A new approach for rapid detection of nearby thresholds in ecosystem time series

Evaluating the performance of temporal and spatial early warning statistics of algal blooms

Regime shifts have large consequences for ecosystems and the services they provide. However, understanding the potential for, causes of, proximity to, and thresholds for regime shifts in nearly all settings is difficult. Generic statistical indicators of resilience have been proposed and studied in a wide range of ecosystems as a method to detect when regime shifts are becoming more likely without direct knowledge of underlying system dynamics or thresholds. These early warning statistics (EWS) have been studied separately but there have been few examples that directly compare temporal and spatial EWS in ecosystem-scale empirical data. To test these methods, we collected high-frequency time series and high-resolution spatial data during a whole-lake fertilization experiment while also monitoring an adjacent reference lake. We calculated two common EWS, standard deviation and autocorrelation, in both time series and spatial data to evaluate their performance prior to the resulting algal bloom. We also applied the quickest detection method to generate binary alarms of resilience change from temporal EWS. One temporal EWS, rolling window standard deviation, provided advanced warning in most variables prior to the bloom, showing trends and between-lake patterns consistent with theory. In contrast, temporal autocorrelation and both measures of spatial EWS (spatial SD, Moran's  I) provided little or no warning. By compiling time series data from this and past experiments with and without nutrient additions, we were able to evaluate temporal EWS performance for both constant and changing resilience conditions. True positive alarm rates were 2.5-8.3 times higher for rolling window standard deviation when a lake was being pushed towards a bloom than the rate of false positives when it was not. For rolling window autocorrelation, alarm rates were much lower and no variable had a higher true positive than false positive alarm rate. Our findings suggest temporal EWS provide advanced warning of algal blooms and that this approach could help managers prepare for and/or minimize negative bloom impacts.

The Invasion Ecology of Sleeper Populations: Prevalence, Persistence, and Abrupt Shifts

It is well established that nonnative species are a key driver of global environmental change, but much less is known about the underlying drivers of nonnative species outbreaks themselves. In the present article, we explore the concept and implications of nonnative sleeper populations in invasion dynamics. Such populations persist at low abundance for years or even decades—a period during which they often go undetected and have negligible impact—until they are triggered by an environmental factor to become highly abundant and disruptive. Population irruptions are commonly misinterpreted as a recent arrival of the nonnative species, but sleeper populations belie a more complex history of inconspicuous occurrence followed by an abrupt shift in abundance and ecological impact. In the present article, we identify mechanisms that can trigger their irruption, and the implications for invasive species risk assessment and management.

Bifurcation or state tipping: assessing transition type in a model trophic cascade

Ecosystems can experience sudden regime shifts due to a variety of mechanisms. Two of the ways a system can cross a tipping point include when a perturbation to the system state is large enough to push the system beyond the basin of attraction of one stable state and into that of another (state tipping), and alternately, when slow changes to some underlying parameter lead to a fold bifurcation that annihilates one of the stable states. The first mechanism does not generate the phenomenon of critical slowing down (CSD), whereas the latter does generate CSD, which has been postulated as a way to detect early warning signs ahead of a sudden shift. Yet distinguishing between the two mechanisms (s-tipping and b-tipping) is not always as straightforward as it might seem. The distinction between "state" and "parameter" that may seem self-evident in mathematical equations depends fundamentally on ecological details in model formulation. This distinction is particularly relevant when considering high-dimensional models involving trophic webs of interacting species, which can only be reduced to a one-dimensional model of a tipping point under appropriate consideration of both the mathematics and biology involved. Here we illustrate that process of dimension reduction and distinguishing between s- and b-tipping for a highly influential trophic cascade model used to demonstrate tipping points and test CSD predictions in silico, and later, in a natural lake ecosystem. Our analysis resolves a previously unclear issue as to the nature of the tipping point involved.

