Gradual regime shifts in spatially extended ecosystems

Ecosystem regime shifts are regarded as abrupt global transitions from one stable state to an alternative stable state, induced by slow environmental changes or by global disturbances. Spatially extended ecosystems, however, can also respond to local disturbances by the formation of small domains of the alternative state. Such a response can lead to gradual regime shifts involving front propagation and the coalescence of alternative-state domains. When one of the states is spatially patterned, a multitude of intermediate stable states appears, giving rise to step-like gradual shifts with extended pauses at these states. Using a minimal model, we study gradual state transitions and show that they precede abrupt transitions. We propose indicators to probe gradual regime shifts, and suggest that a combination of abrupt-shift indicators and gradual-shift indicators might be needed to unambiguously identify regime shifts. Our results are particularly relevant to desertification in drylands where transitions to bare soil take place from spotted vegetation, and the degradation process appears to involve step-like events of local vegetation mortality caused by repeated droughts.     

Changing skewness: an early warning signal of regime shifts in ecosystems

Empirical evidence for large-scale abrupt changes in ecosystems such as lakes and vegetation of semi-arid regions is growing. Such changes, called regime shifts, can lead to degradation of ecological services. We study simple ecological models that show a catastrophic transition as a control parameter is varied and propose a novel early warning signal that exploits two ubiquitous features of ecological systems: nonlinearity and large external fluctuations. Either reduced resilience or increased external fluctuations can tip ecosystems to an alternative stable state. It is shown that changes in asymmetry in the distribution of time series data, quantified by changing skewness, is a model-independent and reliable early warning signal for both routes to regime shifts. Furthermore, using model simulations that mimic field measurements and a simple analysis of real data from abrupt climate change in the Sahara, we study the feasibility of skewness calculations using data available from routine monitoring.     

Tracking unstable states: ecosystem dynamics in a changing world

Ecological systems can show complex and sometimes abrupt responses to environmental change, with important implications for their resilience. Theories of alternate stable states have been used to predict regime shifts of ecosystems as equilibrium responses to sufficiently slow environmental change. The actual rate of environmental change is a key factor affecting the response, yet we are still lacking a non-equilibrium theory that explicitly considers the influence of this rate of environmental change. We present a metacommunity model of predator–prey interactions displaying multiple stable states, and we impose an explicit rate of environmental change in habitat quality (carrying capacity) and connectivity (dispersal rate). We study how regime shifts depend on the rate of environmental change and compare the outcome with a stability analysis in the corresponding constant environment. Our results reveal that in a changing environment, the community can track states that are unstable in the constant environment. This tracking can lead to regime shifts, including local extinctions, that are not predicted by alternative stable state theory. In our metacommunity, tracking unstable states also controls the maintenance of spatial heterogeneity and spatial synchrony. Tracking unstable states can also lead to regime shifts that may be reversible or irreversible. Our study extends current regime shift theories to integrate rate-dependent responses to environmental change. It reveals the key role of unstable states for predicting transient dynamics and long-term resilience of ecological systems to climate change.     

Regime shifts: catastrophic responses of ecosystems to human impacts

Evidence of abrupt changes in ecosystem states, such as sudden eutrophication in lakes, has been increasingly reported in a variety of aquatic and terrestrial systems. Ecosystems may have more than one state with a self-stabilizing mechanism, so that a shift between states does not occur frequently and is not readily reversible. These big changes are termed regime shifts where often one state is preferred over another. Thus, regime shifts are problematic for ecosystem managers, and the need exists for studies that lead to the identification of thresholds of key variables that trigger regime shifts. Regime shifts are currently difficult to predict and in many cases may be caused by the human pursuit of efficiency in land and water productivity in the last few decades. Here I briefly introduce a theoretical approach to predict the shift between a clear-water state and a turbid state in lakes, the best-studied example of regime shifts. This paper also discusses alternative states in other natural systems besides ecosystems to draw more attention to the research currently being performed on regime shifts. Motomi Genkai-Kato is the recipient of the 10th Denzaburo Miyadi Award.     

