Spatial correlation as leading indicator of catastrophic shifts

Generic early-warning signals such as increased autocorrelation and variance have been demonstrated in time-series of systems with alternative stable states approaching a critical transition. However, lag times for the detection of such leading indicators are typically long. Here, we show that increased spatial correlation may serve as a more powerful early-warning signal in systems consisting of many coupled units. We first show why from the universal phenomenon of critical slowing down, spatial correlation should be expected to increase in the vicinity of bifurcations. Subsequently, we explore the applicability of this idea in spatially explicit ecosystem models that can have alternative attractors. The analysis reveals that as a control parameter slowly pushes the system towards the threshold, spatial correlation between neighboring cells tends to increase well before the transition. We show that such increase in spatial correlation represents a better early-warning signal than indicators derived from time-series provided that there is sufficient spatial heterogeneity and connectivity in the system.     

Early detection of ecosystem regime shifts: a multiple method evaluation for management application

Critical transitions between alternative stable states have been shown to occur across an array of complex systems. While our ability to identify abrupt regime shifts in natural ecosystems has improved, detection of potential early-warning signals previous to such shifts is still very limited. Using real monitoring data of a key ecosystem component, we here apply multiple early-warning indicators in order to assess their ability to forewarn a major ecosystem regime shift in the Central Baltic Sea. We show that some indicators and methods can result in clear early-warning signals, while other methods may have limited utility in ecosystem-based management as they show no or weak potential for early-warning. We therefore propose a multiple method approach for early detection of ecosystem regime shifts in monitoring data that may be useful in informing timely management actions in the face of ecosystem change.     

Early warning signals: the charted and uncharted territories

The realization that complex systems such as ecological communities can collapse or shift regimes suddenly and without rapid external forcing poses a serious challenge to our understanding and management of the natural world. The potential to identify early warning signals that would allow researchers and managers to predict such events before they happen has therefore been an invaluable discovery that offers a way forward in spite of such seemingly unpredictable behavior. Research into early warning signals has demonstrated that it is possible to define and detect such early warning signals in advance of a transition in certain contexts. Here, we describe the pattern emerging as research continues to explore just how far we can generalize these results. A core of examples emerges that shares three properties: the phenomenon of rapid regime shifts, a pattern of “critical slowing down” that can be used to detect the approaching shift, and a mechanism of bifurcation driving the sudden change. As research has expanded beyond these core examples, it is becoming clear that not all systems that show regime shifts exhibit critical slowing down, or vice versa. Even when systems exhibit critical slowing down, statistical detection is a challenge. We review the literature that explores these edge cases and highlight the need for (a) new early warning behaviors that can be used in cases where rapid shifts do not exhibit critical slowing down; (b) the development of methods to identify which behavior might be an appropriate signal when encountering a novel system, bearing in mind that a positive indication for some systems is a negative indication in others; and (c) statistical methods that can distinguish between signatures of early warning behaviors and noise.     

Review on detection of critical transition in ecosystems

当一个存在多稳态的生态系统临近突变阈值点时, 外界条件即使发生一个微小变化, 也会引发生态系统的剧烈响应, 使之进入结构和功能截然不同的另一稳定状态, 这种现象称为重大突变(critical transition)。重大突变所导致的稳态转换总是伴随着生态系统服务的急剧变化, 可能对人类可持续发展产生重大影响。预测生态系统突变的发生非常困难, 但科学家在此领域的大量研究结果表明, 通过监测一些通用指标可以判断生态系统是否不断临近重大突变阈值点, 进而可以进行生态系统重大突变预警。该文对近年来生态系统重大突变检测领域所取得的成果进行总结与归纳, 论述了生态系统重大突变的产生机制及其后果, 介绍了生态系统突变预警信号提取的理论基础, 从时间和空间两个维度总结了近年来生态系统重大突变预警信号的提取方法, 概述了当前研究面临的挑战, 指出生态系统突变预警信号的检测应充分利用时空动态数据, 并且联合多个指标, 从多个角度进行综合预警, 此外, 还应重视生态系统结构与重大突变之间的关系, 增强生态系统突变预警能力。     

