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

Resilience assessment in complex natural systems

Ecological resilience is the capability of an ecosystem to maintain the same structure and function and avoid crossing catastrophic tipping points (i.e. undergoing irreversible regime shifts). While fundamental for management, concrete ways to estimate and interpret resilience in real ecosystems are still lacking. Here, we develop an empirical approach to estimate resilience based on the stochastic cusp model derived from catastrophe theory. The cusp model models tipping points derived from a cusp bifurcation. We extend cusp in order to identify the presence of stable and unstable states in complex natural systems. Our Cusp Resilience Assessment (CUSPRA) has three characteristics: (i) it provides estimates on how likely a system is to cross a tipping point (in the form of a cusp bifurcation) characterized by hysteresis, (ii) it assesses resilience in relation to multiple external drivers and (iii) it produces straightforward results for ecosystem-based management. We validate our approach using simulated data and demonstrate its application using empirical time series of an Atlantic cod population and marine ecosystems in the North Sea and the Mediterranean Sea. We show that Cusp Resilience Assessment is a powerful method to empirically estimate resilience in support of a sustainable management of our constantly adapting ecosystems under global climate change.

Analysis of long transients and detection of early warning signals of extinction in a class of predator-prey models exhibiting bistable behavior

In this paper, we develop a method of analyzing long transient dynamics in a class of predator-prey models with two species of predators competing explicitly for their common prey, where the prey evolves on a faster timescale than the predators. In a parameter regime near a singular zero-Hopf bifurcation of the coexistence equilibrium state, we assume that the system under study exhibits bistability between a periodic attractor that bifurcates from the singular Hopf point and another attractor, which could be a periodic attractor or a point attractor, such that the invariant manifolds of the coexistence equilibrium point play central roles in organizing the dynamics. To find whether a solution that starts in a vicinity of the coexistence equilibrium approaches the periodic attractor or the other attractor, we reduce the equations to a suitable normal form, and examine the basin boundary near the singular Hopf point. A key component of our study includes an analysis of the long transient dynamics, characterized by their rapid oscillations with a slow variation in amplitude, by applying a moving average technique. We obtain a set of necessary and sufficient conditions on the initial values of a solution near the coexistence equilibrium to determine whether it lies in the basin of attraction of the periodic attractor. As a result of our analysis, we devise a method of identifying early warning signals, significantly in advance, of a future crisis that could lead to extinction of one of the predators. The analysis is applied to the predator-prey model considered in Sadhu (Discrete Contin Dyn Syst B 26:5251-5279, 2021) and we find that our theory is in good agreement with the numerical simulations carried out for this model.

Application of early warning signs to physiological contexts: a comparison of multivariate indices in patients on long-term hemodialysis

Early warnings signs (EWSs) can anticipate abrupt changes in system state, known as "critical transitions," by detecting dynamic variations, including increases in variance, autocorrelation (AC), and cross-correlation. Numerous EWSs have been proposed; yet no consensus on which perform best exists. Here, we compared 15 multivariate EWSs in time series of 763 hemodialyzed patients, previously shown to present relevant critical transition dynamics. We calculated five EWSs based on AC, six on variance, one on cross-correlation, and three on AC and variance. We assessed their pairwise correlations, trends before death, and mortality predictive power, alone and in combination. Variance-based EWSs showed stronger correlations (r = 0.663 ± 0.222 vs. 0.170 ± 0.205 for AC-based indices) and a steeper increase before death. Two variance-based EWSs yielded HR95 > 9 (HR95 standing for a scale-invariant metric of hazard ratio), but combining them did not improve the area under the receiver-operating curve (AUC) much compared to using them alone (AUC = 0.798 vs. 0.796 and 0.791). Nevertheless, the AUC reached 0.825 when combining 13 indices. While some indicators did not perform overly well alone, their addition to the best performing EWSs increased the predictive power, suggesting that indices combination captures a broader range of dynamic changes occurring within the system. It is unclear whether this added benefit reflects measurement error of a unified phenomenon or heterogeneity in the nature of signals preceding critical transitions. Finally, the modest predictive performance and weak correlations among some indices call into question their validity, at least in this context.

Understanding change in benthic marine systems

BACKGROUND

The unprecedented influence of human activities on natural ecosystems in the 21st century has resulted in increasingly frequent large-scale changes in ecological communities. This has heightened interest in understanding such changes and effective means to manage them. Accurate interpretation of state changes is challenging because of difficulties translating theory to empirical study, and most theory emphasizes systems near equilibrium, which may not be relevant in rapidly changing environments.

SCOPE

We review concepts of long-transient stages and phase shifts between stable community states, both smooth, continuous and discontinuous shifts, and the relationships among them. Three principal challenges emerge when applying these concepts. The first is how to interpret observed change in communities - distinguishing multiple stable states from long transients, or reversible shifts in the phase portrait of single attractor systems. The second is how to quantify the magnitudes of three sources of variability that cause switches between community states: (1) 'noise' in species' abundances, (2) 'wiggle' in system parameters and (3) trends in parameters that affect the topography of the basin of attraction. The third challenge is how variability of the system shapes evidence used to interpret community changes. We outline a novel approach using critical length scales to potentially address these challenges. These concepts are highlighted by a review of recent examples involving macroalgae as key players in marine benthic ecosystems.

CONCLUSIONS

Real-world examples show three or more stable configurations of ecological communities may exist for a given set of parameters, and transient stages may persist for long periods necessitating their respective consideration. The characteristic length scale (CLS) is a useful metric that uniquely identifies a community 'basin of attraction', enabling phase shifts to be distinguished from long transients. Variabilities of CLSs and time series data may likewise provide proactive management measures to mitigate phase shifts and loss of ecosystem services. Continued challenges remain in distinguishing continuous from discontinuous phase shifts because their respective dynamics lack unique signatures.

Variance reflects resilience to disturbance along a stress gradient: Experimental evidence from coastal marshes

Quantifying ecosystem resilience to disturbance is important for understanding the effects of disturbances on ecosystems, especially in an era of rapid global change. However, there are few studies that have used standardized experimental disturbances to compare resilience patterns across abiotic gradients in real-world ecosystems. Theoretical studies have suggested that increased return times are associated with increasing variance during recovery from disturbance. However, this notion has rarely been explicitly tested in field, in part due to the challenges involved in obtaining long-term experimental data. In this study, we examined resilience to disturbance of 12 coastal marsh sites (five low-salinity and seven polyhaline [=salt] marshes) along a salinity gradient in Georgia, USA. We found that recovery times after experimental disturbance ranged from 7 to >127 months, and differed among response variables (vegetation height, cover and composition). Recovery rates decreased along the stress gradient of increasing salinity, presumably due to stress reducing plant vigor, but only when low-salinity and polyhaline sites were analyzed separately, indicating a strong role for traits of dominant plant species. The coefficient of variation of vegetation cover and height in control plots did not vary with salinity. In disturbed plots, however, the coefficient of variation (CV) was consistently elevated during the recovery period and increased with salinity. Moreover, higher CV values during recovery were correlated with slower recovery rates. Our results deepen our understanding of resilience to disturbance in natural ecosystems, and point to novel ways that variance can be used either to infer recent disturbance, or, if measured in areas with a known disturbance history, to predict recovery patterns.

