Transient social-ecological dynamics reveal signals of decoupling in a highly disturbed Anthropocene landscape

Understanding the transient dynamics of interlinked social-ecological systems (SES) is imperative for assessing sustainability in the Anthropocene. However, how to identify critical transitions in real-world SES remains a formidable challenge. In this study, we present an evolutionary framework to characterize these dynamics over an extended historical timeline. Our approach leverages multidecadal rates of change in socioeconomic data, paleoenvironmental, and cutting-edge sedimentary ancient DNA records from China's Yangtze River Delta, one of the most densely populated and intensively modified landscapes on Earth. Our analysis reveals two significant social-ecological transitions characterized by contrasting interactions and feedback spanning several centuries. Initially, the regional SES exhibited a loosely connected and ecologically sustainable regime. Nevertheless, starting in the 1950s, an increasingly interconnected regime emerged, ultimately resulting in the crossing of tipping points and an unprecedented acceleration in soil erosion, water eutrophication, and ecosystem degradation. Remarkably, the second transition occurring around the 2000s, featured a notable decoupling of socioeconomic development from ecoenvironmental degradation. This decoupling phenomenon signifies a more desirable reconfiguration of the regional SES, furnishing essential insights not only for the Yangtze River Basin but also for regions worldwide grappling with similar sustainability challenges. Our extensive multidecadal empirical investigation underscores the value of coevolutionary approaches in understanding and addressing social-ecological system dynamics.

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.

SGAE: single-cell gene association entropy for revealing critical states of cell transitions during embryonic development

The critical point or pivotal threshold of cell transition occurs in early embryonic development when cell differentiation culminates in its transition to specific cell fates, at which the cell population undergoes an abrupt and qualitative shift. Revealing such critical points of cell transitions can track cellular heterogeneity and shed light on the molecular mechanisms of cell differentiation. However, precise detection of critical state transitions proves challenging when relying on single-cell RNA sequencing data due to their inherent sparsity, noise, and heterogeneity. In this study, diverging from conventional methods like differential gene analysis or static techniques that emphasize classification of cell types, an innovative computational approach, single-cell gene association entropy (SGAE), is designed for the analysis of single-cell RNA-seq data and utilizes gene association information to reveal critical states of cell transitions. More specifically, through the translation of gene expression data into local SGAE scores, the proposed SGAE can serve as an index to quantitatively assess the resilience and critical properties of genetic regulatory networks, consequently detecting the signal of cell transitions. Analyses of five single-cell datasets for embryonic development demonstrate that the SGAE method achieves better performance in facilitating the characterization of a critical phase transition compared with other existing methods. Moreover, the SGAE value can effectively discriminate cellular heterogeneity over time and performs well in the temporal clustering of cells. Besides, biological functional analysis also indicates the effectiveness of the proposed approach.

Quantifying resilience and the risk of regime shifts under strong correlated noise

Early warning indicators often suffer from the shortness and coarse-graining of real-world time series. Furthermore, the typically strong and correlated noise contributions in real applications are severe drawbacks for statistical measures. Even under favourable simulation conditions the measures are of limited capacity due to their qualitative nature and sometimes ambiguous trend-to-noise ratio. In order to solve these shortcomings, we analyze the stability of the system via the slope of the deterministic term of a Langevin equation, which is hypothesized to underlie the system dynamics close to the fixed point. The open-source available method is applied to a previously studied seasonal ecological model under noise levels and correlation scenarios commonly observed in real world data. We compare the results to autocorrelation, standard deviation, skewness, and kurtosis as leading indicator candidates by a Bayesian model comparison with a linear and a constant model. We show that the slope of the deterministic term is a promising alternative due to its quantitative nature and high robustness against noise levels and types. The commonly computed indicators apart from the autocorrelation with deseasonalization fail to provide reliable insights into the stability of the system in contrast to a previously performed study in which the standard deviation was found to perform best. In addition, we discuss the significant influence of the seasonal nature of the data to the robust computation of the various indicators, before we determine approximately the minimal amount of data per time window that leads to significant trends for the drift slope estimations.