Early warning signals also precede non‐catastrophic transitions

Synthesis The quickly expanding literature on early warning signals for critical transitions in ecosystems suggests that critical slowing down is a key phenomenon to measure the distance to a tipping point in ecosystems. Such work is broadly misinterpreted as showing that slowing down is specific to tipping points. In this contribution, we show why this is not the case. Early warning signals based on critical slowing down indicate a broader class of situations where a system becomes increasingly sensitive to perturbations. Ecosystem responses to external changes can surprise us by their abruptness and irreversibility. Models have helped identifying indicators of impending catastrophic shifts, referred to as ‘generic early warning signals’. These indicators are linked to a phenomenon known as ‘critical slowing down’ which describes the fact that the recovery rate of a system after a perturbation decreases when the system approaches a bifurcation – such as the classical fold bifurcation associated to catastrophic shifts. However, contrary to what has sometimes been suggested in the literature, a decrease in recovery rate cannot be considered as specific to approaching catastrophic shifts. Here, we analyze the behavior of early warning signals based on critical slowing down in systems approaching a range of catastrophic and non‐catastrophic situations. Our results show that slowing down generally happens in situations where a system is becoming increasingly sensitive to external perturbations, independently of whether the impeding change is catastrophic or not. These results highlight that indicators specific to catastrophic shifts are still lacking. More importantly, they also imply that in systems where we have no reason to expect catastrophic transitions, slowing down may still be used in a more general sense as a warning signal for a potential decrease in stability.     

On the critical behavior of the general epidemic process and dynamical percolation

Scaling laws are formulated for the behavior of a space-dependent fluctuating general epidemic process near the critical point. Restricted to stationary properties, these laws describe also the critical behavior of random percolation. Monte Carlo calculations are used to estimate the critical exponents and the universal shape of the propagating wave, in the case of 2-dimensional space.     

Scaling effects and spatio-temporal multilevel dynamics in epileptic seizures

Epileptic seizures are one of the most well-known dysfunctions of the nervous system. During a seizure, a highly synchronized behavior of neural activity is observed that can cause symptoms ranging from mild sensual malfunctions to the complete loss of body control. In this paper, we aim to contribute towards a better understanding of the dynamical systems phenomena that cause seizures. Based on data analysis and modelling, seizure dynamics can be identified to possess multiple spatial scales and on each spatial scale also multiple time scales. At each scale, we reach several novel insights. On the smallest spatial scale we consider single model neurons and investigate early-warning signs of spiking. This introduces the theory of critical transitions to excitable systems. For clusters of neurons (or neuronal regions) we use patient data and find oscillatory behavior and new scaling laws near the seizure onset. These scalings lead to substantiate the conjecture obtained from mean-field models that a Hopf bifurcation could be involved near seizure onset. On the largest spatial scale we introduce a measure based on phase-locking intervals and wavelets into seizure modelling. It is used to resolve synchronization between different regions in the brain and identifies time-shifted scaling laws at different wavelet scales. We also compare our wavelet-based multiscale approach with maximum linear cross-correlation and mean-phase coherence measures.     

Increased Firing Irregularity as an Emergent Property of Neural-State Transition in Monkey Prefrontal Cortex

Flexible behaviors are organized by complex neural networks in the prefrontal cortex. Recent studies have suggested that such networks exhibit multiple dynamical states, and can switch rapidly from one state to another. In many complex systems such as the brain, the early-warning signals that may predict whether a critical threshold for state transitions is approaching are extremely difficult to detect. We hypothesized that increases in firing irregularity are a crucial measure for predicting state transitions in the underlying neuronal circuits of the prefrontal cortex. We used both experimental and theoretical approaches to test this hypothesis. Experimentally, we analyzed activities of neurons in the prefrontal cortex while monkeys performed a maze task that required them to perform actions to reach a goal. We observed increased firing irregularity before the activity changed to encode goal-to-action information. Theoretically, we constructed theoretical generic neural networks and demonstrated that changes in neuronal gain on functional connectivity resulted in a loss of stability and an altered state of the networks, accompanied by increased firing irregularity. These results suggest that assessing the temporal pattern of neuronal fluctuations provides important clues regarding the state stability of the prefrontal network. We also introduce a novel scheme that the prefrontal cortex functions in a metastable state near the critical point of bifurcation. According to this scheme, firing irregularity in the prefrontal cortex indicates that the system is about to change its state and the flow of information in a flexible manner, which is essential for executive functions. This metastable and/or critical dynamical state of the prefrontal cortex may account for distractibility and loss of flexibility in the prefrontal cortex in major mental illnesses such as schizophrenia.     

