Regime shifts are large, abrupt, systemic changes in the structure and function of a system.1 Where a regime is a characteristic behavior of a system which is maintained by mutually reinforced processes or feedback loops. The change of regime, or the shift, typically occurs when a continuous smooth change in an internal process or an external variable triggers a completely different system behavior with irreversible consequences. Empirical evidence for regime shifts within ecosystems have now been identified within many different types of ecosystems including; kelp forests, coral reefs, drylands, lakes, fisheries, insect outbreak dynamics and grazing systems.2 Interest in the nonlinear dynamics of ecosystems has increased greatly during the last few decades. Reportedly academic papers published on the subject of regime shifts has gone from less than 5 per year prior to the 90s to more than 300 per year by 2010, making it a very active area of research today with many unanswered questions remaining open. The central question of interest here are how ecosystems can flip abruptly from one state of functionality to another. And this encapsulates such questions as how do they move into this state where they are vulnerable to a shift? What are the actual dynamics at the critical state? And is it possible to in some way foresee such events, if so how?
Although such non-linear changes have been widely studied in different disciplines, in particular mathematics and physics, regime shifts have gained importance in ecology because they can substantially affect the flow of ecosystem services that societies rely upon. This recognition of nonlinear regime shifts has also helped to conceptually more attention away from looking at ecosystems as linear and predictable, towards unpredictability and surprise which is characteristic of complex systems. Moreover we should add to its current significance the fact that ecological regime shift occurrence is widely expected to increase in the coming decades as human influence on the planet increases.
Linear & Nonlinear Change
Large change within the state of a system can result from two qualitatively different possible dynamics at play, linear or nonlinear. In a linear situation large effects are the product of some large cause, for example we might see this in the extinction of the dinosaurs, which was a large phenomena caused by the large event of a meteorite hitting Earth. But equally some large events happen without a large cause, here very many, very small events can accumulate over time building up to reach some critical point where it only takes a small input to the system to generate a large systemic change and this is a nonlinear dynamic. Here we are looking at the whole environment of the ecosystem and the feedback loops that affect the system of interest; it is this nonlinear change process within ecosystems that we are talking about when referring to regime shifts.
The theory of ecological regime shifts is today understood within the context of nonlinear dynamics, state spaces and attractors. The basic theory here is that nonlinear systems like ecosystems can have more than one stable basin of attraction, that we would call a regime, which is stable due to a number of negative feedback loops that hold it within that state. Every time one of these negative feedback loops is broken the system moves farther away from this stable equilibrium attractor, as it moves away it moves towards a critical phase transition area far from its equilibrium, an unstable regime governed by positive feedback where some small event can get amplified rapidly driving the system through the phase transition into another basin of attraction. The system then has two or more basins of attraction and can flip between them, this is called bistability.
In ecology, the theory of alternative stable states or equilibria predicts that ecosystems can exist under multiple qualitatively different stable states, which represent some set of unique biotic and abiotic conditions. These alternative states are non-transitory and therefore considered stable over ecologically-relevant timescales. Ecosystems may transition from one stable state to another, in what is known as a regime shift when perturbed. Due to ecological feedback loops, ecosystems display resistance to state shifts and therefore tend to remain in one state unless perturbations are large enough. Multiple states may persist under equal environmental conditions and alternative stable state theory suggests that these discrete states are separated by ecological thresholds.
This bistability has been identified in many ecological systems such as coral reefs which can dramatically shift from pristine coral-dominated systems to degraded algae-dominated systems when populations grazing on algae decline. Another example would be the bistable state to oxygen levels within Earth’s atmosphere, where the oxygen concentration can occupy two stable states, one high density the other low, with both being stable over geological time scales. But probably the most studied example of regime shifts has been the process of lake eutrophication. Lakes work like microcosms which are almost closed systems facilitating experimentation and data gathering. Eutrophication is a well-documented abrupt change from clear water to murky water regimes, which leads to toxic algae blooms and reduction of fish productivity in lakes and coastal ecosystems. Eutrophication is driven by nutrient inputs, particularly those coming from fertilizers used in agriculture. Once the lake has shifted to a murky water regime, a new feedback of phosphorus recycling maintains the system in the eutrophic state even if nutrient inputs are significantly reduced. This is an example of path dependent change and what is called hysteresis.