Early warning signals indicate climate change-induced stress in Norway spruce in the Eastern Carpathians

Climate change is affecting forest ecosystems globally, in particular through warming as well as increases in the frequency and intensity of extreme events. Norway spruce (Picea abies (L.) Karst.) is one of the most important coniferous tree species in Europe. In recent extremely dry years in Central Europe, spruce suffered and large dieback has been observed. In parts of Eastern Europe, however, no large-scale decline in spruce has been reported so far, though anticipated changes in climate pose the question how the future of these forests may look like. To assess the current state of spruce forests in Eastern Europe, we established a tree-ring network consisting of 157 Norway spruce chronologies (from >3000 trees) of different ages distributed along elevational transects in the Eastern Carpathians, Romania. We evaluated early warning signals of climate change-induced stress, i.e. (1) growth decline, (2) increased sensitivity of tree growth (assessed over the statistics first-order autocorrelation and standard deviation), and (3) increased growth synchrony. A pronounced growth decline was observed over the last two decades, which was strongest in younger stands and at lower elevations. However, growth sensitivity and synchrony did not show consistent patterns, suggesting that forest decline may not be immediately imminent. Overall, our findings highlight an increased vulnerability of spruce in the Eastern Carpathians. With ongoing climate change, spruce dieback may be expected in this part of Europe as well.

Anticipating regime shifts by mixing early warning signals from different nodes

Real systems showing regime shifts, such as ecosystems, are often composed of many dynamical elements interacting on a network. Various early warning signals have been proposed for anticipating regime shifts from observed data. However, it is unclear how one should combine early warning signals from different nodes for better performance. Based on theory of stochastic differential equations, we propose a method to optimize the node set from which to construct an early warning signal. The proposed method takes into account that uncertainty as well as the magnitude of the signal affects its predictive performance, that a large magnitude or small uncertainty of the signal in one situation does not imply the signal's high performance, and that combining early warning signals from different nodes is often but not always beneficial. The method performs well particularly when different nodes are subjected to different amounts of dynamical noise and stress.

Natural recovery of corals after severe disturbance

Ecosystem recovery from human-induced disturbances, whether through natural processes or restoration, is occurring worldwide. Yet, recovery dynamics, and their implications for broader ecosystem management, remain unclear. We explored recovery dynamics using coral reefs as a case study. We tracked the fate of 809 individual coral recruits that settled after a severe bleaching event at Lizard Island, Great Barrier Reef. Recruited Acropora corals, first detected in 2020, grew to coral cover levels that were equivalent to global average coral cover within just 2 years. Furthermore, we found that just 11.5 Acropora recruits per square meter were sufficient to reach this cover within 2 years. However, wave exposure, growth form and colony density had a marked effect on recovery rates. Our results underscore the importance of considering natural recovery in management and restoration and highlight how lessons learnt from reef recovery can inform our understanding of recovery dynamics in high-diversity climate-disturbed ecosystems.

Early warning signals have limited applicability to empirical lake data

Research aimed at identifying indicators of persistent abrupt shifts in ecological communities, a.k.a regime shifts, has led to the development of a suite of early warning signals (EWSs). As these often perform inaccurately when applied to real-world observational data, it remains unclear whether critical transitions are the dominant mechanism of regime shifts and, if so, which EWS methods can predict them. Here, using multi-trophic planktonic data on multiple lakes from around the world, we classify both lake dynamics and the reliability of classic and second generation EWSs methods to predict whole-ecosystem change. We find few instances of critical transitions, with different trophic levels often expressing different forms of abrupt change. The ability to predict this change is highly processing dependant, with most indicators not performing better than chance, multivariate EWSs being weakly superior to univariate, and a recent machine learning model performing poorly. Our results suggest that predictive ecology should start to move away from the concept of critical transitions, developing methods suitable for predicting resilience loss not limited to the strict bounds of bifurcation theory.

Moving beyond the panarchy heuristic

Panarchy is a heuristic of complex system change rooted in resilience science. The concept has been rapidly assimilated across scientific disciplines due to its potential to envision and address sustainability challenges, such as climate change and regime shifts, that pose significant challenges for humans in the Anthropocene. However, panarchy has been studied almost exclusively via qualitative research. Quantitative approaches are scarce and preliminary but have revealed novel insights that allow for a more nuanced understanding of the heuristic and resilience science more generally. In this roadmap we discuss the potential for future quantitative approaches to panarchy. Transdisciplinary development of quantitative approaches, combined with advances in data accrual, curation and machine learning, may build on current tools. Combined with qualitative research and traditional approaches used in ecology, quantification of panarchy may allow for broad inference of change in complex systems of people and nature and provide critical information for management of social-ecological systems.

The potential of resilience indicators to anticipate infectious disease outbreaks, a systematic review and guide

To reduce the consequences of infectious disease outbreaks, the timely implementation of public health measures is crucial. Currently used early-warning systems are highly context-dependent and require a long phase of model building. A proposed solution to anticipate the onset or termination of an outbreak is the use of so-called resilience indicators. These indicators are based on the generic theory of critical slowing down and require only incidence time series. Here we assess the potential for this approach to contribute to outbreak anticipation. We systematically reviewed studies that used resilience indicators to predict outbreaks or terminations of epidemics. We identified 37 studies meeting the inclusion criteria: 21 using simulated data and 16 real-world data. 36 out of 37 studies detected significant signs of critical slowing down before a critical transition (i.e., the onset or end of an outbreak), with a highly variable sensitivity (i.e., the proportion of true positive outbreak warnings) ranging from 0.03 to 1 and a lead time ranging from 10 days to 68 months. Challenges include low resolution and limited length of time series, a too rapid increase in cases, and strong seasonal patterns which may hamper the sensitivity of resilience indicators. Alternative types of data, such as Google searches or social media data, have the potential to improve predictions in some cases. Resilience indicators may be useful when the risk of disease outbreaks is changing gradually. This may happen, for instance, when pathogens become increasingly adapted to an environment or evolve gradually to escape immunity. High-resolution monitoring is needed to reach sufficient sensitivity. If those conditions are met, resilience indicators could help improve the current practice of prediction, facilitating timely outbreak response. We provide a step-by-step guide on the use of resilience indicators in infectious disease epidemiology, and guidance on the relevant situations to use this approach.

Connecting distinct realms along multiple dimensions: A meta-ecosystem resilience perspective

Resilience research is central to confront the sustainability challenges to ecosystems and human societies in a rapidly changing world. Given that social-ecological problems span the entire Earth system, there is a critical need for resilience models that account for the connectivity across intricately linked ecosystems (i.e., freshwater, marine, terrestrial, atmosphere). We present a resilience perspective of meta-ecosystems that are connected through the flow of biota, matter and energy within and across aquatic and terrestrial realms, and the atmosphere. We demonstrate ecological resilience sensu Holling using aquatic-terrestrial linkages and riparian ecosystems more generally. A discussion of applications in riparian ecology and meta-ecosystem research (e.g., resilience quantification, panarchy, meta-ecosystem boundary delineations, spatial regime migration, including early warning indications) concludes the paper. Understanding meta-ecosystem resilience may have potential to support decision making for natural resource management (scenario planning, risk and vulnerability assessments).

