 Interest in the nonlinear dynamics of ecosystems has greatly increased during the past few decades. Reportedly, academic papers published on the subject of regime shifts have 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. The central question we're interested in though is 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 that critical point? And is it possible in some way to foresee such events, if so how? Although such nonlinear 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 a society relies upon. This recognition of nonlinear regime shifts has also helped to conceptually move the tension away from looking at ecosystems as linear and predictable towards unpredictability and surprise, which is characteristic of complex systems. However, we should add to its current significance the fact that ecological regime occurrence is widely expected to increase in the coming decades as human influence on the planet increases. As we've previously touched upon, a large change within the state of a system can result from two qualitatively different 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 thought to be caused by the large event of a meteorite hitting Earth. But equally, some large events happen without large causes. 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 have to look 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're talking about when referring to regime shifts. In ecology, regime shifts are large, abrupt, systemic changes in the structure and function of an ecosystem 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 external variable triggers a completely different systems behavior with irreversible consequences. Empirical evidence for regime shifts within ecosystems has now been identified within many different types of ecosystems including kelp forests, coral reefs, dry lands, lakes, fisheries, insect outbreak dynamics and grazing systems. In this module, we'll be talking about a number of topics central to understanding these regime shifts including that of bistability, hysteresis, thresholds, resilience and early warning signals. The theory of ecological regime shifts is today understood within the context of nonlinear dynamics, state spaces and attractors. The basic theory 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 further away from the stable equilibrium attractor. As it moves away, it moves towards a critical phase transition area far from its equilibrium an instable 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 and 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 time scales. Ecosystems may transition from one stable state to another when perturbed and this is what is known as a regime shift. 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 the algae decline. Another example would be the bistability 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 cycling 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 dependence and hysteresis that both tell us that history matters and this is certainly the case with regime shifts. Hysteresis greatly emphasizes the role of history in a system and demonstrate that systems have 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 as we'll be illustrating in a minute. This occurs because systemic change alters feedback processes that maintain the system in a particular regime. When we lose those 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 return it to the original domain of attraction. Conditions at which a system shifts its dynamics from one set of processes to another are 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 where small changes in an environmental driver produce large responses in the ecosystem. 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 the configuration of its parameters. Thresholds will be present however only in nonlinear systems 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. In the graph we can see 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 we can 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 loops have been broken without the help of the plants to clear the water the turbidity suddenly jumps up as there is now a positive feedback loop where more turbidity means less plants, less plants means more turbidity and so on. A runaway positive 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 stability 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 corresponds to negative feedback and the size of the basin of attraction as we previously discussed. At the original state to the system the resilience was very high because of its negative feedback loops it was virtually impossible to change it into a 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 corresponds to a very small attractor as the system comes closer to its limit closer to an unstable state corresponding to a lower level of resilience. 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. We can see this dynamic illustrated in the graphic which is showing 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. For obvious reasons the forecasting of these critical transitions is an active area of research 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 physicists 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 linear transformation of the past it can be qualitatively different and totally unexpected. 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 hypocritical threshold is approaching. Thus the actual distance to such transitions or in other words how much further a parameter needs to be changed 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 area is called critical slowing down. The width and steepness of the basin of attraction determines the capacity of the system to absorb a perturbation without shifting to an alternative state and reflects the resilience of the state of the system. As conditions bring the system closer 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 closer to tipping points. 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. In this video we've been discussing the topic of nonlinear regime shifts within ecosystems looking at how they can flip from one qualitatively different state to another within short periods of time. We talked about bistability as a set of alternative states or equilibria that ecosystems can exist under at any given time representing some set of unique biotic and abiotic conditions. We looked at path dependency and hysteresis within this process where the point at which the system flips from one regime to another is different from the point at which the system flips back. We saw how tipping points are a key part of this dynamic representing a point at which there is an abrupt change in the ecosystem's properties and functionality due to runaway feedback. Finally we talked about resilience and early warning signals that might help us in identifying when an ecosystem is approaching a critical point by probing the speed at which it returns to a stable constant after some intervention.