With all complex systems and dissipative systems there is a strong issue of time and this importance of time can be ascribed to path dependency and hysteresis, that both tell us that history matters and this is certainly the case with regime shifts. Hysteresis greatly emphasises the role of history in a system, and demonstrates that the system has memory in that its dynamics are shaped by past events. The point at which the system flips from one regime to another is different from the point at which the system flips back. This occurs because systemic change alters feedback processes that maintain the system in a particular regime. When we lose these feedback loops it can take only a small perturbation to move the system into a new basin of attraction but to then reverse this process would require a much larger effect. When variables are changed the system is pushed from one basin of attraction to another, yet the same push from the other direction cannot now return it to the original domain of attraction.
Conditions at which a system shifts its dynamics from one set of processes to another are often called thresholds. In ecology for example, a threshold is a point at which there is an abrupt change in an ecosystem’s properties and functionality; or where small changes in an environmental driver produce large responses in the ecology. Thresholds are, however, a function of several interacting parameters, thus they change in time and space. Hence, the same system can present smooth, abrupt or discontinuous change depending on its parameters’ configurations. Thresholds will be present, however, only in cases where abrupt and discontinuous change is possible.
Going back to our example of lake eutrophication, the state of the lake is a function of the amount of nutrients in the lake which makes the water turbid and leads to eutrophication, but having plant vegetation in the water works to make the water more clear. So a lake that has vegetation with the same amount of nutrients will have less turbidity. There are then two states to the system, one with vegetation where there is low turbidity and one without vegetation at a higher turbidity. Now let’s say there is a critical turbidity threshold which if crossed the plants will no longer have enough light and die.
Now let’s take a look at what happens as time passes and we introduce more agriculture and people to the area leading to the nutrient input slowly going up over several decades. Until we reach the critical turbidity and the plants die, this is the tipping point where the negative feedback loop has been broken and without the help of the plants to clear the water the turbidity jumps up as there is now a positive feedback where more turbidity means less plants, less plants means more turbidity and so on, a runaway feedback loop leading to a phase transition as we rapidly cross the threshold into a new basin of attraction where all the plants cease to exist. We have now crossed the threshold and entered into a new stable configuration to the system, the system has gone through a regime shift into a new ecological regime. Now if we come in and reduce the nutrients in the lake we will trace a line back along the graph but because we are in this new regime we can reduce nutrients to a level where the lake was previously clear but the lake will now remain eutrophic because of hysteresis.
We can see also in this example how ecological resilience correlated to negative feedback and the size of the basin of attraction. At the original state to the system the resiliency was very high, because of its negative feedback loops it was virtually impossible to change it into the degraded state. But as we travel along this graph in time we see we are getting closer to the threshold where any small perturbation will drive it out of its current attractor into another, which correlates to a very small attractor as the system comes closer to its limit, closer to an unstable state, corresponding to a low level of resiliency. As we travel through time one basin of attraction is shrinking and the other expanding making the system more unstable, less resilient and more likely to flip. A graph of this system would show how the system goes from one stable basin of attraction, to the emergence of a second attractor, to eventually moving into the new regime without the capacity to return to the first.
The forecasting of these critical transitions is an active research area and of great relevance to the management and preservation of ecological systems. But anticipating the distance to critical transitions remains a challenge, together with predicting the state of the system after these transitions are breached. Although predicting such critical points before they are reached is extremely difficult and we should always be very cautious about the idea of predictability when dealing with complex systems. Complex systems are what physics would call non-ergodic, simply put they are open systems which allows them to evolve over time so that the future is not just some transformation of the past, it can be qualitatively different and totally unexpected.
Early Warning Signals
That being said if the system has a tipping point and we understand something about tipping points in the abstract it might be possible to use this to identify early warning signals. Ongoing research in different scientific fields is now suggesting the possible existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching. Thus, the actual distance to such transitions, or in other words, how much further a parameter needs to change for the system to experience a significant qualitative change in its dynamics, remains an important empirical challenge; so does predicting the state of the system after this point is breached. One of the most promising theories in this areas is called critical slowing down.
Critical Slowing Down
The width and the steepness of the basin of attraction determine the capacity of the system to absorb a perturbation without shifting to an alternative state, and reflects the resilience to the state of the system. As conditions bring the system close to a critical transition, the basin of attraction of the current state of the system shrinks and so does its resilience. At the same time, the steepness of the basin of attraction becomes lower: this means that the same perturbation that may not flip the system will though likely take longer to dissipate, meaning it will take longer for the system to return to its point of equilibrium when close to a tipping point. The simplest way to measure the approach to a potential tipping point then would be to directly measure the recovery rate at which the system returns back to its initial equilibrium state following a perturbation. In cases where the system is close to a tipping point the recovery rate should decrease. This is the essence of critical slowing down and it offers us the potential to probe the dynamics of the system in order to assess its resilience and the risk of an upcoming regime shift.