazing pressure, it turns out that the deviations from power laws seen in the field data also emerge in the model simulations and, importantly, that they always and only occur close to a transition into a desert. The researchers suggest that patch-size distributions may be a warning signal for the onset of desertification, a spatial equivalent of the previously discussed time-signal of a critical transition. The models indicate an important point for managing for resilience: fast, surprise changes may happen and much more effort is needed to bring the system back to its original state than expected from its past. Such events – for instance, the sudden outburst of catastrophic forest fires – have a power law size distribution and are named self-organised criticality. The power law size distribution implies that there are many events of small size but a few of (very) large size. Natural phenomena such as forest fires and earthquakes exhibit such distributions.

Other applications are found in the literature below. Some researchers have looked for indicators that can serve as early warning signals for critical shifts in ecological systems. One such an indicator seems to be the variability in system behaviour: the relative speed at which interacting slow and fast variables take place seems to be important in anticipating regime shift (Carpenter and Brock 2006). The role of changing patterns in fluctuations is also found in other systems (climate, brain) to be an early warning signal.

Literature

Gordon, L., G. Peterson and E. Bennett (2008). Agricultural modifications of hydrological flows create ecological surprises. TRENDS in Ecology and Evolution 23(2008)211

Hirota, M., M. Holmgren, E. van Nes and M. Scheffer (2011). Global Resilience of Tropical Forest and Savanna to Critical Transitions. Science 334(2011)232

Holling, C. (1986). The resilience of terrestrial ecosystems : local surprise and global change. In: Clark, W. and R. Munn (Eds.) (1986). The resilience of terrestrial ecosystems : local surprise and global change. Cambridge University Press / IIASA, Cambridge / IIASA

Kefi, S., M. Rietkerk, C. L. Alados2, Y. Pueyo, V. P. Papanastasis, A. ElAich and P. C. de Ruiter (2007). Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems. Nature 449(2007)213-218

Meadows, D. H. (2008). Thinking in Systems. Chelsea Green Publishing, Vermont

Scheffer, M., S. Carpenter, J. Foley, C. Folke and B. Walker (2001). Catastrophic shifts in ecosystems. Nature 413(2001)591-596

Scheffer, M., and S. Carpenter (2003). Catastrophic regime shifts in ecosystems: linking theory to observation. TRENDS in Ecology and Evolution 18(2003)648

Scheffer, M. (2009). Critical Transitions in Nature and Society. Princeton University, Princeton

Scheffer, M., J. Bascompte, W. Brock et al. (2009). Early-warning signals for critical transitions. Nature 461(2009)53-59

Walker, B., J. Anderies, A. Kinzig and P. Ryan (2006). Exploring resilience in social-ecological systems – comparative studies and theory development. CSIRO Publishing