The single-sample network module biomarkers (sNMB) method reveals the pre-deterioration stage of disease progression

The progression of complex diseases generally involves a pre-deterioration stage that occurs during the transition from a healthy state to disease deterioration, at which a drastic and qualitative shift occurs. The development of an effective approach is urgently needed to identify such a pre-deterioration stage or critical state just before disease deterioration, which allows the timely implementation of appropriate measures to prevent a catastrophic transition. However, identifying the pre-deterioration stage is a challenging task in clinical medicine, especially when only a single sample is available for most patients, which is responsible for the failure of most statistical methods. In this study, a novel computational method, called single-sample network module biomarkers (sNMB), is presented to predict the pre-deterioration stage or critical point using only a single sample. Specifically, the proposed single-sample index effectively quantifies the disturbance caused by a single sample against a group of given reference samples. Our method successfully detected the early warning signal of the critical transitions when applied to both a numerical simulation and four real datasets, including acute lung injury, stomach adenocarcinoma, esophageal carcinoma, and rectum adenocarcinoma. In addition, it provides signaling biomarkers for further practical application, which helps to discover prognostic indicators and reveal the underlying molecular mechanisms of disease progression.

[Research advances in critical transition and its ecological mechanisms of terrestrial ecosystems.]

With the exacerbating disturbances of climate changes and human activities to terrestrial ecosystems, more and more studies realize that ecosystems are at the risk of shifts without warning in structural and functional states and recovery from perturbations require more time. Developing an early warning model to identify critical transition and understanding its ecological mechanism of typical ecosystems have become hotspot in ecological researches. At present, based on theoretical and experimental researches across multiple spatiotemporal scales, a variety of theoretical frameworks and indicators of early warning signals (EWSs) were proposed to signal terrestrial ecosystem critical transition. Here, in order to more thoroughly understand and construct theoretical frameworks and indicators of early warning signals, we reviewed advances in critical transitions from aspects of theoretical methods and processing mechanisms. Catastrophe theory and critical slowing down (CSD) are the two basic theories for early-warning ecosystem state transitions. Self-organization and feedback mechanisms are the primary ecological mechanisms to shape alternative stable state. Understanding cascade effects networks (CENet) among biological and environmental elements, and clarifying the equilibrium relationships between input and output of key ecosystem parameters are theoretical foundation of critical transition model. These theoretical cognitions could provide useful references to early warning of ecosystem disasters, ecological environment management and restoration.

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.

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.

Progression of Physical Frailty and the Risk of All-Cause Mortality: Is There a Point of No Return?

OBJECTIVES

To investigate the rate and patterns of accumulation of frailty manifestations in relationship to all-cause mortality and whether there is a point in the progression of frailty beyond which the process becomes irreversible and death becomes imminent (a.k.a. point of no return).

DESIGN

Longitudinal observational study.

SETTING

Community or a non-nursing home residential care setting.

PARTICIPANTS

Two thousand five hundred and fifty seven robust older adults identified at baseline in 2011 with follow-up for all-cause mortality between 2011 and 2018.

MEASUREMENTS

Frailty was measured by the physical frailty phenotype. Cox models were used to study the relationships of the number of frailty criteria (0-5) at each point in time and its accumulation patterns with all-cause mortality. Markov state-transition models were used to study annual transitions between health states (i.e., frailty, recovery, and death) after becoming frail among those with frailty onset (n = 373).

RESULTS

There was a nonlinear association between greater number of frailty criteria and increasing risk of mortality, with a notable risk acceleration after having accumulated all five criteria (hazard ratio (HR) = 32.6 vs none, 95% confidence interval (CI) = 15.7-67.5). In addition, the risk of one-year mortality tripled, and the likelihood of recovery (i.e., reverting to be robust or pre-frail) halved among those with five frailty criteria compared to those with three or four criteria. A 50% increase in mortality risk was also associated with frailty onset without (vs with) a prior history of pre-frailty (HR = 1.51, 95% CI = 1.20-1.90).

CONCLUSION

Both the number and rate of accumulation of frailty criteria were associated with mortality risk. Although there was insufficient evidence to declare a point of no return, having all five-frailty criteria signals the beginning of a transition toward a point of no return. Ongoing monitoring of frailty progression could aid clinical and personal decision-making regarding timing of intervention and eventual transition from curative to palliative care.