Reorganization of a large marine ecosystem due to atmospheric and anthropogenic pressure: a discontinuous regime shift in the Central Baltic Sea

Marine ecosystems such as the Baltic Sea are currently under strong atmospheric and anthropogenic pressure. Besides natural and human-induced changes in climate, major anthropogenic drivers such as overfishing and anthropogenic eutrophication are significantly affecting ecosystem structure and function. Recently, studies demonstrated the existence of alternative stable states in various terrestrial and aquatic ecosystems. These so-called ecosystem regime shifts have been explained mainly as a result of multiple causes, e.g. climatic regime shifts, overexploitation or a combination of both. The occurrence of ecosystem regime shifts has important management implications, as they can cause significant losses of ecological and economic resources. Because of hysteresis in ecosystem responses, restoring regimes considered as favourable may require drastic and expensive management actions. Also the Baltic Sea, the largest brackish water body in the world ocean, and its ecosystems are strongly affected by atmospheric and anthropogenic drivers. Here, we present results of an analysis of the state and development of the Central Baltic Sea ecosystem integrating hydroclimatic, nutrient, phyto- and zooplankton as well as fisheries data. Our analyses of 52 biotic and abiotic variables using multivariate statistics demonstrated a major reorganization of the ecosystem and identified two stable states between 1974 and 2005, separated by a transition period in 1988–1993. We show the change in Baltic ecosystem structure to have the characteristics of a discontinuous regime shift, initiated by climate-induced changes in the abiotic environment and stabilized by fisheries-induced feedback loops in the food web. Our results indicate the importance of maintaining the resilience of an ecosystem to atmospherically induced environmental change by reducing the anthropogenic impact.     

Alternate attractors in the population dynamics of a tree-killing bark beetle

Among the most striking changes in ecosystems are those that happen abruptly and resist return to the original condition (i.e., regime shifts). This frequently involves conspicuous changes in the abundance of one species (e.g., an oubreaking pest or keystone species). Alternate attractors in population dynamics could explain switches between low and high levels of abundance, and could underlie some cases of regime shifts in ecosystems; this longstanding theoretical possibility has been difficult to test in nature. We compared the ability of an alternate attractors model versus two competing models to explain population fluctuations in the tree-killing bark beetle, Dendroctonus frontalis. Frequency distributions of abundance were distinctly bimodal, a prediction of the alternate attractors model, strongly indicating the lack of a single, noisy equilibrium. Time series abundance data refuted the existence of strong delayed density-dependence or nonlinearities, as required by the endogenous cycles model. The model of alternate attractors was further supported by the existence of positive density-dependence at intermediate beetle abundances. Experimental manipulations show that interactions with competitors and shared enemies could create a locally stable equilibrium in small populations of D. frontalis. High variation among regions and years in the abundance of predators and competitors could permit switches between alternate states. Dendroctonus frontalis now provides the strongest case that we know of for alternate attractors in natural population dynamics. The accompanying demographic instability appears to underlie spatially extensive outbreaks that have lasting impacts on forest ecosystems. Understanding feedbacks in populations with alternate attractors can help to identify thresholds underlying regime shifts, and potentially manage them to avoid undesirable impacts.     

Evolutionary regime shifts in simulated ecosystems

Catastrophic regime shifts in ecosystems occur when the system is tipped into a new attractor state under some external forcing. Here we consider whether evolutionary adaptations within ecosystems can trigger similar transitions. We use an individual‐based, evolutionary model of interconnected ecosystems to analyze nonlinear changes in global state resulting from local adaptations. Transitions between periods of stability occur when new traits arise that allow exploitation of under‐utilized resources. Subsequent rapid growth of the population carrying the new trait causes abrupt environmental change that drives incumbent species extinct. We call these transitions ‘evolutionary regime shifts’. These internally generated perturbations can result in ecosystem collapse, followed by recovery to an alternate stable state, or occasionally system‐wide extinction. While these disruptions may have a negative impact on ecosystem productivity in individual simulation runs, mean results over many simulations show a trend for increasing ecosystem productivity and stability over time. Feedback between life and the abiotic environment in the model creates a ‘long‐tailed’ distribution of extinction sizes without any external trigger for large extinction events.     

