Early warning signals of extinction in deteriorating environments

Conceptualizing ecosystem tipping points within a physiological framework

Connecting the nonlinear and often counterintuitive physiological effects of multiple environmental drivers to the emergent impacts on ecosystems is a fundamental challenge. Unfortunately, the disconnect between the way "stressors" (e.g., warming) is considered in organismal (physiological) and ecological (community) contexts continues to hamper progress. Environmental drivers typically elicit biphasic physiological responses, where performance declines at levels above and below some optimum. It is also well understood that species exhibit highly variable response surfaces to these changes so that the optimum level of any environmental driver can vary among interacting species. Thus, species interactions are unlikely to go unaltered under environmental change. However, while these nonlinear, species-specific physiological relationships between environment and performance appear to be general, rarely are they incorporated into predictions of ecological tipping points. Instead, most ecosystem-level studies focus on varying levels of "stress" and frequently assume that any deviation from "normal" environmental conditions has similar effects, albeit with different magnitudes, on all of the species within a community. We consider a framework that realigns the positive and negative physiological effects of changes in climatic and nonclimatic drivers with indirect ecological responses. Using a series of simple models based on direct physiological responses to temperature and ocean pCO 2, we explore how variation in environment-performance relationships among primary producers and consumers translates into community-level effects via trophic interactions. These models show that even in the absence of direct mortality, mismatched responses resulting from often subtle changes in the physical environment can lead to substantial ecosystem-level change.

Anticipating the emergence of infectious diseases

In spite of medical breakthroughs, the emergence of pathogens continues to pose threats to both human and animal populations. We present candidate approaches for anticipating disease emergence prior to large-scale outbreaks. Through use of ideas from the theories of dynamical systems and stochastic processes we develop approaches which are not specific to a particular disease system or model, but instead have general applicability. The indicators of disease emergence detailed in this paper can be classified into two parallel approaches: a set of early-warning signals based around the theory of critical slowing down and a likelihood-based approach. To test the reliability of these two approaches we contrast theoretical predictions with simulated data. We find good support for our methods across a range of different model structures and parameter values.

Body size shifts and early warning signals precede the historic collapse of whale stocks

Predicting population declines is a key challenge in the face of global environmental change. Abundance-based early warning signals have been shown to precede population collapses; however, such signals are sensitive to the low reliability of abundance estimates. Here, using historical data on whales harvested during the 20th century, we demonstrate that early warning signals can be present not only in the abundance data, but also in the more reliable body size data of wild populations. We show that during the period of commercial whaling, the mean body size of caught whales declined dramatically (by up to 4 m over a 70-year period), leading to early warning signals being detectable up to 40 years before the global collapse of whale stocks. Combining abundance and body size data can reduce the length of the time series required to predict collapse, and decrease the chances of false positive early warning signals.

Vegetation recovery in tidal marshes reveals critical slowing down under increased inundation

A declining rate of recovery following disturbance has been proposed as an important early warning for impending tipping points in complex systems. Despite extensive theoretical and laboratory studies, this ‘critical slowing down' remains largely untested in the complex settings of real-world ecosystems. Here, we provide both observational and experimental support of critical slowing down along natural stress gradients in tidal marsh ecosystems. Time series of aerial images of European marsh development reveal a consistent lengthening of recovery time as inundation stress increases. We corroborate this finding with transplantation experiments in European and North American tidal marshes. In particular, our results emphasize the power of direct observational or experimental measures of recovery over indirect statistical signatures, such as spatial variance or autocorrelation. Our results indicate that the phenomenon of critical slowing down can provide a powerful tool to probe the resilience of natural ecosystems.

Theory and controlled experiments have shown that the recovery rate of an ecological variable from perturbation slows down before a critical tipping point. Here, van Belzen and colleagues demonstrate that slowed vegetation recovery to disturbance is also apparent in the natural system of a tidal marsh.