A dynamic management framework for socio-ecological system stewardship: A case study for the United States Bureau of Ocean Energy Management

An effective and efficient stewardship of natural resources requires consistency across all decision-informing approaches and components involved, i.e., managerial, governmental, political, and legal. To achieve this consistency, these elements must be aligned under an overarching management goal that is consistent with current and well-accepted knowledge. In this article, we investigate the adoption by the US Bureau of Ocean Energy Management of an environmental resilience-centered system that manages for resilience of marine ecological resources and its associated social elements. Although the framework is generally tailored for this Bureau, it could also be adapted to other federal or non-federal organizations. This paper presents a dynamic framework that regards change as an inherent element of the socio-ecological system in which management structures, e.g., federal agencies, are embedded. The overall functioning of the management framework being considered seeks to mimic and anticipate environmental change in line with well-accepted elements of resilience-thinking. We also investigate the goal of using management for resilience as a platform to enhance socio-ecological sustainability by setting specific performance metrics embedded in pre-defined and desired social and/or ecological scenarios. Dynamic management frameworks that couple social and ecological systems as described in this paper can facilitate the efficient and effective utilization of resources, reduce uncertainty for decision and policy makers, and lead to more defensible decisions on resources.

Indicators of transitions in biological systems

In the face of global biodiversity declines, predicting the fate of biological systems is a key goal in ecology. One popular approach is the search for early warning signals (EWSs) based on alternative stable states theory. In this review, we cover the theory behind nonlinearity in dynamic systems and techniques to detect the loss of resilience that can indicate state transitions. We describe the research done on generic abundance-based signals of instability that are derived from the phenomenon of critical slowing down, which represent the genesis of EWSs research. We highlight some of the issues facing the detection of such signals in biological systems - which are inherently complex and show low signal-to-noise ratios. We then document research on alternative signals of instability, including measuring shifts in spatial autocorrelation and trait dynamics, and discuss potential future directions for EWSs research based on detailed demographic and phenotypic data. We set EWSs research in the greater field of predictive ecology and weigh up the costs and benefits of simplicity vs. complexity in predictive models, and how the available data should steer the development of future methods. Finally, we identify some key unanswered questions that, if solved, could improve the applicability of these methods.

Dynamical predictors of an imminent phenotypic switch in bacteria

Single cells can stochastically switch across thresholds imposed by regulatory networks. Such thresholds can act as a tipping point, drastically changing global phenotypic states. In ecology and economics, imminent transitions across such tipping points can be predicted using dynamical early warning indicators. A typical example is 'flickering' of a fast variable, predicting a longer-lasting switch from a low to a high state or vice versa. Considering the different timescales between metabolite and protein fluctuations in bacteria, we hypothesized that metabolic early warning indicators predict imminent transitions across a network threshold caused by enzyme saturation. We used stochastic simulations to determine if flickering predicts phenotypic transitions, accounting for a variety of molecular physiological parameters, including enzyme affinity, burstiness of enzyme gene expression, homeostatic feedback, and rates of metabolic precursor influx. In most cases, we found that metabolic flickering rates are robustly peaked near the enzyme saturation threshold. The degree of fluctuation was amplified by product inhibition of the enzyme. We conclude that sensitivity to flickering in fast variables may be a possible natural or synthetic strategy to prepare physiological states for an imminent transition.

Early warning of critical transitions in biodiversity from compositional disorder

Global environmental change presents a clear need for improved leading indicators of critical transitions, especially those that can be generated from compositional data and that work in empirical cases. Ecological theory of community dynamics under environmental forcing predicts an early replacement of slowly replicating and weakly competitive “canary” species by slowly replicating but strongly competitive “keystone” species. Further forcing leads to the eventual collapse of the keystone species as they are replaced by weakly competitive but fast‐replicating “weedy” species in a critical transition to a significantly different state. We identify a diagnostic signal of these changes in the coefficients of a correlation between compositional disorder and biodiversity. Compositional disorder measures unpredictability in the composition of a community, while biodiversity measures the amount of species in the community. In a stochastic simulation, sequential correlations over time switch from positive to negative as keystones prevail over canaries, and back to positive with domination of weedy species. The model finds support in empirical tests on multi‐decadal time series of fossil diatom and chironomid communities from lakes in China. The characteristic switch from positive to negative correlation coefficients occurs for both communities up to three decades preceding a critical transition to a sustained alternate state. This signal is robust to unequal time increments that beset the identification of early‐warning signals from other metrics.

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.