浅水湖泊生态系统稳态转换的阈值判定方法

浅水湖泊生态系统对人类干扰的反应会随着干扰力度的改变或增强而出现突然的变化,即发生稳态转换;对其机理和驱动机制的揭示将有助于对湖泊富营养化的控制及恢复.基于“多稳态”理论的稳态转换研究已广泛开展,但对浅水湖泊生态系统稳态转换的驱动机制结论各异,采用的阈值判定方法相差很大,主要有实验观测、模型模拟和统计分析3种.实验观测多关注少数特定指标,指标筛选过程复杂且工作量大;模型模拟虽能从较为全面的尺度上理解生态系统稳态变化的特征和主要机理过程,但在模型误差和不确定性的处理等问题上尚存在不足;统计分析方法基于对长时间序列数据的统计变化规律分析,用以判断或者预警稳态转换现象的发生,是目前最为常用的方法.目前稳态转换领域的研究大都是对已发生的稳态转换进行机制分析或过程反演,对未来预测与预警的问题仍然亟需加强.     

Low biodiversity state persists two decades after cessation of nutrient enrichment

Although nutrient enrichment frequently decreases biodiversity, it remains unclear whether such biodiversity losses are readily reversible, or are critical transitions between alternative low‐ and high‐diversity stable states that could be difficult to reverse. Our 30‐year grassland experiment shows that plant diversity decreased well below control levels after 10 years of chronic high rates (95–270 kg N ha⁻¹ year⁻¹) of nitrogen addition, and did not recover to control levels 20 years after nitrogen addition ceased. Furthermore, we found a hysteretic response of plant diversity to increases and subsequent decreases in soil nitrate concentrations. Our results suggest that chronic nutrient enrichment created an alternative low‐diversity state that persisted despite decreases in soil nitrate after cessation of nitrogen addition, and despite supply of propagules from nearby high‐diversity plots. Thus, the regime shifts between alternative stable states that have been reported for some nutrient‐enriched aquatic ecosystems may also occur in grasslands.     

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.     

How Regime Shifts in Connected Aquatic Ecosystems Are Affected by the Typical Downstream Increase of Water Flow

All over the world freshwater ecosystems like ponds, ditches and lakes suffer from nutrient-driven regime shifts from submerged plants to dominance by algae or free-floating plants. Although freshwaters are often connected and part of a network, most of our current knowledge on regime shifts comes from studies of isolated ecosystems. The few studies that have assessed the spatial manifestation of regime shifts overlooked the hydrological fact that the water flow through connected waters typically increases in the downstream direction. Here, we use a complex ecosystem model to show that this increase in flow does not lead to spatial differences in ecosystem state. We support these findings with a simple, analytically tractable, nutrient retention model on connected waterbodies. The model shows that all bodies have the same nutrient concentration despite spatial gradients in the flow of water as well as nutrients carried by the water. As a consequence, each connected waterbody is equally vulnerable to a regime shift, implying a regime shift to be system-wide. Furthermore, it appeared that each connected waterbody behaves the same as an isolated waterbody, implying that the vast body of theory on isolated systems, like alternative stable states theory, can still be useful for connected systems. Although these findings are violated when there is heterogeneity in lateral runoff or waterbody characteristics—leading to spatial differences in ecosystem state and therefore to differences in the vulnerability to a regime shift—they show that the typical downstream build-up of water flow does not necessarily lead to differences in ecological state, and thereby provide a basic concept to better understand the ecology of connected freshwaters.     

