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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.

Early‐warning signals of delicate design are used to predict critical transitions in complex systems, which makes it possible to render the systems far away from the catastrophic state by introducing timely interventions. Traditional signals including the dynamical network biomarker (DNB), based on statistical properties such as variance and autocorrelation of nodal dynamics, overlook directional interactions and thus have limitations in capturing underlying mechanisms and simultaneously sustaining robustness against noise perturbations. This study therefore introduces a framework of causal network markers (CNMs) by incorporating causality indicators, which reflect the directional influence between variables. Actually, to detect and identify the tipping points ahead of critical transition, two markers are designed: the causal network marker from Granger causality (CNM‐GC), for linear causality, and the causal network marker from transfer entropy (CNM‐TE), for non‐linear causality, as well as a functional representation of different causality indicators and a clustering technique to verify the system's dominant group. Through demonstrations using computational benchmark models and real‐world datasets of epileptic seizure, the framework of CNMs shows higher predictive power and accuracy than the traditional DNB. It is believed that, due to the versatility and scalability, the CNMs are suitable for comprehensively evaluating the systems. The most possible direction for application includes the identification of tipping points in clinical disease. The study proposes a causal network markers (CNMs) framework to identify early‐warning signals preceding critical transitions. It validates CNMs on various computational benchmark models and real‐world datasets, demonstrating higher accuracy and flexibility compared to existing approaches. CNMs also reveal the potential causal patterns in epileptic seizures, thereby deepening the understanding of neurodynamics.

Shrub encroachment, forest decline and wildfires have caused large-scale changes in semi-arid vegetation over the past 50 years. Climate is a primary determinant of plant growth in semi-arid ecosystems, yet it remains difficult to forecast large-scale vegetation shifts (i.e. biome shifts) in response to climate change. We highlight recent advances from four conceptual perspectives that are improving forecasts of semi-arid biome shifts. Moving from small to large scales, first, tree-level models that simulate the carbon costs of drought-induced plant hydraulic failure are improving predictions of delayed-mortality responses to drought. Second, tracer-informed water flow models are improving predictions of species coexistence as a function of climate. Third, new applications of ecohydrological models are beginning to simulate small-scale water movement processes at large scales. Fourth, remotely-sensed measurements of plant traits such as relative canopy moisture are providing early-warning signals that predict forest mortality more than a year in advance. We suggest that a community of researchers using modeling approaches (e.g. machine learning) that can integrate these perspectives will rapidly improve forecasts of semi-arid biome shifts. Better forecasts can be expected to help prevent catastrophic changes in vegetation states by identifying improved monitoring approaches and by prioritizing high-risk areas for management.

1. Evaluations of wildlife population dynamics have the potential to convey valuable information on the type of pressure affecting a population and could help predict future changes in the population's trajectory. Greater understanding of different patterns of population declines could provide a useful mechanism for assessing decline severity in the wild and identifying those populations that are more likely to exhibit severe declines. 2. We identified 93 incidences of decline within 75 populations of mammalian species using a time-series analysis method. These included linear, quadratic convex (accelerating) declines, exponential concave (decelerating) declines and quadratic concave declines (representing recovering populations). Excluding linear declines left a data set of 85 declines to model the relationship between each decline-curve type and a range of biological, anthropogenic and time-series descriptor explanatory variables. 3. None of the decline-curve types were spatially or phylogenetically clustered. The only characteristic that could be consistently associated with any curve type was the time at which they were more likely to occur within a time series. Quadratic convex declines were more likely to occur at the start of the time series, while recovering curve shapes (quadratic concave declines) were more likely at the end of the time series. 4. Synthesis and applications. The ability to link certain factors with specific decline dynamics across a number of mammalian populations is useful for management purposes as it provides decision-makers with potential triggers upon which to base their conservation actions. We propose that the identification of quadratic convex declines could be used as an early-warning signal of potentially severe decline dynamics. For such a population, increased population monitoring effort should be deployed to diagnose the cause of its decline and avert possible extinctions. Conversely, the presence of a quadratic concave decline suggests that the population has already undergone a period of serious decline but is now in the process of recovery. Such populations will require different types of conservation actions, focussing on enhancing their chances of recovery.