Optimal parameterizing manifolds for anticipating tipping points and higher-order critical transitions

A general, variational approach to derive low-order reduced models from possibly non-autonomous systems is presented. The approach is based on the concept of optimal parameterizing manifold (OPM) that substitutes more classical notions of invariant or slow manifolds when the breakdown of "slaving" occurs, i.e., when the unresolved variables cannot be expressed as an exact functional of the resolved ones anymore. The OPM provides, within a given class of parameterizations of the unresolved variables, the manifold that averages out optimally these variables as conditioned on the resolved ones. The class of parameterizations retained here is that of continuous deformations of parameterizations rigorously valid near the onset of instability. These deformations are produced through the integration of auxiliary backward-forward systems built from the model's equations and lead to analytic formulas for parameterizations. In this modus operandi, the backward integration time is the key parameter to select per scale/variable to parameterize in order to derive the relevant parameterizations which are doomed to be no longer exact away from instability onset due to the breakdown of slaving typically encountered, e.g., for chaotic regimes. The selection criterion is then made through data-informed minimization of a least-square parameterization defect. It is thus shown through optimization of the backward integration time per scale/variable to parameterize, that skilled OPM reduced systems can be derived for predicting with accuracy higher-order critical transitions or catastrophic tipping phenomena, while training our parameterization formulas for regimes prior to these transitions takes place.

Systematic analysis and optimization of early warning signals for critical transitions using distribution data

Abrupt shifts between alternative regimes occur in complex systems, from cell regulation to brain functions to ecosystems. Several model-free early warning signals (EWS) have been proposed to detect impending transitions, but failure or poor performance in some systems have called for better investigation of their generic applicability. Notably, there are still ongoing debates whether such signals can be successfully extracted from data in particular from biological experiments. In this work, we systematically investigate properties and performance of dynamical EWS in different deteriorating conditions, and we propose an optimized combination to trigger warnings as early as possible, eventually verified on experimental data from microbiological populations. Our results explain discrepancies observed in the literature between warning signs extracted from simulated models and from real data, provide guidance for EWS selection based on desired systems and suggest an optimized composite indicator to alert for impending critical transitions using distribution data.

Harnessing Insights from Indicators-Based Resilience Assessment for Enhancing Sustainability in the Gurage Socio-Ecological Production Landscape of Ethiopia

Even though the mosaic of different land-use/land-cover types has long contributed to the resilience of socio-ecological production landscapes and seascapes in Ethiopia, recent data indicate that their sustainability is under threat. This study aims to evaluate landscape resilience by adopting a set of indicators for enhancing sustainability in the Gurage socio-ecological production landscape in Ethiopia. The authors employed a toolkit of indicators in the production landscape through a community-based scoring approach (1-5 Likert scale). The information from household surveys, land-use/land-cover analysis, and satellite-based drought incidents assessment was integrated with the ranking analysis to support the evaluations. The results revealed that landscape diversity, ecosystem protection, local governance, and social equity indicators had the highest landscape resilience ranks. In contrast, lower ranks are associated with knowledge, innovation, livelihoods, and well-being indicators. The overall resilience of the Gurage socio-ecological production landscape was estimated to be below average. Thus, strategies that enhance the resilience and sustainability of this socio-ecological landscape are essential. The findings could help draw the attention of policymakers and natural resource managers to building and strengthening the resilience of the landscape. This study demonstrates that indicators could aid in evaluating landscape resilience status along with other ancillary information, particularly in data-sparse regions. Methods of assessing resilience must be creative in such regions, and this paper may inform such efforts. In addition, the study recommends that landscape resilience indicators be improved by reducing subjective matter and including spatial-explicit dimensions for evaluating resilience.

Characterization of lacustrine harmful algal blooms using multiple biomarkers: Historical processes, driving synergy, and ecological shifts

Harmful algal blooms (HABs) producing toxic metabolites are increasingly threatening environmental and human health worldwide. Unfortunately, long-term process and mechanism triggering HABs remain largely unclear due to the scarcity of temporal monitoring. Retrospective analysis of sedimentary biomarkers using up-to-date chromatography and mass spectrometry techniques provide a potential means to reconstruct the past occurrence of HABs. By combining aliphatic hydrocarbons, photosynthetic pigments, and cyanotoxins, we quantified herein century-long changes in abundance, composition, and variability of phototrophs, particularly toxigenic algal blooms, in China's third largest freshwater Lake Taihu. Our multi-proxy limnological reconstruction revealed an abrupt ecological shift in the 1980s characterized by elevated primary production, Microcystis-dominated cyanobacterial blooms, and exponential microcystin production, in response to nutrient enrichment, climate change, and trophic cascades. The empirical results from ordination analysis and generalized additive models support climate warming and eutrophication synergy through nutrient recycling and their feedback through buoyant cyanobacterial proliferation, which sustain bloom-forming potential and further promote the occurrence of increasingly-toxic cyanotoxins (e.g., microcystin-LR) in Lake Taihu. Moreover, temporal variability of the lake ecosystem quantified using variance and rate of change metrics rose continuously after state change, indicating increased ecological vulnerability and declined resilience following blooms and warming. With the persistent legacy effects of lake eutrophication, nutrient reduction efforts mitigating toxic HABs probably be overwhelmed by climate change effects, emphasizing the need for more aggressive and integrated environmental strategies.

Paleo-diatom records reveal ecological change not detected using traditional measures of lake eutrophication

Lakes provide crucial ecosystem services and harbour unique and rich biodiversity, yet despite decades of research and management focus, cultural eutrophication remains a predominant threat to their health. Our ability to manage lake eutrophication is restricted by the lack of long-term monitoring records. To circumvent this, we developed a bio-indicator approach for inferring trophic level from lake diatom communities and applied this to sediment cores from two lakes experiencing eutrophication stress. Diatom indicators strongly predicted observed trophic levels, and when applied to sediment cores, diatom predicted trophic level reconstructions were consistent with monitoring data and land-use histories. However, there were significant recent shifts in diatom communities not captured by the diatom-based index or monitoring data, suggesting that conventional trophic level indices obscure important ecological change. New approaches, such as the one in this study, are critical to detect early changes in water quality and prevent the decline of lake ecosystems worldwide.

Aquatic quillworts, Isoëtes echinospora and I. lacustris under acidic stress-A review from a temperate refuge

Quillworts (Isoëtes) represent highly specialized flora of softwater lakes, that is, freshwater ecosystems potentially sensitive to acidification. In this paper, we combine a review of previous studies and our new results to address unrecognized reproduction strategies of quillworts to overcome long-term environmental stresses. These strategies play an important role in the plant's ability to overcome atmospheric acidification of freshwaters, protecting the plants until their environment can recover. Environmental drivers of recovery of Isoëtes echinospora and I. lacustris were studied in two acidified lakes in the Bohemian Forest (Central Europe). Both populations survived more than 50 years of severe acidification, although they failed to recruit new sporelings. Their survival depended entirely on the resistance of long-living adult plants because the quillworts do not grow clonally. During the past two decades, a renewal of I. echinospora population inhabiting Plešné Lake has been observed, while no such renewal of I. lacustris, dwelling in Černé Lake, was evident, despite similar changes in water composition occurring in both lakes undergoing advanced recovery from acidification. Our in vitro experiments revealed that the threshold acidity and toxic aluminium concentrations for sporeling survival and recruitment success differed between I. echinospora (pH ≤ 4.0 and ≥300 μg L^-1 Al at pH 5) and I. lacustris (pH ≤ 5.0 and ≥100 μg L^-1Al at pH 5). The higher sensitivity of I. lacustris to both stressors likely stems from its year-long germination period and underlines the risk of exposure to chronic or episodic acidification in recovering lakes. By contrast, the shorter germination period of I. echinospora (2-3 months) enables its faster and deeper rooting, protecting this quillwort from periodic acidification during the next snowmelt. Our study brings novel insights into widely discussed environmental issues related to the long-term degradation of softwater lakes, which represent important hotspots of pan-European biodiversity and conservation efforts.