Towards a common methodology for developing logistic tree mortality models based on ring-width data

Tree mortality is a key process shaping forest dynamics. Thus, there is a growing need for indicators of the likelihood of tree death. During the last decades, an increasing number of tree-ring based studies have aimed to derive growth-mortality functions, mostly using logistic models. The results of these studies, however, are difficult to compare and synthesize due to the diversity of approaches used for the sampling strategy (number and characteristics of alive and death observations), the type of explanatory growth variables included (level, trend, etc.), and the length of the time window (number of years preceding the alive/death observation) that maximized the discrimination ability of each growth variable. We assess the implications of key methodological decisions when developing tree-ring based growth-mortality relationships using logistic mixed-effects regression models. As examples, we use published tree-ring datasets from Abies alba (13 different sites), Nothofagus dombeyi (one site), and Quercus petraea (one site). Our approach is based on a constant sampling size and aims at (1) assessing the dependency of growth-mortality relationships on the statistical sampling scheme used, (2) determining the type of explanatory growth variables that should be considered, and (3) identifying the best length of the time window used to calculate them. The performance of tree-ring-based mortality models was reasonably high for all three species (area under the receiving operator characteristics curve, AUC > 0.7). Growth level variables were the most important predictors of mortality probability for two species (A. alba, N. dombeyi), while growth-trend variables need to be considered for Q. petraea. In addition, the length of the time window used to calculate each growth variable was highly uncertain and depended on the sampling scheme, as some growth-mortality relationships varied with tree age. The present study accounts for the main sampling-related biases to determine reliable species-specific growth-mortality relationships. Our results highlight the importance of using a sampling strategy that is consistent with the research question. Moving towards a common methodology for developing reliable growth-mortality relationships is an important step towards improving our understanding of tree mortality across species and its representation in dynamic vegetation models.

Resilience and tipping points of an exploited fish population over six decades

Complex natural systems with eroded resilience, such as populations, ecosystems and socio-ecological systems, respond to small perturbations with abrupt, discontinuous state shifts, or critical transitions. Theory of critical transitions suggests that such systems exhibit fold bifurcations featuring folded response curves, tipping points and alternate attractors. However, there is little empirical evidence of fold bifurcations occurring in actual complex natural systems impacted by multiple stressors. Moreover, resilience of complex systems to change currently lacks clear operational measures with generic application. Here, we provide empirical evidence for the occurrence of a fold bifurcation in an exploited fish population and introduce a generic measure of ecological resilience based on the observed fold bifurcation attributes. We analyse the multivariate development of Barents Sea cod (Gadus morhua), which is currently the world's largest cod stock, over six decades (1949-2009), and identify a population state shift in 1981. By plotting a multivariate population index against a multivariate stressor index, the shift mechanism was revealed suggesting that the observed population shift was a nonlinear response to the combined effects of overfishing and climate change. Annual resilience values were estimated based on the position of each year in relation to the fitted attractors and assumed tipping points of the fold bifurcation. By interpolating the annual resilience values, a folded stability landscape was fit, which was shaped as predicted by theory. The resilience assessment suggested that the population may be close to another tipping point. This study illustrates how a multivariate analysis, supported by theory of critical transitions and accompanied by a quantitative resilience assessment, can clarify shift mechanisms in data-rich complex natural systems.

Resilience indicators: prospects and limitations for early warnings of regime shifts

In the vicinity of tipping points—or more precisely bifurcation points—ecosystems recover slowly from small perturbations. Such slowness may be interpreted as a sign of low resilience in the sense that the ecosystem could easily be tipped through a critical transition into a contrasting state. Indicators of this phenomenon of ‘critical slowing down (CSD)’ include a rise in temporal correlation and variance. Such indicators of CSD can provide an early warning signal of a nearby tipping point. Or, they may offer a possibility to rank reefs, lakes or other ecosystems according to their resilience. The fact that CSD may happen across a wide range of complex ecosystems close to tipping points implies a powerful generality. However, indicators of CSD are not manifested in all cases where regime shifts occur. This is because not all regime shifts are associated with tipping points. Here, we review the exploding literature about this issue to provide guidance on what to expect and what not to expect when it comes to the CSD-based early warning signals for critical transitions.