Slow Recovery from Local Disturbances as an Indicator for Loss of Ecosystem Resilience

A range of indicators have been proposed for identifying the elevated risk of critical transitions in ecosystems. Most indicators are based on the idea that critical slowing down can be inferred from changes in statistical properties of natural fluctuations and spatial patterns. However, identifying these signals in nature has remained challenging. An alternative approach is to infer changes in resilience from differences in standardized experimental perturbations. However, system-wide experimental perturbations are rarely feasible. Here we evaluate the potential to infer the risk of large-scale systemic transitions from local experimental or natural perturbations. We use models of spatially explicit landscapes to illustrate how recovery rates upon small-scale perturbations decrease as an ecosystem approaches a tipping point for a large-scale collapse. We show that the recovery trajectory depends on: (1) the resilience of the ecosystem at large scale, (2) the dispersal rate of organisms, and (3) the scale of the perturbation. In addition, we show that recovery of natural disturbances in a heterogeneous environment can potentially function as an indicator of resilience of a large-scale ecosystem. Our analyses reveal fundamental differences between large-scale weak and local-scale strong perturbations, leading to an overview of opportunities and limitations of the use of local disturbance-recovery experiments.

Elevated nonlinearity as an indicator of shifts in the dynamics of populations under stress

Populations occasionally experience abrupt changes, such as local extinctions, strong declines in abundance or transitions from stable dynamics to strongly irregular fluctuations. Although most of these changes have important ecological and at times economic implications, they remain notoriously difficult to detect in advance. Here, we study changes in the stability of populations under stress across a variety of transitions. Using a Ricker-type model, we simulate shifts from stable point equilibrium dynamics to cyclic and irregular boom-bust oscillations as well as abrupt shifts between alternative attractors. Our aim is to infer the loss of population stability before such shifts based on changes in nonlinearity of population dynamics. We measure nonlinearity by comparing forecast performance between linear and nonlinear models fitted on reconstructed attractors directly from observed time series. We compare nonlinearity to other suggested leading indicators of instability (variance and autocorrelation). We find that nonlinearity and variance increase in a similar way prior to the shifts. By contrast, autocorrelation is strongly affected by oscillations. Finally, we test these theoretical patterns in datasets of fisheries populations. Our results suggest that elevated nonlinearity could be used as an additional indicator to infer changes in the dynamics of populations under stress.

A universal indicator of critical state transitions in noisy complex networked systems

Critical transition, a phenomenon that a system shifts suddenly from one state to another, occurs in many real-world complex networks. We propose an analytical framework for exactly predicting the critical transition in a complex networked system subjected to noise effects. Our prediction is based on the characteristic return time of a simple one-dimensional system derived from the original higher-dimensional system. This characteristic time, which can be easily calculated using network data, allows us to systematically separate the respective roles of dynamics, noise and topology of the underlying networked system. We find that the noise can either prevent or enhance critical transitions, playing a key role in compensating the network structural defect which suffers from either internal failures or environmental changes, or both. Our analysis of realistic or artificial examples reveals that the characteristic return time is an effective indicator for forecasting the sudden deterioration of complex networks.

Socio-ecological dynamics and challenges to the governance of Neglected Tropical Disease control

The current global attempts to control the so-called “Neglected Tropical Diseases (NTDs)” have the potential to significantly reduce the morbidity suffered by some of the world’s poorest communities. However, the governance of these control programmes is driven by a managerial rationality that assumes predictability of proposed interventions, and which thus primarily seeks to improve the cost-effectiveness of implementation by measuring performance in terms of pre-determined outputs. Here, we argue that this approach has reinforced the narrow normal-science model for controlling parasitic diseases, and in doing so fails to address the complex dynamics, uncertainty and socio-ecological context-specificity that invariably underlie parasite transmission. We suggest that a new governance approach is required that draws on a combination of non-equilibrium thinking about the operation of complex, adaptive, systems from the natural sciences and constructivist social science perspectives that view the accumulation of scientific knowledge as contingent on historical interests and norms, if more effective control approaches sufficiently sensitive to local disease contexts are to be devised, applied and managed. At the core of this approach is an emphasis on the need for a process that assists with the inclusion of diverse perspectives, social learning and deliberation, and a reflexive approach to addressing system complexity and incertitude, while balancing this flexibility with stability-focused structures. We derive and discuss a possible governance framework and outline an organizational structure that could be used to effectively deal with the complexity of accomplishing global NTD control. We also point to examples of complexity-based management structures that have been used in parasite control previously, which could serve as practical templates for developing similar governance structures to better manage global NTD control. Our results hold important wider implications for global health policy aiming to effectively control and eradicate parasitic diseases across the world.