Effects of interactions between anthropogenic stressors and recurring perturbations on ecosystem resilience and collapse

Insights into declines in ecosystem resilience and their causes and effects can inform preemptive action to avoid ecosystem collapse and loss of biodiversity, ecosystem services, and human well-being. Empirical studies of ecosystem collapse are rare and hampered by ecosystem complexity, nonlinear and lagged responses, and interactions across scales. We investigated how an anthropogenic stressor could diminish ecosystem resilience to a recurring perturbation by altering a critical ecosystem driver. We studied groundwater-dependent, peat-accumulating, fire-prone wetlands known as upland swamps in southeastern Australia. We hypothesized that underground mining (stressor) reduces resilience of these wetlands to landscape fires (perturbation) by diminishing groundwater, a key ecosystem driver. We monitored soil moisture as an indicator of ecosystem resilience during and after underground mining. After landscape fire, we compared responses of multiple state variables representing ecosystem structure, composition, and function in swamps within the mining footprint with unmined reference swamps. Soil moisture declined without recovery in swamps with mine subsidence (i.e., undermined), but was maintained in reference swamps over 8 years (effect size 1.8). Relative to burned reference swamps, burned undermined swamps showed greater loss of peat via substrate combustion; reduced cover, height, and biomass of regenerating vegetation; reduced postfire plant species richness and abundance; altered plant species composition; increased mortality rates of woody plants; reduced postfire seedling recruitment; and extirpation of a hydrophilic animal. Undermined swamps therefore showed strong symptoms of postfire ecosystem collapse, whereas reference swamps regenerated vigorously. We found that an anthropogenic stressor diminished the resilience of an ecosystem to recurring perturbations, predisposing it to collapse. Avoidance of ecosystem collapse hinges on early diagnosis of mechanisms and preventative risk reduction. It may be possible to delay or ameliorate symptoms of collapse or to restore resilience, but the latter appears unlikely in our study system due to fundamental alteration of a critical ecosystem driver. Efectos de las interacciones entre los estresantes antropogénicos y las perturbaciones recurrentes sobre la resiliencia y el colapso de los ecosistemas.

Anticipating the occurrence and type of critical transitions

Critical transition can occur in many real-world systems. The ability to forecast the occurrence of transition is of major interest in a range of contexts. Various early warning signals (EWSs) have been developed to anticipate the coming critical transition or distinguish types of transition. However, no effective method allows to establish practical threshold indicating the condition when the critical transition is most likely to occur. Here, we introduce a powerful EWS, named dynamical eigenvalue (DEV), that is rooted in bifurcation theory of dynamical systems to estimate the dominant eigenvalue of the system. Theoretically, the absolute value of DEV approaches 1 when the system approaches bifurcation, while its position in the complex plane indicates the type of transition. We demonstrate the efficacy of the DEV approach in model systems with known bifurcation types and also test the DEV approach on various critical transitions in real-world systems.

Exploring the role of the potential surface in the behaviour of early warning signals

The theory of critical slowing down states that a system displays increasing relaxation times as it approaches a critical transition. These changes can be seen in statistics generated from timeseries data, which can be used as early warning signals of a transition. Such early warning signals would be of value for emerging infectious diseases or to understand when an endemic disease is close to elimination. However, in applications to a variety of epidemiological models there is frequent disagreement with the general theory of critical slowing down, with some indicators performing well on prevalence data but not when applied to incidence data. Furthermore, the alternative theory of critical speeding up predicts contradictory behaviour of early warning signals prior to some stochastic transitions. To investigate the possibility of observing critical speeding up in epidemiological models we characterise the behaviour of common early warning signals in terms of a system's potential surface and noise around a quasi-steady state. We then describe a method to obtain these key features from timeseries data, taking as a case study a version of the SIS model, adapted to demonstrate either critical slowing down or critical speeding up. We show this method accurately reproduces the analytic potential surface and diffusion function, and that these results can be used to determine the behaviour of early warning signals and correctly identify signs of both critical slowing down and critical speeding up.

Understanding the depth limit of the seagrass Cymodocea nodosa as a critical transition: Field and modeling evidence

Changes in light and sediment conditions can sometimes trigger abrupt regime shifts in seagrass meadows resulting in dramatic and unexpected die-offs of seagrass. Light attenuates rapidly with depth, and in seagrass systems with non-linear behaviours, can serve as a sharp boundary beyond which the meadow transitions to bare sand. Determining system behaviour is therefore essential to ensuring resilience is maintained and to prevent stubborn critical ecosystem transitions caused by declines in water quality. Here we combined field and modelling studies to explore the transition from meadow to bare sand in the seagrass Cymodocea nodosa at the limit of its depth distribution in a shallow, light-limited bay. We first describe the relationship between light availability and seagrass density along a depth gradient in an extensive unfragmented meadow (Alfacs bay, NE Spain). We then develop a simple mechanistic model to characterise system behaviour. In the field, we identified sharp decline in shoot density beyond a threshold of ∼1.9 m depth, shifting from a vegetated state to bare sand. The dynamic population model we developed assumes light-dependent growth and an inverse density-dependent mortality due to facilitation between shoots (mortality rate decreases as shoot density increases). The model closely tracked our empirical observations, and both the model and the field data showed signs of bistability. This strongly suggests that the depth limit of C. nodosa is a critical transition driven by photosynthetic light requirements. While the mechanisms still need to be confirmed with experimental evidence, recognizing the non-linear behaviour of C. nodosa meadows is vital not only in improving our understanding of light effects on seagrass dynamics, but also in managing shallow-water meadows. Given the shallow threshold (<2m), light-limited systems may experience significant and recalcitrant meadow retractions with even small changes in sediment and light conditions. Understanding the processes underlying meadow resilience can inform the maintenance and restoration of meadows worldwide.

Applying early warning indicators to predict critical transitions in a lake undergoing multiple changes

Lakes are dynamic ecosystems that can transition among stable states. Since ecosystem-scale transitions can be detrimental and difficult to reverse, being able to predict impending critical transitions in state variables has become a major area of research. However, not all transitions are detrimental, and there is considerable interest in better evaluating the success of management interventions to support adaptive management strategies. Here, we retrospectively evaluated the agreement between time series statistics (i.e., standard deviation, autocorrelation, skewness, and kurtosis-also known as early warning indicators) and breakpoints in state variables in a lake (Lake Simcoe, Ontario, Canada) that has improved from a state of eutrophication. Long-term (1980 to 2019) monitoring data collected fortnightly throughout the ice-free season were used to evaluate historical changes in 15 state variables (e.g., dissolved organic carbon, phosphorus, chlorophyll a) and multivariate-derived time series at three monitoring stations (shallow, middepth, deep) in Lake Simcoe. Time series results from the two deep-water stations indicate that over this period Lake Simcoe transitioned from an algal-dominated state toward a state with increased water clarity (i.e., Secchi disk depth) and silica and lower nutrient and chlorophyll a concentrations, which coincided with both substantial management intervention and the establishment of invasive species (e.g., Dreissenid mussels). Consistent with improvement, Secchi depth at the deep-water stations demonstrated expected trends in statistical indicators prior to identified breakpoints, whereas total phosphorus and chlorophyll a revealed more nuanced patterns. Overall, state variables were largely found to yield inconsistent trends in statistical indicators, so many breakpoints were likely not reflective of traditional bifurcation critical transitions. Nevertheless, statistical indicators of state variable time series may be a valuable tool for the adaptive management and long-term monitoring of lake ecosystems, but we call for more research within the domain of early warning indicators to establish a better understanding of state variable behavior prior to lake changes.