To decrease human and economic damage owing to earthquakes, it is necessary to discover signals preceding earthquakes. We focus on the concept of “early warning signals” developed in bifurcation analysis, in which an increase in the variances of variables precedes its transition. If we can treat earthquakes as one of the transition phenomena that moves from one state to the other state, this concept is useful for detecting earthquakes before they start. We develop a covariance matrix from multi-channel time series data observed by an observatory on the seafloor and calculate the first eigenvalue and corresponding eigenstate of the matrix. By comparing the time dependence of the eigenstate to some past earthquakes, it is shown that the contribution from specific observational channels to the eigenstate increases before earthquakes, and there is a case in which the eigenvalue increases as predicted in early warning signals. This result suggests the first eigenvalue and eigenstate of multi-channel data are useful to identify signals preceding earthquakes.

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.

Complex systems can exhibit sudden transitions or regime shifts from one stable state to another, typically referred to as critical transitions. It becomes a great challenge to identify a robust warning sufficiently early that action can be taken to avert a regime shift. We employ landscape-flux theory from nonequilibrium statistical mechanics as a general framework to quantify the global stability of ecological systems and provide warning signals for critical transitions. We quantify the average flux as the nonequilibrium driving force and the dynamical origin of the nonequilibrium transition while the entropy production rate as the nonequilibrium thermodynamic cost and thermodynamic origin of the nonequilibrium transition. Average flux, entropy production, nonequilibrium free energy, and time irreversibility quantified by the difference in cross-correlation functions forward and backward in time can serve as early warning signals for critical transitions much earlier than other conventional predictors.Weutilize a classical shallow lake model as an exemplar for our early warning prediction. Our proposed method is general and can be readily applied to assess the resilience of many other ecological systems. The early warning signals proposed here can potentially predict critical transitions earlier than established methods and perhaps even sufficiently early to avert catastrophic shifts.

The Greenland Ice Sheet (GrIS) is a potentially unstable component of the Earth system and may exhibit a critical transition under ongoing global warming. Mass reductions of the GrIS have substantial impacts on global sea level and the speed of the Atlantic Meridional Overturning Circulation, due to the additional freshwater caused by increased meltwater runoff into the northern Atlantic. The stability of the GrIS depends crucially on the positive melt-elevation feedback (MEF), by which melt rates increase as the overall ice sheet height decreases under rising temperatures. Melting rates across Greenland have accelerated nonlinearly in recent decades, and models predict a critical temperature threshold beyond which the current ice sheet state is not maintainable. Here, we investigate long-term melt rate and ice sheet height reconstructions from the central-western GrIS in combination with model simulations to quantify the stability of this part of the GrIS. We reveal significant early-warning signals (EWS) indicating that the central-western GrIS is close to a critical transition. By relating the statistical EWS to underlying physical processes, our results suggest that the MEF plays a dominant role in the observed, ongoing destabilization of the central-western GrIS. Our results suggest substantial further GrIS mass loss in the near future and call for urgent, observation-constrained stability assessments of other parts of the GrIS.

Ecological resilience is the ability of a system to persist in the face of perturbations. Although resilience has been a highly influential concept, its interpretation has remained largely qualitative. Here we describe an emerging family of methods for quantifying resilience on the basis of observations. A first set of methods is based on the phenomenon of critical slowing down, which implies that recovery upon small perturbations becomes slower as a system approaches a tipping point. Such slowing down can be measured experimentally but may also be indirectly inferred from changes in natural fluctuations and spatial patterns. A second group of methods aims to characterize the resilience of alternative states in probabilistic terms based on large numbers of observations as in long time series or satellite images. These generic approaches to measuring resilience complement the system-specific knowledge needed to infer the effects of environmental change on the resilience of complex systems.

In complex systems, a critical transition is a shift in a system’s dynamical regime from its current state to a strongly contrasting state as external conditions move beyond a tipping point. These transitions are often preceded by characteristic early warning signals such as increased system variability. However, early warning signals in complex, coupled human–environment systems (HESs) remain little studied. Here, we compare critical transitions and their early warning signals in a coupled HES model to an equivalent environment model uncoupled from the human system. We parameterize the HES model, using social and ecological data from old-growth forests in Oregon. We find that the coupled HES exhibits a richer variety of dynamics and regime shifts than the uncoupled environment system.Moreover, the early warning signals in the coupled HES can be ambiguous, heralding either an era of ecosystem conservationism or collapse of both forest ecosystems and conservationism. The presence of human feedback in the coupled HES can also mitigate the early warning signal, making it more difficult to detect the oncoming regime shift. We furthermore show how the coupled HES can be “doomed to criticality”: Strategic human interactions cause the system to remain perpetually in the vicinity of a collapse threshold, as humans become complacent when the resource seems protected but respond rapidly when it is under immediate threat. We conclude that the opportunities, benefits, and challenges of modeling regime shifts and early warning signals in coupled HESs merit further research.