Resilience in the global food system

Ensuring food security requires food production and distribution systems function throughout disruptions. Understanding the factors that contribute to the global food system's ability to respond and adapt to such disruptions (i.e. resilience) is critical for understanding the long-term sustainability of human populations. Variable impacts of production shocks on food supply between countries indicate a need for national-scale resilience indicators that can provide global comparisons. However, methods for tracking changes in resilience have had limited application to food systems. We developed an indicator-based analysis of food systems resilience for the years 1992-2011. Our approach is based on three dimensions of resilience: socio-economic access to food in terms of income of the poorest quintile relative to food prices, biophysical capacity to intensify or extensify food production, and the magnitude and diversity of current domestic food production. The socio-economic indicator has large variability, but with low values concentrated in Africa and Asia. The biophysical capacity indicator is highest in Africa and Eastern Europe, in part because of high potential for extensification of cropland and for yield gap closure in cultivated areas. However, the biophysical capacity indicator has declined globally in recent years. The production diversity indicator has increased slightly, with a relatively even geographic distribution. Few countries had exclusively high or low values for all indicators. Collectively, these results are the basis for global comparisons of resilience between nations, and provide necessary context for developing generalizations about the resilience in the global food system.

Detecting spatial regimes in ecosystems

Research on early warning indicators has generally focused on assessing temporal transitions with limited application of these methods to detecting spatial regimes. Traditional spatial boundary detection procedures that result in ecoregion maps are typically based on ecological potential (i.e. potential vegetation), and often fail to account for ongoing changes due to stressors such as land use change and climate change and their effects on plant and animal communities. We use Fisher information, an information theory-based method, on both terrestrial and aquatic animal data (U.S. Breeding Bird Survey and marine zooplankton) to identify ecological boundaries, and compare our results to traditional early warning indicators, conventional ecoregion maps and multivariate analyses such as nMDS and cluster analysis. We successfully detected spatial regimes and transitions in both terrestrial and aquatic systems using Fisher information. Furthermore, Fisher information provided explicit spatial information about community change that is absent from other multivariate approaches. Our results suggest that defining spatial regimes based on animal communities may better reflect ecological reality than do traditional ecoregion maps, especially in our current era of rapid and unpredictable ecological change.

Reversal of a cyanobacterial bloom in response to early warnings

Directional change in environmental drivers sometimes triggers regime shifts in ecosystems. Theory and experiments suggest that regime shifts can be detected in advance, and perhaps averted, by monitoring resilience indicators such as variance and autocorrelation of key ecosystem variables. However, it is uncertain whether management action prompted by a change in resilience indicators can prevent an impending regime shift. We caused a cyanobacterial bloom by gradually enriching an experimental lake while monitoring an unenriched reference lake and a continuously enriched reference lake. When resilience indicators exceeded preset boundaries, nutrient enrichment was stopped in the experimental lake. Concentrations of algal pigments, dissolved oxygen saturation, and pH rapidly declined following cessation of nutrient enrichment and became similar to the unenriched lake, whereas a large bloom occurred in the continuously enriched lake. This outcome suggests that resilience indicators may be useful in management to prevent unwanted regime shifts, at least in some situations. Nonetheless, a safer approach to ecosystem management would build and maintain the resilience of desirable ecosystem conditions, for example, by preventing excessive nutrient input to lakes and reservoirs.

Early warning signals for critical transitions in a thermoacoustic system

Dynamical systems can undergo critical transitions where the system suddenly shifts from one stable state to another at a critical threshold called the tipping point. The decrease in recovery rate to equilibrium (critical slowing down) as the system approaches the tipping point can be used to identify the proximity to a critical transition. Several measures have been adopted to provide early indications of critical transitions that happen in a variety of complex systems. In this study, we use early warning indicators to predict subcritical Hopf bifurcation occurring in a thermoacoustic system by analyzing the observables from experiments and from a theoretical model. We find that the early warning measures perform as robust indicators in the presence and absence of external noise. Thus, we illustrate the applicability of these indicators in an engineering system depicting critical transitions.