Early warning signal for a tipping point suggested by a millennial Atlantic Multidecadal Variability reconstruction

Atlantic multidecadal variability is a coherent mode of natural climate variability occurring in the North Atlantic Ocean, with strong impacts on human societies and ecosystems worldwide. However, its periodicity and drivers are widely debated due to the short temporal extent of instrumental observations and competing effects of both internal and external climate factors acting on North Atlantic surface temperature variability. Here, we use a paleoclimate database and an advanced statistical framework to generate, evaluate, and compare 312 reconstructions of the Atlantic multidecadal variability over the past millennium, based on different indices and regression methods. From this process, the best reconstruction is obtained with the random forest method, and its robustness is checked using climate model outputs and independent oceanic paleoclimate data. This reconstruction shows that memory in variations of Atlantic multidecadal variability have strongly increased recently—a potential early warning signal for the approach of a North Atlantic tipping point.

This study presents a last millennium reconstruction of Atlantic Multidecadal Variability fluctuations. This sufficiently long and validated reconstruction suggests the potential approach of a tipping point in the North Atlantic current system.

Destabilisation of the Subpolar North Atlantic prior to the Little Ice Age

The cooling transition into the Little Ice Age was the last notable shift in the climate system prior to anthropogenic global warming. It is hypothesised that sea-ice to ocean feedbacks sustained an initial cooling into the Little Ice Age by weakening the subpolar gyre circulation; a system that has been proposed to exhibit bistability. Empirical evidence for bistability within this transition has however been lacking. Using statistical indicators of resilience in three annually-resolved bivalve proxy records from the North Icelandic shelf, we show that the subpolar North Atlantic climate system destabilised during two episodes prior to the Little Ice Age. This loss of resilience indicates reduced attraction to one stable state, and a system vulnerable to an abrupt transition. The two episodes preceded wider subpolar North Atlantic change, consistent with subpolar gyre destabilisation and the approach of a tipping point, potentially heralding the transition to Little Ice Age conditions.

Bivalves reveal that the subpolar North Atlantic destabilised and shows signs of having crossed a tipping point during the transition into the Little Ice Age.

Ecological complexity and the biosphere: the next 30 years

Global warming, habitat loss and overexploitation of limited resources are leading to alarming biodiversity declines. Ecosystems are complex adaptive systems that display multiple alternative states and can shift from one to another in abrupt ways. Some of these tipping points have been identified and predicted by mathematical and computational models. Moreover, multiple scales are involved and potential mitigation or intervention scenarios are tied to particular levels of complexity, from cells to human–environment coupled systems. In dealing with a biosphere where humans are part of a complex, endangered ecological network, novel theoretical and engineering approaches need to be considered. At the centre of most research efforts is biodiversity, which is essential to maintain community resilience and ecosystem services. What can be done to mitigate, counterbalance or prevent tipping points? Using a 30-year window, we explore recent approaches to sense, preserve and restore ecosystem resilience as well as a number of proposed interventions (from afforestation to bioengineering) directed to mitigate or reverse ecosystem collapse. The year 2050 is taken as a representative future horizon that combines a time scale where deep ecological changes will occur and proposed solutions might be effective.

This article is part of the theme issue ‘Ecological complexity and the biosphere: the next 30 years’.

Anticipating infectious disease re-emergence and elimination: a test of early warning signals using empirically based models

Timely forecasts of the emergence, re-emergence and elimination of human infectious diseases allow for proactive, rather than reactive, decisions that save lives. Recent theory suggests that a generic feature of dynamical systems approaching a tipping point-early warning signals (EWS) due to critical slowing down (CSD)-can anticipate disease emergence and elimination. Empirical studies documenting CSD in observed disease dynamics are scarce, but such demonstration of concept is essential to the further development of model-independent outbreak detection systems. Here, we use fitted, mechanistic models of measles transmission in four cities in Niger to detect CSD through statistical EWS. We find that several EWS accurately anticipate measles re-emergence and elimination, suggesting that CSD should be detectable before disease transmission systems cross key tipping points. These findings support the idea that statistical signals based on CSD, coupled with decision-support algorithms and expert judgement, could provide the basis for early warning systems of disease outbreaks.

Emerging signals of declining forest resilience under climate change

Forest ecosystems depend on their capacity to withstand and recover from natural and anthropogenic perturbations (that is, their resilience)¹. Experimental evidence of sudden increases in tree mortality is raising concerns about variation in forest resilience², yet little is known about how it is evolving in response to climate change. Here we integrate satellite-based vegetation indices with machine learning to show how forest resilience, quantified in terms of critical slowing down indicators^3–5, has changed during the period 2000–2020. We show that tropical, arid and temperate forests are experiencing a significant decline in resilience, probably related to increased water limitations and climate variability. By contrast, boreal forests show divergent local patterns with an average increasing trend in resilience, probably benefiting from warming and CO₂ fertilization, which may outweigh the adverse effects of climate change. These patterns emerge consistently in both managed and intact forests, corroborating the existence of common large-scale climate drivers. Reductions in resilience are statistically linked to abrupt declines in forest primary productivity, occurring in response to slow drifting towards a critical resilience threshold. Approximately 23% of intact undisturbed forests, corresponding to 3.32 Pg C of gross primary productivity, have already reached a critical threshold and are experiencing a further degradation in resilience. Together, these signals reveal a widespread decline in the capacity of forests to withstand perturbation that should be accounted for in the design of land-based mitigation and adaptation plans.

Post-disturbance reorganization of forest ecosystems in a changing world

Forest ecosystems are strongly impacted by continuing climate change and increasing disturbance activity, but how forest dynamics will respond remains highly uncertain. Here, we argue that a short time window after disturbance (i.e., a discrete event that disrupts prevailing ecosystem structure and composition and releases resources) is pivotal for future forest development. Trees that establish during this reorganization phase can shape forest structure and composition for centuries, providing operational early indications of forest change. While forest change has been fruitfully studied through a lens of resilience, profound ecological changes can be masked by a resilience versus regime shift dichotomy. We present a framework for characterizing the full spectrum of change after disturbance, analyzing forest reorganization along dimensions of forest structure (number, size, and spatial arrangement of trees) and composition (identity and diversity of tree species). We propose four major pathways through which forest cover can persist but reorganize following disturbance: resilience (no change in structure and composition), restructuring (structure changes but composition does not), reassembly (composition changes but structure does not), and replacement (structure and composition both change). Regime shifts occur when vegetation structure and composition are altered so profoundly that the emerging trajectory leads to nonforest. We identify fundamental processes underpinning forest reorganization which, if disrupted, deflect ecosystems away from resilience. To understand and predict forest reorganization, assessing these processes and the traits modulating them is crucial. A new wave of experiments, measurements, and models emphasizing the reorganization phase will further the capacity to anticipate future forest dynamics.