Alternative (un)stable states in a stochastic predator–prey model

Stochastic models sometimes behave qualitatively differently from their deterministic analogues. We explore the implications of this in ecosystems that shift suddenly from one state to another. This phenomenon is usually studied through deterministic models with multiple stable equilibria under a single set of conditions, with stability defined through linear stability analysis. However, in stochastic systems, some unstable states can trap stochastic dynamics for long intervals, essentially masquerading as additional stable states. Using a predator–prey model, we demonstrate that this effect is sufficient to make a stochastic system with one stable state exhibit the same characteristics as an analogous system with alternative stable states. Although this result is surprising with respect to how stability is defined by standard analyses, we show that it is well-anticipated by an alternative approach based on the system's “quasi-potential.” Broadly, understanding the risk of sudden state shifts will require a more holistic understanding of stability in stochastic systems.     

Hydrologic variability in dryland regions: impacts on ecosystem dynamics and food security

Research on ecosystem and societal response to global environmental change typically considers the effects of shifts in mean climate conditions. There is, however, some evidence of ongoing changes also in the variance of hydrologic and climate fluctuations. A relatively high interannual variability is a distinctive feature of the hydrologic regime of dryland regions, particularly at the desert margins. Hydrologic variability has an important impact on ecosystem dynamics, food security and societal reliance on ecosystem services in water-limited environments. Here, we investigate some of the current patterns of hydrologic variability in drylands around the world and review the major effects of hydrologic fluctuations on ecosystem resilience, maintenance of biodiversity and food security. We show that random hydrologic fluctuations may enhance the resilience of dryland ecosystems by obliterating bistable deterministic behaviours and threshold-like responses to external drivers. Moreover, by increasing biodiversity and the associated ecosystem redundancy, hydrologic variability can indirectly enhance post-disturbance recovery, i.e. ecosystem resilience.     

Functional diversity can facilitate the collapse of an undesirable ecosystem state

Biodiversity may increase ecosystem resilience. However, we have limited understanding if this holds true for ecosystems that respond to gradual environmental change with abrupt shifts to an alternative state. We used a mathematical model of anoxic–oxic regime shifts and explored how trait diversity in three groups of bacteria influences resilience. We found that trait diversity did not always increase resilience: greater diversity in two of the groups increased but in one group decreased resilience of their preferred ecosystem state. We also found that simultaneous trait diversity in multiple groups often led to reduced or erased diversity effects. Overall, our results suggest that higher diversity can increase resilience but can also promote collapse when diversity occurs in a functional group that negatively influences the state it occurs in. We propose this mechanism as a potential management approach to facilitate the recovery of a desired ecosystem state.     

Heavy-Tailed Fluctuations in the Spiking Output Intensity of Semiconductor Lasers with Optical Feedback

Although heavy-tailed fluctuations are ubiquitous in complex systems, a good understanding of the mechanisms that generate them is still lacking. Optical complex systems are ideal candidates for investigating heavy-tailed fluctuations, as they allow recording large datasets under controllable experimental conditions. A dynamical regime that has attracted a lot of attention over the years is the so-called low-frequency fluctuations (LFFs) of semiconductor lasers with optical feedback. In this regime, the laser output intensity is characterized by abrupt and apparently random dropouts. The statistical analysis of the inter-dropout-intervals (IDIs) has provided many useful insights into the underlying dynamics. However, the presence of large temporal fluctuations in the IDI sequence has not yet been investigated. Here, by applying fluctuation analysis we show that the experimental distribution of IDI fluctuations is heavy-tailed, and specifically, is well-modeled by a non-Gaussian stable distribution. We find a good qualitative agreement with simulations of the Lang-Kobayashi model. Moreover, we uncover a transition from a less-heavy-tailed state at low pump current to a more-heavy-tailed state at higher pump current. Our results indicate that fluctuation analysis can be a useful tool for investigating the output signals of complex optical systems; it can be used for detecting underlying regime shifts, for model validation and parameter estimation.     