Rate of forcing and the forecastability of critical transitions

Critical transitions are qualitative changes of state that occur when a stochastic dynamical system is forced through a critical point. Many critical transitions are preceded by characteristic fluctuations that may serve as model‐independent early warning signals, implying that these events may be predictable in applications ranging from physics to biology. In nonbiological systems, the strength of such early warning signals has been shown partly to be determined by the speed at which the transition occurs. It is currently unknown whether biological systems, which are inherently high dimensional and typically display low signal‐to‐noise ratios, also exhibit this property, which would have important implications for how ecosystems are managed, particularly where the forces exerted on a system are anthropogenic. We examine whether the rate of forcing can alter the strength of early warning signals in (1) a model exhibiting a fold bifurcation where a state shift is driven by the harvesting of individuals, and (2) a model exhibiting a transcritical bifurcation where a state shift is driven by increased grazing pressure. These models predict that the rate of forcing can alter the detectability of early warning signals regardless of the underlying bifurcation the system exhibits, but that this result may be more pronounced in fold bifurcations. These findings have important implications for the management of biological populations, particularly harvested systems such as fisheries, and suggest that knowing the class of bifurcations a system will manifest may help discriminate between true‐positive and false‐positive signals.

Early warning signals detect critical impacts of experimental warming

Earth's surface temperatures are projected to increase by ~1-4°C over the next century, threatening the future of global biodiversity and ecosystem stability. While this has fueled major progress in the field of physiological trait responses to warming, it is currently unclear whether routine population monitoring data can be used to predict temperature-induced population collapse. Here, we integrate trait performance theory with that of critical tipping points to test whether early warning signals can be reliably used to anticipate thermally induced extinction events. We find that a model parameterized by experimental growth rates exhibits critical slowing down in the vicinity of an experimentally tested critical threshold, suggesting that dynamical early warning signals may be useful in detecting the potentially precipitous onset of population collapse due to global climate change.

Slowing Down of Recovery as Generic Risk Marker for Acute Severity Transitions in Chronic Diseases

OBJECTIVE

We propose a novel paradigm to predict acute attacks and exacerbations in chronic episodic disorders such as asthma, cardiac arrhythmias, migraine, epilepsy, and depression. A better generic understanding of acute transitions in chronic dynamic diseases is increasingly important in critical care medicine because of the higher prevalence and incidence of these chronic diseases in our aging societies.

DATA SOURCES

PubMed, Medline, and Web of Science.

STUDY SELECTION

We selected studies from biology and medicine providing evidence of slowing down after a perturbation as a warning signal for critical transitions.

DATA EXTRACTION

Recent work in ecology, climate, and systems biology has shown that slowing down of recovery upon perturbations can indicate loss of resilience across complex, nonlinear biologic systems that are approaching a tipping point. This observation is supported by the empiric studies in pathophysiology and controlled laboratory experiments with other living systems, which can flip from one state of clinical balance to a contrasting one. We discuss examples of such evidence in bodily functions such as blood pressure, heart rate, mood, and respiratory regulation when a tipping point for a transition is near.

CONCLUSIONS

We hypothesize that in a range of chronic episodic diseases, indicators of critical slowing down, such as rising variance and temporal correlation, may be used to assess the risk of attacks, exacerbations, and even mortality. Identification of such early warning signals over a range of diseases will enhance the understanding of why, how, and when attacks and exacerbations will strike and may thus improve disease management in critical care medicine.

Predicting catastrophic shifts

Catastrophic shifts are known to pose a serious threat to ecology, and a reliable set of early warning indicators is desperately needed. However, the tools suggested so far have two problems. First, they cannot discriminate between a smooth transition and an imminent irreversible shift. Second, they aimed at predicting the tipping point where a state loses its stability, but in noisy spatial system the actual transition occurs when an alternative state invades. Here we suggest a cluster tracking technique that solves both problems, distinguishing between smooth and catastrophic transitions and to identify an imminent shift in both cases. Our method may allow for the prediction, and thus hopefully the prevention of such transitions, avoiding their destructive outcomes.