Prediction of Mortality in Hemodialysis Patients Using Moving Multivariate Distance

There is an increasingly widespread use of biomarkers in network physiology to evaluate an organism’s physiological state. A recent study showed that albumin variability increases before death in chronic hemodialysis patients. We hypothesized that a multivariate statistical approach would better allow us to capture signals of impending physiological collapse/death. We proposed a Moving Multivariate Distance (MMD), based on the Mahalanobis distance, to quantify the variability of the multivariate biomarker profile as a whole from one visit to the next. Biomarker profiles from a visit were used as the reference to calculate MMD at the subsequent visit. We selected 16 biomarkers (of which 11 are measured every 2 weeks) from blood samples of 763 chronic kidney disease patients hemodialyzed at the CHUS hospital in Quebec, who visited the hospital regularly (∼every 2 weeks) to perform routine blood tests. MMD tended to increase markedly preceding death, indicating an increasing intraindividual multivariate variability presaging a critical transition. In survival analysis, the hazard ratio between the 97.5th percentile and the 2.5th percentile of MMD reached as high as 21.1 [95% CI: 14.3, 31.2], showing that higher variability indicates substantially higher mortality risk. Multivariate approaches to early warning signs of critical transitions hold substantial clinical promise to identify early signs of critical transitions, such as risk of death in hemodialysis patients; future work should also explore whether the MMD approach works in other complex systems (i.e., ecosystems, economies), and should compare it to other multivariate approaches to quantify system variability.

Detecting and distinguishing tipping points using spectral early warning signals

Theory and observation tell us that many complex systems exhibit tipping points—thresholds involving an abrupt and irreversible transition to a contrasting dynamical regime. Such events are commonly referred to as critical transitions. Current research seeks to develop early warning signals (EWS) of critical transitions that could help prevent undesirable events such as ecosystem collapse. However, conventional EWS do not indicate the type of transition, since they are based on the generic phenomena of critical slowing down. For instance, they may fail to distinguish the onset of oscillations (e.g. Hopf bifurcation) from a transition to a distant attractor (e.g. Fold bifurcation). Moreover, conventional EWS are less reliable in systems with density-dependent noise. Other EWS based on the power spectrum (spectral EWS) have been proposed, but they rely upon spectral reddening, which does not occur prior to critical transitions with an oscillatory component. Here, we use Ornstein–Uhlenbeck theory to derive analytic approximations for EWS prior to each type of local bifurcation, thereby creating new spectral EWS that provide greater sensitivity to transition proximity; higher robustness to density-dependent noise and bifurcation type; and clues to the type of approaching transition. We demonstrate the advantage of applying these spectral EWS in concert with conventional EWS using a population model, and show that they provide a characteristic signal prior to two different Hopf bifurcations in data from a predator–prey chemostat experiment. The ability to better infer and differentiate the nature of upcoming transitions in complex systems will help humanity manage critical transitions in the Anthropocene Era.

Forecasting resilience profiles of the run-up to regime shifts in nearly-one-dimensional systems

The forecasting of sudden, irreversible shifts in natural systems is a challenge of great importance, whose realization could allow pre-emptive action to be taken to avoid or mitigate catastrophic transitions, or to help systems adapt to them. In recent years, there have been many advances in the development of such early warning signals. However, much of the current toolbox is based around the tracking of statistical trends and therefore does not aim to estimate the future time scale of transitions or resilience loss. Metric-based indicators are also difficult to implement when systems have inherent oscillations which can dominate the indicator statistics. To resolve these gaps in the toolbox, we use additional system properties to fit parsimonious models to dynamics in order to predict transitions. Here, we consider nearly-one-dimensional systems-higher dimensional systems whose dynamics can be accurately captured by one-dimensional discrete time maps. We show how the nearly one-dimensional dynamics can be used to produce model-based indicators for critical transitions which produce forecasts of the resilience and the time of transitions in the system. A particularly promising feature of this approach is that it allows us to construct early warning signals even for critical transitions of chaotic systems. We demonstrate this approach on two model systems: of phosphorous recycling in a shallow lake, and of an overcompensatory fish population.

