Regime Shifts in the Sahara and Sahel: Interactions between Ecological and Climatic Systems in Northern Africa

Appendix: A Conceptual Model of “Regime Shifts”

In this paper, we have documented two “regime shifts” that occurred in the Sahara and Sahel during the last 6000 years. Such regime shifts may be linked to the existence of alternative stable states (or regimes) in an environmental system, which in turn are usually explained through strong positive feedbacks among the component parts of the system. Here we have suggested that strong feedbacks between vegetation and the atmosphere give rise to alternative stable states in the climate and ecosystems of northern Africa, thereby leading to a predisposition to regime shifts. In this Appendix, we briefly elaborate on these ideas and discuss some common misconceptions.

Positive feedbacks occur at various levels in many complex systems. For instance, as discussed in this review, vegetation cover may have a positive effect on local precipitation patterns. Furthermore, increases in local rainfall will, in turn, stimulate vegetation growth (Figure A1). One can easily imagine that such a feedback between precipitation and vegetation cover could lead to two alternative stable states: If there is no vegetation, water availability is too low for vegetation growth and plants cannot colonize; however, once vegetation cover is present, it may enhance water availability enough to ensure persistence of the vegetation.

To obtain a better intuitive feeling for the properties of a system with alternative stable states, imagine a situation in which large-scale, external climate drivers (for example, the Earth’s orbital forcing, atmospheric carbon dioxide concentration) control precipitation over a dry region, but local precipitation is higher in the presence of vegetation than over desert (Figure A2). In the hypothetical case that vegetation dies and disappears at a critical precipitation level, this gives rise to alternative stable states of the coupled climate–vegetation system over a range of external climate drivers. (Obviously, the assumption that vegetation disappears completely from a region at a critical precipitation level is a crude oversimplification. Some sites will always be more suitable than others, leading to a more gradual response of vegetation cover to precipitation).

More realistic models confirm that alternative stable states may arise in environmental systems with strong positive feedbacks among components, and that this is part of a continuum of possibilities (Scheffer and others 2001). For example, some ecosystems may respond in a smooth, continuous way to environmental change (Figure A3a). But another system may be quite inert over certain ranges of conditions, responding more strongly when conditions approach a certain critical level (Figure A3b). Finally, if positive feedbacks are of overriding importance, the ecosystem response curve is “folded” backward (Figure A3c). This final example corresponds to our simple graphical model (Figure A2), implying that for certain environmental conditions the ecosystem has two alternative stable states, separated by an unstable equilibrium that marks the border between the basins of attraction of the alternative stable states.

A system with alternative stable states typically responds in a discontinuous way to external forcing, making the exact timing of regime shifts difficult, if not impossible, to forecast. For example, in our simple model (Figure A2), when conditions are wet and vegetation cover is present, the state of the system lies on the upper branch of the diagram. However, if external climatic drivers gradually change and precipitation slowly decreases, the vegetation cover will remain present until the threshold (F _d) is passed and a sudden shift to a low-rainfall/desert state occurs. It is important to note that there is very little change in the state of the system before the regime shift. As a result, there is little or no early warning of the impending regime shift before it occurs.

Regime shifts can also be difficult to reverse. In our conceptual model, it is interesting to observe that returning the system back to the original state (F _d) does not occur easily. Simply restoring the external climate driving parameters back to their original values is not sufficient to induce a switch back to the upper branch. Instead, the climate needs to move beyond the other switch point (F _c) before the system can be restored to the original state. In dynamical systems theory, this phenomenon—where the forward and the backward switches occur at different conditions—is known as hysteresis. (Note that this is a more strict definition of hysteresis than the general meaning of “a tendency to remain constant in spite of external forcing changes.”)

The reader should note that a sudden shift in environmental conditions does not necessarily imply that there are alternative stable states in the system. Systems that have no alternative stable states may also respond in a discontinuous way to environmental change (for example, Figure A3b), although they will show no hysteresis. In practice, one cannot divide systems simply into those that have multiple attractors and those that have not. Also, in models, there is usually a gradual range of possibilities between strong hysteresis and merely a relatively steep response around a certain threshold which can vary depending on parameter settings (Brovkin and others 1998; Claussen and others 1999).

Another important aspect of systems with alternative equilibria is that stochastic events, such as extreme weather episodes, can bring the system into the basin of attraction of another state (Figure A4). If the valley of attraction (resilience rom Holling 1973) around the current state of the system is small, a minor perturbation may be enough to cause a shift to the alternative stable state. Thus, even if in our example global climatic change may seem to have little effect on the state of the systems, the resilience may shrink, making the system more fragile in the sense that it can be easily tipped into a contrasting state by an adverse event.

Please note that these conceptual models of environmental systems are oversimplifications of reality. For instance, no states are truly “stable” in the sense that they could persist forever. Also, these states are certainly never stable in the sense that they are perfectly constant. Rather they are dynamic regimes in which random variation in weather and other conditions interact with the internal dynamics of the system to produce erratic fluctuations (Ellner and Turchin 1995). This makes regime shifts a rather appropriate term to describe the changes we refer to in this paper.