Including trait-based early warning signals helps predict population collapse

Foreseeing population collapse is an on-going target in ecology, and this has led to the development of early warning signals based on expected changes in leading indicators before a bifurcation. Such signals have been sought for in abundance time-series data on a population of interest, with varying degrees of success. Here we move beyond these established methods by including parallel time-series data of abundance and fitness-related trait dynamics. Using data from a microcosm experiment, we show that including information on the dynamics of phenotypic traits such as body size into composite early warning indices can produce more accurate inferences of whether a population is approaching a critical transition than using abundance time-series alone. By including fitness-related trait information alongside traditional abundance-based early warning signals in a single metric of risk, our generalizable approach provides a powerful new way to assess what populations may be on the verge of collapse.

Predicting population collapse by monitoring key early warning signals in time-series data may highlight when interventions are needed. Here, the authors show that including information on phenotypic traits like body size can more accurately predict critical transitions than abundance data alone.

Identifying early-warning signals of critical transitions with strong noise by dynamical network markers

Identifying early-warning signals of a critical transition for a complex system is difficult, especially when the target system is constantly perturbed by big noise, which makes the traditional methods fail due to the strong fluctuations of the observed data. In this work, we show that the critical transition is not traditional state-transition but probability distribution-transition when the noise is not sufficiently small, which, however, is a ubiquitous case in real systems. We present a model-free computational method to detect the warning signals before such transitions. The key idea behind is a strategy: “making big noise smaller” by a distribution-embedding scheme, which transforms the data from the observed state-variables with big noise to their distribution-variables with small noise, and thus makes the traditional criteria effective because of the significantly reduced fluctuations. Specifically, increasing the dimension of the observed data by moment expansion that changes the system from state-dynamics to probability distribution-dynamics, we derive new data in a higher-dimensional space but with much smaller noise. Then, we develop a criterion based on the dynamical network marker (DNM) to signal the impending critical transition using the transformed higher-dimensional data. We also demonstrate the effectiveness of our method in biological, ecological and financial systems.

Predictability of critical transitions

Critical transitions in multistable systems have been discussed as models for a variety of phenomena ranging from the extinctions of species to socioeconomic changes and climate transitions between ice ages and warm ages. From bifurcation theory we can expect certain critical transitions to be preceded by a decreased recovery from external perturbations. The consequences of this critical slowing down have been observed as an increase in variance and autocorrelation prior to the transition. However, especially in the presence of noise, it is not clear whether these changes in observation variables are statistically relevant such that they could be used as indicators for critical transitions. In this contribution we investigate the predictability of critical transitions in conceptual models. We study the quadratic integrate-and-fire model and the van der Pol model under the influence of external noise. We focus especially on the statistical analysis of the success of predictions and the overall predictability of the system. The performance of different indicator variables turns out to be dependent on the specific model under study and the conditions of accessing it. Furthermore, we study the influence of the magnitude of transitions on the predictive performance.

Forecasting Bifurcations from Large Perturbation Recoveries in Feedback Ecosystems

Forecasting bifurcations such as critical transitions is an active research area of relevance to the management and preservation of ecological systems. In particular, anticipating the distance to critical transitions remains a challenge, together with predicting the state of the system after these transitions are breached. In this work, a new model-less method is presented that addresses both these issues based on monitoring recoveries from large perturbations. The approach uses data from recoveries of the system from at least two separate parameter values before the critical point, to predict both the bifurcation and the post-bifurcation dynamics. The proposed method is demonstrated, and its performance evaluated under different levels of measurement noise, with two ecological models that have been used extensively in previous studies of tipping points and alternative steady states. The first one considers the dynamics of vegetation under grazing; the second, those of macrophyte and phytoplankton in shallow lakes. Applications of the method to more complex situations are discussed together with the kinds of empirical data needed for its implementation.