Transient indicators of tipping points in infectious diseases

The majority of known early warning indicators of critical transitions rely on asymptotic resilience and critical slowing down. In continuous systems, critical slowing down is mathematically described by a decrease in magnitude of the dominant eigenvalue of the Jacobian matrix on the approach to a critical transition. Here, we show that measures of transient dynamics, specifically, reactivity and the maximum of the amplification envelope, also change systematically as a bifurcation is approached in an important class of models for epidemics of infectious diseases. Furthermore, we introduce indicators designed to detect trends in these measures and find that they reliably classify time series of case notifications simulated from stochastic models according to levels of vaccine uptake. Greater attention should be focused on the potential for systems to exhibit transient amplification of perturbations as a critical threshold is approached, and should be considered when searching for generic leading indicators of tipping points. Awareness of this phenomenon will enrich understanding of the dynamics of complex systems on the verge of a critical transition.

Critical slowing down associated with critical transition and risk of collapse in crypto-currency

The year 2017 saw the rise and fall of the crypto-currency market, followed by high variability in the price of all crypto-currencies. In this work, we study the abrupt transition in crypto-currency residuals, which is associated with the critical transition (the phenomenon of critical slowing down) or the stochastic transition phenomena. We find that, regardless of the specific crypto-currency or rolling window size, the autocorrelation always fluctuates around a high value, while the standard deviation increases monotonically. Therefore, while the autocorrelation does not display the signals of critical slowing down, the standard deviation can be used to anticipate critical or stochastic transitions. In particular, we have detected two sudden jumps in the standard deviation, in the second quarter of 2017 and at the beginning of 2018, which could have served as the early warning signals of two major price collapses that have happened in the following periods. We finally propose a mean-field phenomenological model for the price of crypto-currency to show how the use of the standard deviation of the residuals is a better leading indicator of the collapse in price than the time-series' autocorrelation. Our findings represent a first step towards a better diagnostic of the risk of critical transition in the price and/or volume of crypto-currencies.

Unveiling tipping points in long-term ecological records from Sphagnum-dominated peatlands

Unveiling past tipping points is a prerequisite for a better understanding of how individual species and entire ecosystems will respond to future climate change. Such knowledge is key for the implementation of biodiversity conservation. We identify the relationships between peatland vegetation and hydrological conditions over the past 2000 years using plant macrofossils, testate amoebae-based quantitative hydrological reconstructions and Sphagnum-moss functional traits from seven Polish peatland records. Using threshold indicator taxa analysis, we discovered that plant community composition strongly converged at a water level of ca 11.7 cm, indicating a community-level tipping point. We identified 45 plant taxa that showed either an increase or a decrease in their relative abundance between 8 and 17 cm of water-level depth. Our analysis of Sphagnum community traits further showed that Sphagnum functional diversity was remarkably stable over time despite Sphagnum species sensitivity to hydrological conditions. Our results suggest that past hydrological shifts did not influence major functions of the Sphagnum community, such as photosynthetic capacity, growth and productivity, owing to species replacement with a similar functional space. Although further studies including trait plasticity will be required, our findings suggest that the capacity of the Sphagnum community to gain carbon remained stable despite hydrological changes.

Identifying Critical State of Complex Diseases by Single-Sample-Based Hidden Markov Model

The progression of complex diseases is generally divided as a normal state, a pre-disease state or tipping point, and a disease state. Developing individual-specific method that can identify the pre-disease state just before a catastrophic deterioration, is critical for patients with complex diseases. However, with only a case sample, it is challenging to detect a pre-disease state which has little significant differences comparing with a normal state in terms of phenotypes and gene expressions. In this study, by regarding the tipping point as the end point of a stationary Markov process, we proposed a single-sample-based hidden Markov model (HMM) approach to explore the dynamical differences between a normal and a pre-disease states, and thus can signal the upcoming critical transition immediately after a pre-disease state. Using this method, we identified the pre-disease state or tipping point in a numerical simulation and two real datasets including stomach adenocarcinoma and influenza infection, which demonstrate the effectiveness of the method.