Early warning signals of demographic regime shifts in invading populations

The Allee effect can cause alternative stable states in population abundance of invasive species. Sudden eruption of invading populations from low to high abundance may be viewed as a regime shift from one alternative state to another. Previous research proposed several types of early warning signals to predict regime shifts in ecological systems such as polluted lakes and semiarid grasslands. This paper explores theoretically the potential of such indicators in predicting demographic regime shifts of invading populations. I analyzed a stochastic differential equation model for the population dynamics of an invasive species subject to Allee effects and propagule pressure. Diffusion approximation to the stochastic model suggests that persistent propagule pressure makes demographic regime shifts inevitable, but Allee effects can lengthen the mean time until regime shifts virtually indefinitely. To compare the potential of indicators, I examined standard deviation, skewness, and estimated return rates of longitudinal population abundance. I found that standard deviation showed a distinct increase as regime shifts became more likely, but skewness and return rates showed no clear trends. This result suggests that standard deviation might be a useful warning signal for forecasting an impending demographic regime shift of invading populations during the period when their abundance is still low.     

Crossing habitat boundaries: coupling dynamics of ecosystems through complex life cycles

Ecosystems are often indirectly connected through consumers with complex life cycles (CLC), in which different life stages inhabit different ecosystems. Using a structured consumer resource model that accounts for the independent effects of two resources on consumer growth and reproductive rates, we show that such indirect connections between ecosystems can result in alternative stable states characterized by adult-dominated and juvenile-dominated consumer populations. As a consequence, gradual changes in ecosystem productivity or mortality rates of the consumer can lead to dramatic and abrupt regime shifts across different ecosystems, hysteresis and counterintuitive changes in the consumer abundances. Whether these counter intuitive or abrupt responses occur depend on the relative productivity of both habitats and which consumer life-stage inhabits the manipulated ecosystem. These results demonstrate the strong yet complex interactions between ecosystems coupled through consumers with CLC and the need to think across ecosystems to reliably predict the consequences of natural or anthropogenic changes.     

Robustness of early warning signals of regime shifts in time-delayed ecological models

Various ecological and other complex dynamical systems may exhibit abrupt regime shifts or critical transitions, wherein they reorganize from one stable state to another over relatively short time scales. Because of potential losses to ecosystem services, forecasting such unexpected shifts would be valuable. Using mathematical models of regime shifts, ecologists have proposed various early warning signals of imminent shifts. However, their generality and applicability to real ecosystems remain unclear because these mathematical models are considered too simplistic. Here, we investigate the robustness of recently proposed early warning signals of regime shifts in two well-studied ecological models, but with the inclusion of time-delayed processes. We find that the average variance may either increase or decrease prior to a regime shift and, thus, may not be a robust leading indicator in time-delayed ecological systems. In contrast, changing average skewness, increasing autocorrelation at short time lags, and reddening power spectra of time series of the ecological state variable all show trends consistent with those of models with no time delays. Our results provide insights into the robustness of early warning signals of regime shifts in a broader class of ecological systems.     

Fish as proxies of ecological and environmental change

Anthropogenic impacts have shifted aquatic ecosystems far from prehistoric baseline states; yet, understanding these impacts is impeded by a lack of available long-term data that realistically reflects the organisms and their habitats prior to human disturbance. Fish are excellent, and largely underused, proxies for elucidating the degree, direction and scale of shifts in aquatic ecosystems. This paper highlights potential sources of qualitative and quantitative data derived from contemporary, archived and ancient fish samples, and then, using key examples, discusses the types of long-term temporal information that can be obtained. This paper identifies future research needs with a focus on the Southern Hemisphere, as baseline shifts are poorly described relative to the Northern Hemisphere. Temporal data sourced from fish can improve our understanding of how aquatic ecosystems have changed, particularly when multiple sources of data are used, enhancing our ability to interpret the current state of aquatic ecosystems and establish effective measures to safeguard against further adverse shifts. The range of biological, ecological and environmental data obtained from fish can be integrated to better define ecosystem baseline states on which to establish policy goals for future conservation and exploitation practices.