Early warning signs for saddle-escape transitions in complex networks

Many real world systems are at risk of undergoing critical transitions, leading to sudden qualitative and sometimes irreversible regime shifts. The development of early warning signals is recognized as a major challenge. Recent progress builds on a mathematical framework in which a real-world system is described by a low-dimensional equation system with a small number of key variables, where the critical transition often corresponds to a bifurcation. Here we show that in high-dimensional systems, containing many variables, we frequently encounter an additional non-bifurcative saddle-type mechanism leading to critical transitions. This generic class of transitions has been missed in the search for early-warnings up to now. In fact, the saddle-type mechanism also applies to low-dimensional systems with saddle-dynamics. Near a saddle a system moves slowly and the state may be perceived as stable over substantial time periods. We develop an early warning sign for the saddle-type transition. We illustrate our results in two network models and epidemiological data. This work thus establishes a connection from critical transitions to networks and an early warning sign for a new type of critical transition. In complex models and big data we anticipate that saddle-transitions will be encountered frequently in the future.

Relation between stability and resilience determines the performance of early warning signals under different environmental drivers

Shifting patterns of temporal fluctuations have been found to signal critical transitions in a variety of systems, from ecological communities to human physiology. However, failure of these early warning signals in some systems calls for a better understanding of their limitations. In particular, little is known about the generality of early warning signals in different deteriorating environments. In this study, we characterized how multiple environmental drivers influence the dynamics of laboratory yeast populations, which was previously shown to display alternative stable states [Dai et al., Science, 2012]. We observed that both the coefficient of variation and autocorrelation increased before population collapse in two slowly deteriorating environments, one with a rising death rate and the other one with decreasing nutrient availability. We compared the performance of early warning signals across multiple environments as "indicators for loss of resilience." We find that the varying performance is determined by how a system responds to changes in a specific driver, which can be captured by a relation between stability (recovery rate) and resilience (size of the basin of attraction). Furthermore, we demonstrate that the positive correlation between stability and resilience, as the essential assumption of indicators based on critical slowing down, can break down in this system when multiple environmental drivers are changed simultaneously. Our results suggest that the stability-resilience relation needs to be better understood for the application of early warning signals in different scenarios.

Experimental Perturbations Modify the Performance of Early Warning Indicators of Regime Shift

Ecosystems may shift abruptly between alternative states in response to environmental perturbations. Early warning indicators have been proposed to anticipate such regime shifts, but experimental field tests of their validity are rare. We exposed rocky intertidal algal canopies to a gradient of press perturbations and recorded the response of associated assemblages over 7 years. Reduced cover and biomass of algal canopies promoted the invasion of algal turfs, driving understory assemblages toward collapse upon total canopy removal. A dynamic model indicated the existence of a critical threshold separating the canopy- and turf-dominated states. We evaluated common indicators of regime shift as the system approached the threshold, including autocorrelation, SD, and skewness. These indicators captured changes in understory cover due to colonization of algal turfs. All indicators increased significantly as the system approached the critical threshold, in agreement with theoretical predictions. The performance of indicators changed when we superimposed a pulse disturbance on the press perturbation that amplified environmental noise. This treatment caused several experimental units to switch repeatedly between the canopy- and the turf-dominated state, resulting in a significant increase in overall variance of understory cover, a negligible effect on skewness and no effect on autocorrelation. Power analysis indicated that autocorrelation and SD were better suited at anticipating a regime shift under mild and strong fluctuations of the state variable, respectively. Our results suggest that regime shifts may be anticipated under a broad range of fluctuating conditions using the appropriate indicator.

Heteroskedasticity as a leading indicator of desertification in spatially explicit data

Regime shifts are abrupt transitions between alternate ecosystem states including desertification in arid regions due to drought or overgrazing. Regime shifts may be preceded by statistical anomalies such as increased autocorrelation, indicating declining resilience and warning of an impending shift. Tests for conditional heteroskedasticity, a type of clustered variance, have proven powerful leading indicators for regime shifts in time series data, but an analogous indicator for spatial data has not been evaluated. A spatial analog for conditional heteroskedasticity might be especially useful in arid environments where spatial interactions are critical in structuring ecosystem pattern and process. We tested the efficacy of a test for spatial heteroskedasticity as a leading indicator of regime shifts with simulated data from spatially extended vegetation models with regular and scale-free patterning. These models simulate shifts from extensive vegetative cover to bare, desert-like conditions. The magnitude of spatial heteroskedasticity increased consistently as the modeled systems approached a regime shift from vegetated to desert state. Relative spatial autocorrelation, spatial heteroskedasticity increased earlier and more consistently. We conclude that tests for spatial heteroskedasticity can contribute to the growing toolbox of early warning indicators for regime shifts analyzed with spatially explicit data.