Detecting early-warning signals of influenza outbreak based on dynamic network marker

The seasonal outbreaks of influenza infection cause globally respiratory illness, or even death in all age groups. Given early‐warning signals preceding the influenza outbreak, timely intervention such as vaccination and isolation management effectively decrease the morbidity. However, it is usually a difficult task to achieve the real‐time prediction of influenza outbreak due to its complexity intertwining both biological systems and social systems. By exploring rich dynamical and high‐dimensional information, our dynamic network marker/biomarker (DNM/DNB) method opens a new way to identify the tipping point prior to the catastrophic transition into an influenza pandemics. In order to detect the early‐warning signals before the influenza outbreak by applying DNM method, the historical information of clinic hospitalization caused by influenza infection between years 2009 and 2016 were extracted and assembled from public records of Tokyo and Hokkaido, Japan. The early‐warning signal, with an average of 4‐week window lead prior to each seasonal outbreak of influenza, was provided by DNM‐based on the hospitalization records, providing an opportunity to apply proactive strategies to prevent or delay the onset of influenza outbreak. Moreover, the study on the dynamical changes of hospitalization in local district networks unveils the influenza transmission dynamics or landscape in network level.

Dynamical state transitions into addictive behaviour and their early-warning signals

The theory of critical transitions in complex systems (ecosystems, climate, etc.), and especially its ability to predict abrupt changes by early-warning signals based on analysis of fluctuations close to tipping points, is seen as a promising avenue to study disease dynamics. However, the biomedical field still lacks a clear demonstration of this concept. Here, we used a well-established animal model in which initial alcohol exposure followed by deprivation and subsequent reintroduction of alcohol induces excessive alcohol drinking as an example of disease onset. Intensive longitudinal data (ILD) of rat drinking behaviour and locomotor activity were acquired by a fully automated drinkometer device over 14 weeks. Dynamical characteristics of ILD were extracted using a multi-scale computational approach. Our analysis shows a transition into addictive behaviour preceded by early-warning signals such as instability of drinking patterns and locomotor circadian rhythms, and a resultant increase in low frequency, ultradian rhythms during the first week of deprivation. We find evidence that during prolonged deprivation, a critical transition takes place pushing the system to excessive alcohol consumption. This study provides an adaptable framework for processing ILD from clinical studies and for examining disease dynamics and early-warning signals in the biomedical field.

Supply and demand drive a critical transition to dysfunctional fisheries

Recent years have witnessed strenuous ongoing debate about the sustainability of many commercial fisheries. Here we apply commonly accepted principles of fishery science to consider the impact of price flexibility on long-term fishery sustainability in an era of increasing demand due to population increase and rising economic expectations. We apply this model to two commercial oceanic fisheries (cod and pollock) to demonstrate that harvest and price statistics that are commonly available for commercial fisheries can be used to diagnose the degree to which a given fishery has been overharvested. More importantly, the same heuristic can also be used to identify plausible targets for fishery rehabilitation and evaluate the effectiveness of alternative policy options to achieve those goals.

There is growing awareness of the need for fishery management policies that are robust to changing environmental, social, and economic pressures. Here we use conventional bioeconomic theory to demonstrate that inherent biological constraints combined with nonlinear supply−demand relationships can generate threshold effects due to harvesting. As a result, increases in overall demand due to human population growth or improvement in real income would be expected to induce critical transitions from high-yield/low-price fisheries to low-yield/high-price fisheries, generating severe strains on social and economic systems as well as compromising resource conservation goals. As a proof of concept, we show that key predictions of the critical transition hypothesis are borne out in oceanic fisheries (cod and pollock) that have experienced substantial increase in fishing pressure over the past 60 y. A hump-shaped relationship between price and historical harvest returns, well demonstrated in these empirical examples, is particularly diagnostic of fishery degradation. Fortunately, the same heuristic can also be used to identify reliable targets for fishery restoration yielding optimal bioeconomic returns while safely conserving resource abundance.

Catastrophic Shifts in Semiarid Vegetation-Soil Systems May Unfold Rapidly or Slowly

Under gradual change of a driver, complex systems may switch between contrasting stable states. For many ecosystems it is unknown how rapidly such a critical transition unfolds. Here we explore the rate of change during the degradation of a semiarid ecosystem with a model coupling the vegetation and geomorphological system. Two stable states-vegetated and bare-are identified, and it is shown that the change between these states is a critical transition. Surprisingly, the critical transition between the vegetated and bare state can unfold either rapidly over a few years or gradually over decennia up to millennia, depending on parameter values. An important condition for the phenomenon is the linkage between slow and fast ecosystems components. Our results show that, next to climate change and disturbance rates, the geological and geomorphological setting of a semiarid ecosystem is crucial in predicting its fate.