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.

Community structure determines the predictability of population collapse

Early warning signals (EWS) are phenomenological tools that have been proposed as predictors of the collapse of biological systems. Although a growing body of work has shown the utility of EWS based on either statistics derived from abundance data or shifts in phenotypic traits such as body size, so far this work has largely focused on single species populations.

However, to predict reliably the future state of ecological systems, which inherently could consist of multiple species, understanding how reliable such signals are in a community context is critical.

Here, reconciling quantitative trait evolution and Lotka–Volterra equations, which allow us to track both abundance and mean traits, we simulate the collapse of populations embedded in mutualistic and multi‐trophic predator–prey communities. Using these simulations and warning signals derived from both population‐ and community‐level data, we showed the utility of abundance‐based EWS, as well as metrics derived from stability‐landscape theory (e.g. width and depth of the basin of attraction), were fundamentally linked. Thus, the depth and width of such stability‐landscape curves could be used to identify which species should exhibit the strongest EWS of collapse.

The probability a species displays both trait and abundance‐based EWS was dependent on its position in a community, with some species able to act as indicator species. In addition, our results also demonstrated that in general trait‐based EWS were less reliable in comparison with abundance‐based EWS in forecasting species collapses in our simulated communities. Furthermore, community‐level abundance‐based EWS were fairly reliable in comparison with their species‐level counterparts in forecasting species‐level collapses.

Our study suggests a holistic framework that combines abundance‐based EWS and metrics derived from stability‐landscape theory that may help in forecasting species loss in a community context.

Bridging Theories for Ecosystem Stability Through Structural Sensitivity Analysis of Ecological Models in Equilibrium

Ecologists are challenged by the need to bridge and synthesize different approaches and theories to obtain a coherent understanding of ecosystems in a changing world. Both food web theory and regime shift theory shine light on mechanisms that confer stability to ecosystems, but from different angles. Empirical food web models are developed to analyze how equilibria in real multi-trophic ecosystems are shaped by species interactions, and often include linear functional response terms for simple estimation of interaction strengths from observations. Models of regime shifts focus on qualitative changes of equilibrium points in a slowly changing environment, and typically include non-linear functional response terms. Currently, it is unclear how the stability of an empirical food web model, expressed as the rate of system recovery after a small perturbation, relates to the vulnerability of the ecosystem to collapse. Here, we conduct structural sensitivity analyses of classical consumer-resource models in equilibrium along an environmental gradient. Specifically, we change non-proportional interaction terms into proportional ones, while maintaining the equilibrium biomass densities and material flux rates, to analyze how alternative model formulations shape the stability properties of the equilibria. The results reveal no consistent relationship between the stability of the original models and the proportionalized versions, even though they describe the same biomass values and material flows. We use these findings to critically discuss whether stability analysis of observed equilibria by empirical food web models can provide insight into regime shift dynamics, and highlight the challenge of bridging alternative modelling approaches in ecology and beyond.

Visualizing Invisible Phase Transitions in Blue Phase Liquid Crystals Using Early Warning Indicators

Changes in the statistical properties of data as a system approaches a critical transition is studied intensively as early warning signals, but their application to materials science, where phase transitions-a type of critical transition-are of fundamental importance, are limited. Here, a critical transition analysis is applied to time-series data from a microscopic 3D ordered soft material-blue phase liquid crystals (BPLC)-and demonstrates that phase transitions that are invisible under ambient conditions can be visualized through the choice of appropriate early warning indicators. After discussing how a phase transition affects the statistical properties in a system with a Landau-de Gennes type free energy potential, the predicted changes are experimentally observed at the two types of phase transitions that occur in a BPLC: the isotropic to simple cubic, and simple cubic to body-centered cubic transitions. In particular, it is shown that the skewness of the intensity distribution inverts its sign at the phase transition, enabling temporally and spatially resolved mapping of phase transitions. This approach can be easily adapted to a wide variety of material systems and microscopy techniques, providing a powerful tool for studying complex critical transition phenomena.

Conceptualising and assessing health system resilience to shocks: a cross-disciplinary view

Health systems worldwide face major challenges in anticipating, planning for and responding to shocks from infectious disease epidemics, armed conflict, climatic and other crises. Although the literature on health system resilience has grown substantially in recent years, major uncertainties remain concerning approaches to resilience conceptualisation and measurement. This narrative review revisits literatures from a range of fields outside health to identify lessons relevant to health systems. Four key insights emerge. Firstly, shocks can only be understood by clarifying how, where and over what timescale they interact with a system of interest, and the dynamic effects they produce within it. Shock effects are contingent on historical path-dependencies, and on the presence of factors or system pathways (e.g. financing models, health workforce capabilities or supply chain designs) that may amplify or dampen impact in unexpected ways. Secondly, shocks often produce cascading effects across multiple scales, whereas the focus of much of the health resilience literature has been on macro-level, national systems. In reality, health systems bring together interconnected sub-systems across sectors and geographies, with different components, behaviours and sometimes even objectives - all influencing how a system responds to a shock. Thirdly, transformability is an integral feature of resilient social systems: cross-scale interactions help explain how systems can show both resilience and transformational capability at the same time. We illustrate these first three findings by extending the socioecological concept of adaptive cycles in social systems to health, using the example of maternal and child health service delivery. Finally, we argue that dynamic modelling approaches, under-utilised in research on health system resilience to date, have significant promise for identification of shock-moderating or shock-amplifying pathways, for understanding effects at multiple levels and ultimately for building resilience.

Resilience integrates concepts in aging research

Aging research is unparalleled in the breadth of disciplines it encompasses, from evolutionary studies examining the forces that shape aging to molecular studies uncovering the underlying mechanisms of age-related functional decline. Despite a common focus to advance our understanding of aging, these disciplines have proceeded along distinct paths with little cross-talk. We propose that the concept of resilience can bridge this gap. Resilience describes the ability of a system to respond to perturbations by returning to its original state. Although resilience has been applied in a few individual disciplines in aging research such as frailty and cognitive decline, it has not been explored as a unifying conceptual framework that is able to connect distinct research fields. We argue that because a resilience-based framework can cross broad physiological levels and time scales it can provide the missing links that connect these diverse disciplines. The resulting framework will facilitate predictive modeling and validation and influence targets and directions in research on the biology of aging.

Pattern formation in marsh ecosystems modeled through the interaction of marsh vegetation, mussels and sediment

Spatial self-organization, a common feature of multi-species communities, can provide important insights into ecosystem structure and resilience. As environmental conditions gradually worsen (e.g., resource depletion, erosion intensified by storms, drought), some ecological systems collapse to an irreversible state once a tipping point is reached. Spatial patterning may be one way for them to cope with such changes. We use a mathematical model to describe self-organization of an eroding marsh shoreline based on three-way interactions between sediment volume and two ecosystem engineers - smooth cordgrass Spartina alterniflora and ribbed mussels Geukensia demissa. Our model indicates that scale-dependent interactions between multiple ecosystem engineers drive the self-organization of eroding marsh edges and regulate the spatial scale of shoreline morphology. Spatial self-organization of the marsh edge increases the system's productivity, allows it to withstand erosion, and delays degradation that otherwise would occur in the absence of strong species interactions. Further, changes in wavelength and variance of the spatial patterns give insight into marsh recession. Finally, we find that the presence of mussels in the system modulates the spatial scale of the patterns, generates patterns with shorter wavelengths, and allows the system to tolerate a greater level of erosion. Although previous studies suggest that self-organization can emerge from local interactions and can result in increased ecosystem persistence and stability in various ecosystems, our findings extend these concepts to coastal salt marshes, emphasizing the importance of the ecosystem engineers, smooth cordgrass and ribbed mussels, and demonstrating the potential value of self-organization for ecosystem management and restoration.

