Egbert H. van Nes

Early-warning signals for critical transitions

Complex dynamical systems, ranging from ecosystems to financial markets and the climate, can have tipping points at which a sudden shift to a contrasting dynamical regime may occur. Although predicting such critical points before they are reached is extremely difficult, work in different scientific fields is now suggesting the existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching.

Anticipating Critical Transitions

All Change Research on early warning signals for critical transitions in complex systems such as ecosystems, climate, and global finance systems recently has been gathering pace. At the same time, studies on complex networks are starting to reveal which architecture may cause systems to be vulnerable to systemic collapse. Scheffer et al. (p. 344) review how previously isolated lines of work can be connected, conclude that many critical transitions (such as escape from the poverty trap) can have positive outcomes, and highlight how the new approaches to sensing fragility can help to detect both risks and opportunities for desired change. Tipping points in complex systems may imply risks of unwanted collapse, but also opportunities for positive change. Our capacity to navigate such risks and opportunities can be boosted by combining emerging insights from two unconnected fields of research. One line of work is revealing fundamental architectural features that may cause ecological networks, financial markets, and other complex systems to have tipping points. Another field of research is uncovering generic empirical indicators of the proximity to such critical thresholds. Although sudden shifts in complex systems will inevitably continue to surprise us, work at the crossroads of these emerging fields offers new approaches for anticipating critical transitions.

Slowing down as an early warning signal for abrupt climate change

In the Earths history, periods of relatively stable climate have often been interrupted by sharp transitions to a contrasting state. One explanation for such events of abrupt change is that they happened when the earth system reached a critical tipping point. However, this remains hard to prove for events in the remote past, and it is even more difficult to predict if and when we might reach a tipping point for abrupt climate change in the future. Here, we analyze eight ancient abrupt climate shifts and show that they were all preceded by a characteristic slowing down of the fluctuations starting well before the actual shift. Such slowing down, measured as increased autocorrelation, can be mathematically shown to be a hallmark of tipping points. Therefore, our results imply independent empirical evidence for the idea that past abrupt shifts were associated with the passing of critical thresholds. Because the mechanism causing slowing down is fundamentally inherent to tipping points, it follows that our way to detect slowing down might be used as a universal early warning signal for upcoming catastrophic change. Because tipping points in ecosystems and other complex systems are notoriously hard to predict in other ways, this is a promising perspective.

ON THE DOMINANCE OF FILAMENTOUS CYANOBACTERIA IN SHALLOW, TURBID LAKES

The phytoplankton community of eutrophic shallow lakes is often dominated by filamentous cyanobacteria of the family Oscillatoriaceae. In this paper we follow two independent approaches to show that this situation is likely to be one of two alternative stable states of the algal community. First we analyze patterns of cyanobacterial dominance observed in the field, and show that these patterns imply that the algal community is a hysteretic system with two alternative equilibria. Then, we construct a simple competition model to show that hysteresis should in fact be expected from differences in physiology between cyanobacteria and algae. The basic mechanism is that cyanobacteria are the superior competitors under conditions of low light, but also promote such conditions, as they can cause a higher turbidity per unit of phosphorus than other algae. This mechanism of hys- teresis offers an explanation for the resistance of cyanobacteria dominance in shallow lakes to restoration efforts by means of nutrient reduction.

Shallow lakes theory revisited: various alternative regimes driven by climate, nutrients, depth and lake size

Shallow lakes have become the archetypical example of ecosystems with alternative stable states. However, since the early conception of that theory, the image of ecosystem stability has been elaborated for shallow lakes far beyond the simple original model. After discussing how spatial heterogeneity and fluctuation of environmental conditions may affect the stability of lakes, we review work demonstrating that the critical nutrient level for lakes to become turbid is higher for smaller lakes, and seems likely to be affected by climatic change too. We then show how the image of just two contrasting states has been elaborated. Different groups of primary producers may dominate shallow lakes, and such states dominated by a particular group may often represent alternative stable states. In tropical lakes, or small stagnant temperate waters, free-floating plants may represent an alternative stable state. Temperate shallow lakes may be dominated alternatively by charophytes, submerged angiosperms, green algae or cyanobacteria. The change of the lake communities along a gradient of eutrophication may therefore be seen as a continuum in which gradual species replacements are interrupted at critical points by more dramatic shifts to a contrasting alternative regime dominated by different species. The originally identified shift between a clear and a turbid state remains one of the more dramatic examples, but is surely not the only discontinuity that can be observed in the response of these ecosystems to environmental change.

slow recovery from perturbations as a generic indicator of a nearby catastrophic shift

The size of the basin of attraction in ecosystems with alternative stable states is often referred to as “ecological resilience.” Ecosystems with a low ecological resilience may easily be tipped into an alternative basin of attraction by a stochastic event. Unfortunately, it is very difficult to measure ecological resilience in practice. Here we show that the rate of recovery from small perturbations (sometimes called “engineering resilience”) is a remarkably good indicator of ecological resilience. Such recovery rates decrease as a catastrophic regime shift is approached, a phenomenon known in physics as “critical slowing down.” We demonstrate the robust occurrence of critical slowing down in six ecological models and outline a possible experimental approach to quantify differences in recovery rates. In all the models we analyzed, critical slowing down becomes apparent quite far from a threshold point, suggesting that it may indeed be of practical use as an early warning signal. Despite the fact that critical slowing down could also indicate other critical transitions, such as a stable system becoming oscillatory, the robustness of the phenomenon makes it a promising indicator of loss of resilience and the risk of upcoming regime shifts in a system.

Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data

Many dynamical systems, including lakes, organisms, ocean circulation patterns, or financial markets, are now thought to have tipping points where critical transitions to a contrasting state can happen. Because critical transitions can occur unexpectedly and are difficult to manage, there is a need for methods that can be used to identify when a critical transition is approaching. Recent theory shows that we can identify the proximity of a system to a critical transition using a variety of so-called ‘early warning signals’, and successful empirical examples suggest a potential for practical applicability. However, while the range of proposed methods for predicting critical transitions is rapidly expanding, opinions on their practical use differ widely, and there is no comparative study that tests the limitations of the different methods to identify approaching critical transitions using time-series data. Here, we summarize a range of currently available early warning methods and apply them to two simulated time series that are typical of systems undergoing a critical transition. In addition to a methodological guide, our work offers a practical toolbox that may be used in a wide range of fields to help detect early warning signals of critical transitions in time series data.

Soil microbes drive the classic plant diversity-productivity pattern

Ecosystem productivity commonly increases asymptotically with plant species diversity, and determining the mechanisms responsible for this well-known pattern is essential to predict potential changes in ecosystem productivity with ongoing species loss. Previous studies attributed the asymptotic diversity-productivity pattern to plant competition and differential resource use (e.g., niche complementarity). Using an analytical model and a series of experiments, we demonstrate theoretically and empirically that host-specific soil microbes can be major determinants of the diversity-productivity relationship in grasslands. In the presence of soil microbes, plant disease decreased with increasing diversity, and productivity increased nearly 500%, primarily because of the strong effect of density-dependent disease on productivity at low diversity. Correspondingly, disease was higher in plants grown in conspecific-trained soils than heterospecific-trained soils (demonstrating host-specificity), and productivity increased and host-specific disease decreased with increasing community diversity, suggesting that disease was the primary cause of reduced productivity in species-poor treatments. In sterilized, microbe-free soils, the increase in productivity with increasing plant species number was markedly lower than the increase measured in the presence of soil microbes, suggesting that niche complementarity was a weaker determinant of the diversity-productivity relationship. Our results demonstrate that soil microbes play an integral role as determinants of the diversity-productivity relationship.

Floating plant dominance as a stable state

Invasion by mats of free-floating plants is among the most important threats to the functioning and biodiversity of freshwater ecosystems ranging from temperate ponds and ditches to tropical lakes. Dark, anoxic conditions under thick floating-plant cover leave little opportunity for animal or plant life, and they can have large negative impacts on fisheries and navigation in tropical lakes. Here, we demonstrate that floating-plant dominance can be a self-stabilizing ecosystem state, which may explain its notorious persistence in many situations. Our results, based on experiments, field data, and models, represent evidence for alternative domains of attraction in ecosystems. An implication of our findings is that nutrient enrichment reduces the resilience of freshwater systems against a shift to floating-plant dominance. On the other hand, our results also suggest that a single drastic harvest of floating plants can induce a permanent shift to an alternative state dominated by rooted, submerged growth forms.

IMPLICATIONS OF SPATIAL HETEROGENEITY FOR CATASTROPHIC REGIME SHIFTS IN ECOSYSTEMS

Although alternative stable states are commonly found in simple models, it seems reasonable to assume that the response of real ecosystems to environmental change should often be smoothed by spatial heterogeneity and other stabilizing mechanisms. Here, we systematically explore the effect of spatial heterogeneity on regime shifts for three different models, which we run on a one-dimensional lattice with different spatial distributions of an environmental factor (e.g., soil fertility, water level). If dispersion between patches is negligible, the response to gradual change in some overall stressor (e.g., precipitation, nutrient load) is straightforward. Because of the environmental heterogeneity, each patch shifts to the other stable state at different values of the overall control variable. Therefore, the response of the ecosystem as a whole is gradual (i.e., the average of many asynchronous small shifts) instead of catastrophic. However, in response to a reverse change in the global stressor, the system always shows hysteresis, as each individual patch shifts back to the original state at a different value of the control parameter than the critical threshold for the forward shift. If dispersion between patches occurs, the response to change in the overall control parameter becomes dependent on the spatial pattern of environmental heterogeneity. If the environmental parameter is randomly distributed in space, the overall response tends to remain surprisingly catastrophic, and hysteresis is hardly reduced as compared to the homogeneous case. By contrast, in a smooth environmental gradient, the response of the overall system is gradual, and hysteresis is much smaller. In fact, hysteresis is largely reduced to the initial phases, in which none of the patches have shifted to the alternative state yet. As soon as the first patch shifts, a domino effect occurs, pushing over the neighboring patches. In conclusion, our results suggest that spatial heterogeneity may weaken the tendency for large-scale catastrophic regime shifts if dispersion is unimportant or if local environmental characteristics vary along a smooth gradient.