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

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

Social interactions among grazing reef fish drive material flux in a coral reef ecosystem

In human financial and social systems, exchanges of information among individuals cause speculative bubbles, behavioral cascades, and other correlated actions that profoundly influence system-level function. Exchanges of information are also widespread in ecological systems, but their effects on ecosystem-level processes are largely unknown. Herbivory is a critical ecological process in coral reefs, where diverse assemblages of fish maintain reef health by controlling the abundance of algae. Here, we show that social interactions have a major effect on fish grazing rates in a reef ecosystem. We combined a system for observing and manipulating large foraging areas in a coral reef with a class of dynamical decision-making models to reveal that reef fish use information about the density and actions of nearby fish to decide when to feed on algae and when to flee foraging areas. This "behavioral coupling" causes bursts of feeding activity that account for up to 68% of the fish community's consumption of algae. Moreover, correlations in fish behavior induce a feedback, whereby each fish spends less time feeding when fewer fish are present, suggesting that reducing fish stocks may not only reduce total algal consumption but could decrease the amount of algae each remaining fish consumes. Our results demonstrate that social interactions among consumers can have a dominant effect on the flux of energy and materials through ecosystems, and our methodology paves the way for rigorous in situ measurements of the behavioral rules that underlie ecological rates in other natural systems.

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

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

Allowing variance may enlarge the safe operating space for exploited ecosystems

Variable flows of food, water, or other ecosystem services complicate planning. Management strategies that decrease variability and increase predictability may therefore be preferred. However, actions to decrease variance over short timescales (2-4 y), when applied continuously, may lead to long-term ecosystem changes with adverse consequences. We investigated the effects of managing short-term variance in three well-understood models of ecosystem services: lake eutrophication, harvest of a wild population, and yield of domestic herbivores on a rangeland. In all cases, actions to decrease variance can increase the risk of crossing critical ecosystem thresholds, resulting in less desirable ecosystem states. Managing to decrease short-term variance creates ecosystem fragility by changing the boundaries of safe operating spaces, suppressing information needed for adaptive management, cancelling signals of declining resilience, and removing pressures that may build tolerance of stress. Thus, the management of variance interacts strongly and inseparably with the management of resilience. By allowing for variation, learning, and flexibility while observing change, managers can detect opportunities and problems as they develop while sustaining the capacity to deal with them.

Identifying critical differentiation state of MCF-7 cells for breast cancer by dynamical network biomarkers

Identifying the pre-transition state just before a critical transition during a complex biological process is a challenging task, because the state of the system may show neither apparent changes nor clear phenomena before this critical transition during the biological process. By exploring rich correlation information provided by high-throughput data, the dynamical network biomarker (DNB) can identify the pre-transition state. In this work, we apply DNB to detect an early-warning signal of breast cancer on the basis of gene expression data of MCF-7 cell differentiation. We find a number of the related modules and pathways in the samples, which can be used not only as the biomarkers of cancer cells but also as the drug targets. Both functional and pathway enrichment analyses validate the results.

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.

Critical slowing down as early warning for the onset of collapse in mutualistic communities

Tipping points are crossed when small changes in external conditions cause abrupt unexpected responses in the current state of a system. In the case of ecological communities under stress, the risk of approaching a tipping point is unknown, but its stakes are high. Here, we test recently developed critical slowing-down indicators as early-warning signals for detecting the proximity to a potential tipping point in structurally complex ecological communities. We use the structure of 79 empirical mutualistic networks to simulate a scenario of gradual environmental change that leads to an abrupt first extinction event followed by a sequence of species losses until the point of complete community collapse. We find that critical slowing-down indicators derived from time series of biomasses measured at the species and community level signal the proximity to the onset of community collapse. In particular, we identify specialist species as likely the best-indicator species for monitoring the proximity of a community to collapse. In addition, trends in slowing-down indicators are strongly correlated to the timing of species extinctions. This correlation offers a promising way for mapping species resilience and ranking species risk to extinction in a given community. Our findings pave the road for combining theory on tipping points with patterns of network structure that might prove useful for the management of a broad class of ecological networks under global environmental change.