Visualizing the features of inflection point shown on a temporal bar graph using the data of COVID-19 pandemic

BACKGROUND

Exponential-like infection growth leading to peaks (denoted by inflection points [IP] or turning points) is usually the hallmark of infectious disease outbreaks, including coronaviruses. To determine the IPs of the novel coronavirus (COVID-19), we applied the item response theory model to detect phase transitions for each country/region and characterize the IP feature on the temporal bar graph (TBG).

METHODS

The IP (using the item difficulty parameter to locate) was verified by the differential equation in calculus and interpreted by the TBG with 2 virtual and real empirical data (i.e., from Collatz conjecture and COVID-19 pandemic in 2020). Comparisons of IPs, R2, and burst strength [BS = ln() denoted by the infection number at IP(Nip) and the item slope parameter(a) in item response theory were made for countries/regions and continents on the choropleth map and the forest plot.

RESULTS

We found that the evolution of COVID-19 on the TBG makes the data clear and easy to understand, the shorter IP (=53.9) was in China and the longest (=247.3) was in Europe, and the highest R2 (as the variance explained by the model) was in the US, with a mean R2 of 0.98. We successfully estimated the IPs for countries/regions on COVID-19 in 2020 and presented them on the TBG.

CONCLUSION

Temporal visualization is recommended for researchers in future relevant studies (e.g., the evolution of keywords in a specific discipline) and is not merely limited to the IP search in COVID-19 pandemics as we did in this study.

Paleoecological Investigation of Vegetation, Climate and Fire History in, and Adjacent to, Kootenay National Park, Southeastern British Columbia, Canada

Paleoecological investigation of two montane lakes in the Kootenay region of southeast British Columbia, Canada, reveal changes in vegetation in response to climate and fire throughout the Holocene. Pollen, charcoal, and lake sediment carbon accumulation rate analyses show seven distinct zones at Marion Lake, presently in the subalpine Engelmann Spruce-Subalpine Fir (ESSF) biogeoclimatic (BEC) zone of Kootenay Valley, British Columbia. Comparison of these records to nearby Dog Lake of Kootenay National Park of Canada in the Montane Spruce (MS) BEC zone of Kootenay Valley, British Columbia reveals unique responses of ecosystems in topographically complex regions. The two most dramatic shifts in vegetation at Marion Lake occur firstly in the early Holocene/late Pleistocene in ML Zone 3 (11,010–10,180 cal. yr. B.P.) possibly reflecting Younger Dryas Chronozone cooling followed by early Holocene xerothermic warming noted by the increased presence of the dry adapted conifer, Douglas-fir (Pseudotsuga menziesii) and increasing fire frequency. The second most prominent change occurred at the transition from ML Zone 5 through 6a (∼2,500 cal. yr. B.P.). This zone transitions from a warmer to a cooler/wetter climate as indicated by the increase in western hemlock (Tsuga heterophylla) and subsequent drop in fire frequency. The overall cooling trend and reduction in fire frequency appears to have occurred ∼700 years later than at Dog Lake (∼43 km to the south and 80 m lower in elevation), resulting in a closed montane spruce forest, whereas Marion Lake developed into a subalpine ecosystem. The temporal and ecological differences between the two study sites likely reflects the particular climate threshold needed to move these ecosystems from developed forests to subalpine conditions, as well as local site climate and fire conditions. These paleoecological records indicate future warming may result in the MS transitioning into an Interior Douglas Fir (IDF) dominated landscape, while the ESSF may become more forested, similar to the modern MS, or develop into a grassland-like landscape dependent on fire frequency. These results indicate that climate and disturbance over a regional area can dictate very different localized vegetative states. Local management implications of these dynamic landscapes will need to understand how ecosystems respond to climate and disturbance at the local or ecosystem/habitat scale.

Towards a Data-Driven Estimation of Resilience in Networked Dynamical Systems: Designing a Versatile Testbed

Estimating resilience of adaptive, networked dynamical systems remains a challenge. Resilience refers to a system's capacity "to absorb exogenous and/or endogenous disturbances and to reorganize while undergoing change so as to still retain essentially the same functioning, structure, and feedbacks." The majority of approaches to estimate resilience requires exact knowledge of the underlying equations of motion; the few data-driven approaches so far either lack appropriate strategies to verify their suitability or remain subject of considerable debate. We develop a testbed that allows one to modify resilience of a multistable networked dynamical system in a controlled manner. The testbed also enables generation of multivariate time series of system observables to evaluate the suitability of data-driven estimators of resilience. We report first findings for such an estimator.

Permutation Entropy as a Universal Disorder Criterion: How Disorders at Different Scale Levels Are Manifestations of the Same Underlying Principle

What do bacteria, cells, organs, people, and social communities have in common? At first sight, perhaps not much. They involve totally different agents and scale levels of observation. On second thought, however, perhaps they share everything. A growing body of literature suggests that living systems at different scale levels of observation follow the same architectural principles and process information in similar ways. Moreover, such systems appear to respond in similar ways to rising levels of stress, especially when stress levels approach near-lethal levels. To explain such communalities, we argue that all organisms (including humans) can be modeled as hierarchical Bayesian controls systems that are governed by the same biophysical principles. Such systems show generic changes when taxed beyond their ability to correct for environmental disturbances. Without exception, stressed organisms show rising levels of 'disorder' (randomness, unpredictability) in internal message passing and overt behavior. We argue that such changes can be explained by a collapse of allostatic (high-level integrative) control, which normally synchronizes activity of the various components of a living system to produce order. The selective overload and cascading failure of highly connected (hub) nodes flattens hierarchical control, producing maladaptive behavior. Thus, we present a theory according to which organic concepts such as stress, a loss of control, disorder, disease, and death can be operationalized in biophysical terms that apply to all scale levels of organization. Given the presumed universality of this mechanism, 'losing control' appears to involve the same process anywhere, whether involving bacteria succumbing to an antibiotic agent, people suffering from physical or mental disorders, or social systems slipping into warfare. On a practical note, measures of disorder may serve as early warning signs of system failure even when catastrophic failure is still some distance away.

Early warning signal reliability varies with COVID-19 waves

Early warning signals (EWSs) aim to predict changes in complex systems from phenomenological signals in time series data. These signals have recently been shown to precede the emergence of disease outbreaks, offering hope that policymakers can make predictive rather than reactive management decisions. Here, using a novel, sequential analysis in combination with daily COVID-19 case data across 24 countries, we suggest that composite EWSs consisting of variance, autocorrelation and skewness can predict nonlinear case increases, but that the predictive ability of these tools varies between waves based upon the degree of critical slowing down present. Our work suggests that in highly monitored disease time series such as COVID-19, EWSs offer the opportunity for policymakers to improve the accuracy of urgent intervention decisions but best characterize hypothesized critical transitions.