Factors influencing the detectability of early warning signals of population collapse

The recent description of potentially generic early warning signals is a promising development that may help conservationists to anticipate a population's collapse prior to its occurrence. So far, the majority of such warning signals documented have been in highly controlled laboratory systems or in theoretical models. Data from wild populations, however, are typically restricted both temporally and spatially due to limited monitoring resources and intrinsic ecological heterogeneity-limitations that may affect the detectability of generic early warning signals, as they add additional stochasticity to population abundance estimates. Consequently, spatial and temporal subsampling may serve to either muffle or magnify early warning signals. Using a combination of theoretical models and analysis of experimental data, we evaluate the extent to which statistical warning signs are robust to data corruption.

Eluding catastrophic shifts

Transitions between regimes with radically different properties are ubiquitous in nature. Such transitions can occur either smoothly or in an abrupt and catastrophic fashion. Important examples of the latter can be found in ecology, climate sciences, and economics, to name a few, where regime shifts have catastrophic consequences that are mostly irreversible (e.g., desertification, coral reef collapses, and market crashes). Predicting and preventing these abrupt transitions remains a challenging and important task. Usually, simple deterministic equations are used to model and rationalize these complex situations. However, stochastic effects might have a profound effect. Here we use 1D and 2D spatially explicit models to show that intrinsic (demographic) stochasticity can alter deterministic predictions dramatically, especially in the presence of other realistic features such as limited mobility or spatial heterogeneity. In particular, these ingredients can alter the possibility of catastrophic shifts by giving rise to much smoother and easily reversible continuous ones. The ideas presented here can help further understand catastrophic shifts and contribute to the discussion about the possibility of preventing such shifts to minimize their disruptive ecological, economic, and societal consequences.

Spatially variable habitat quality contributes to within-population variation in reproductive success

Variation in habitat quality is common across terrestrial, freshwater, and marine habitats. We investigated how habitat quality influenced the reproductive potential of mud crabs across 30 oyster reefs that were degraded to different extents. We further coupled this field survey with a laboratory experiment designed to mechanistically determine the relationship between resource consumption and reproductive performance. We show a >10-fold difference in average reproductive potential for crabs across reefs of different quality. Calculated consumption rates for crabs in each reef, based on a type II functional response, suggest that differences in reproductive performance may be attributed to resource limitation in poor quality reefs. This conclusion is supported by results of our laboratory experiment where crabs fed a higher quality diet of abundant animal tissue had greater reproductive performance. Our results demonstrate that spatial variation in habitat quality can be a considerable contributor to within-population individual variation in reproductive success (i.e., demographic heterogeneity). This finding has important implications for assessing population extinction risk.

Resilience of alternative states in spatially extended ecosystems

Alternative stable states in ecology have been well studied in isolated, well-mixed systems. However, in reality, most ecosystems exist on spatially extended landscapes. Applying existing theory from dynamic systems, we explore how such a spatial setting should be expected to affect ecological resilience. We focus on the effect of local disturbances, defining resilience as the size of the area of a strong local disturbance needed to trigger a shift. We show that in contrast to well-mixed systems, resilience in a homogeneous spatial setting does not decrease gradually as a bifurcation point is approached. Instead, as an environmental driver changes, the present dominant state remains virtually ‘indestructible’, until at a critical point (the Maxwell point) its resilience drops sharply in the sense that even a very local disturbance can cause a domino effect leading eventually to a landscape-wide shift to the alternative state. Close to this Maxwell point the travelling wave moves very slow. Under these conditions both states have a comparable resilience, allowing long transient co-occurrence of alternative states side-by-side, and also permanent co-existence if there are mild spatial barriers. Overall however, hysteresis may mostly disappear in a spatial context as one of both alternative states will always tend to be dominant. Our results imply that local restoration efforts on a homogeneous landscape will typically either fail or trigger a landscape-wide transition. For extensive biomes with alternative stable states, such as tundra, steppe and forest, our results imply that, as climatic change reduces the stability, the effect might be difficult to detect until a point where local disturbances inevitably induce a spatial cascade to the alternative state.