Abrupt shifts in 21st-century plankton communities

Marine microbial communities sustain ocean food webs and mediate global elemental cycles. These communities will change with climate; these changes can be gradual or foreseeable but likely have much more substantial consequences when sudden and unpredictable. In a complex virtual marine microbial ecosystem, we find that climate change–driven shifts over the 21st century are often abrupt, large in amplitude and extent, and unpredictable using standard early warning signals. Phytoplankton with unique resource needs, especially fast-growing species such as diatoms, are more prone to abrupt shifts. Abrupt shifts in biomass, productivity, and community structure are concentrated in Atlantic and Pacific subtropics. Abrupt changes in environmental variables such as temperature and nutrients rarely precede these ecosystem shifts, indicating that rapid community restructuring can occur in response to gradual environmental changes, particularly in nutrient supply rate ratios.

Critical transitions and ecological resilience of large marine ecosystems in the Northwestern Pacific in response to global warming

Natural systems can undergo critical transitions, leading to substantial socioeconomic and ecological outcomes. "Ecological resilience" has been proposed to describe the capacity of natural systems to absorb external perturbation and reorganize while undergoing change so as to still retain essentially the same function, structure, identity, and feedbacks. However, the mere application of ecological resilience in theoretical research and the lack of quantitative approaches present considerable obstacles for predicting critical transitions and understanding their mechanisms. Large marine ecosystems (LMEs) in the Northwestern Pacific are characterized by great biodiversity and productivity, as well as remarkable warming in recent decades. However, no information is available on the critical transitions and ecological resilience of LMEs in response to warming. Therefore, we applied an integrated resilience assessment framework to fisheries catch data from seven LMEs covering a wide range of regions, from tropical to subarctic, in the Northwestern Pacific to identify critical transitions, assess ecological resilience, and reconstruct folded stability landscapes, with a specific focus on the effects of warming. The results provide evidence of the occurrence of critical transitions, with fold bifurcation and hysteresis in response to increasing sea surface temperatures (SSTs) in the seven LMEs. In addition, these LMEs show similarities and synchronies in structure variations and critical transitions forced by warming. Both dramatic increases in SST and small fluctuations at the corresponding thresholds may trigger critical transitions. Ecological resilience decreases when approaching the tipping points and is repainted as the LMEs shift to alternative stable states with different resilient dynamics. Folded stability landscapes indicate that the responses of LMEs to warming are discontinuous, which may be caused by the reorganization of LMEs as their sensitivity to warming changes. Our study clarifies the nonlinear responses of LMEs to anthropogenic warming and provides examples of quantifying ecological resilience in empirical systems at unprecedented spatial and temporal scales.

River connectivity and climate behind the long-term evolution of tropical American floodplain lakes

This study presents the long-term evolution of two floodplains lakes (San Juana and Barbacoas) of the Magdalena River in Colombia with varying degree of connectivity to the River and with different responses to climate events (i.e., extreme floods and droughts). Historical limnological changes were identified through a multiproxy-based reconstruction including diatoms, sedimentation, and sediment geochemistry, while historical climatic changes were derived from the application of the Standardised Precipitation-Evapotranspiration Index. The main gradients in climatic and limnological change were assessed via multivariate analysis and generalized additive models. The reconstruction of the more isolated San Juana Lake spanned the last c. 500 years. Between c. 1,620 and 1,750 CE, riverine-flooded conditions prevailed as indicated by high detrital input, reductive conditions, and dominance of planktonic diatoms. Since the early 1800s, the riverine meander became disconnected, conveying into a marsh-like environment rich in aerophil diatoms and organic matter. The current lake was then formed around the mid-1960s with a diverse lake diatom flora including benthic and planktonic diatoms, and more oxygenated waters under a gradual increase in sedimentation and nutrients. The reconstruction for Barbacoas Lake, a waterbody directly connected to the Magdalena River, spanned the last 60 years and showed alternating riverine-wetland-lake conditions in response to varying ENSO conditions. Wet periods were dominated by planktonic and benthic diatoms, while aerophil diatom species prevailed during dry periods; during the two intense ENSO periods of 1987 and 1992, the lake almost desiccated and sedimentation rates spiked. A gradual increase in sedimentation rates post-2000 suggests that other factors rather than climate are also influencing sediment deposition in the lake. We propose that hydrological connectivity to the Magdalena River is a main factor controlling lake long-term responses to human pressures, where highly connected lakes respond more acutely to ENSO events while isolated lakes are more sensitive to local land-use changes.

Distinctive patterns and signals at major environmental events and collapse zone boundaries

We studied the patterns of pre-collapse communities, the small-scale and the large-scale signals of collapses, and the environmental events before the collapses using four paleoecological and one modern data series. We applied and evaluated eight indicators in our analysis: the relative abundance of species, hierarchical cluster analysis, principal component analysis, total abundance, species richness, standard deviation (without a rolling window), first-order autoregression, and the relative abundance of the dominant species. We investigated the signals at the probable collapse triggering unusual environmental events and at the collapse zone boundaries, respectively. We also distinguished between pulse and step environmental events to see what signals the indicators give at these two different types of events. Our results show that first-order autoregression is not a good environmental event indicator, but it can forecast or indicate the collapse zones in climate change. The rest of the indicators are more sensitive to the pulse events than to the step events. Step events during climate change might have an essential role in initiating collapses. These events probably push the communities with low resilience beyond a critical threshold, so it is crucial to detect them. Before collapses, the total abundance and the species richness increase, the relative abundance of the species decreases. The hierarchical cluster analysis and the relative abundance of species together designate the collapse zone boundaries. We suggest that small-scale signals should be involved in analyses because they are often earlier than large-scale signals.

Deep learning for early warning signals of tipping points

Early warning signals (EWS) of tipping points are vital to anticipate system collapse or other sudden shifts. However, existing generic early warning indicators designed to work across all systems do not provide information on the state that lies beyond the tipping point. Our results show how deep learning algorithms (artificial intelligence) can provide EWS of tipping points in real-world systems. The algorithm predicts certain qualitative aspects of the new state, and is also more sensitive and generates fewer false positives than generic indicators. We use theory about system behavior near tipping points so that the algorithm does not require data from the study system but instead learns from a universe of possible models.

Many natural systems exhibit tipping points where slowly changing environmental conditions spark a sudden shift to a new and sometimes very different state. As the tipping point is approached, the dynamics of complex and varied systems simplify down to a limited number of possible “normal forms” that determine qualitative aspects of the new state that lies beyond the tipping point, such as whether it will oscillate or be stable. In several of those forms, indicators like increasing lag-1 autocorrelation and variance provide generic early warning signals (EWS) of the tipping point by detecting how dynamics slow down near the transition. But they do not predict the nature of the new state. Here we develop a deep learning algorithm that provides EWS in systems it was not explicitly trained on, by exploiting information about normal forms and scaling behavior of dynamics near tipping points that are common to many dynamical systems. The algorithm provides EWS in 268 empirical and model time series from ecology, thermoacoustics, climatology, and epidemiology with much greater sensitivity and specificity than generic EWS. It can also predict the normal form that characterizes the oncoming tipping point, thus providing qualitative information on certain aspects of the new state. Such approaches can help humans better prepare for, or avoid, undesirable state transitions. The algorithm also illustrates how a universe of possible models can be mined to recognize naturally occurring tipping points.