Labile cochlear tuning in the mustached bat

Summary Acoustic stimuli near 60 kHz elicit pronounced resonance in the cochlea of the mustached bat (Pteronotus parnellii parnellii). The cochlear resonance frequency (CRF) is near the second harmonic, constant frequency (CF2) component of the bat's biosonar signals. Within narrow bands where CF2 and third harmonic (CF3) echoes are maintained, the cochlea has sharp tuning characteristics that are conserved throughout the central auditory system. The purpose of this study was to examine the effects of temperature-related shifts in the CRF on the tuning properties of neurons in the cochlear nucleus and inferior colliculus.Eighty-two single and multi-unit recordings were characterizedin 6 awake bats with chronically implanted cochlear microphonic electrodes. As the CRF changed with body temperature, the tuning curves of neurons sharply tuned to frequencies near the CF2 and CF3 shifted with the CRF in every case, yielding a change in the unit's best frequency. The results show that cochlear tuning is labile in the mustached bat, and that this lability produces tonotopic shifts in the frequency response of central auditory neurons. Furthermore, results provide evidence of shifts in the frequency-to-place code within the sharply tuned CF2 and CF3 regions of the cochlea. In conjunction with the finding that biosonar emission frequency and the CRF shift concomitantly with temperature and flight, it is concluded that the adjustment of biosonar signals accommodates the shifts in cochlear and neural tuning that occur with active echolocation.Abbreviations BF best frequency - CF characteristic frequency - CF2, CF3 second and third harmonic, constant frequency components of the biosonar signal - CM cochlear microphonic - CN cochlear nucleus - CRF cochlear resonance frequency - IC inferior colliculus - MT minimum threshold - OAE otoacoustic emission - Q_10dB BF (or CF) divided by the response bandwidth at 10 dB above MT     

Critical Slowing Down Governs the Transition to Neuron Spiking

Many complex systems have been found to exhibit critical transitions, or so-called tipping points, which are sudden changes to a qualitatively different system state. These changes can profoundly impact the functioning of a system ranging from controlled state switching to a catastrophic break-down; signals that predict critical transitions are therefore highly desirable. To this end, research efforts have focused on utilizing qualitative changes in markers related to a system’s tendency to recover more slowly from a perturbation the closer it gets to the transition—a phenomenon called critical slowing down. The recently studied scaling of critical slowing down offers a refined path to understand critical transitions: to identify the transition mechanism and improve transition prediction using scaling laws.Here, we outline and apply this strategy for the first time in a real-world system by studying the transition to spiking in neurons of the mammalian cortex. The dynamical system approach has identified two robust mechanisms for the transition from subthreshold activity to spiking, saddle-node and Hopf bifurcation. Although theory provides precise predictions on signatures of critical slowing down near the bifurcation to spiking, quantitative experimental evidence has been lacking. Using whole-cell patch-clamp recordings from pyramidal neurons and fast-spiking interneurons, we show that 1) the transition to spiking dynamically corresponds to a critical transition exhibiting slowing down, 2) the scaling laws suggest a saddle-node bifurcation governing slowing down, and 3) these precise scaling laws can be used to predict the bifurcation point from a limited window of observation. To our knowledge this is the first report of scaling laws of critical slowing down in an experiment. They present a missing link for a broad class of neuroscience modeling and suggest improved estimation of tipping points by incorporating scaling laws of critical slowing down as a strategy applicable to other complex systems.     

生态系统状态跃变的早期预警信号及检测

生态系统在气候变化和土地利用及人类活动等的影响下其状态会由某一稳态转变到另一稳态。由于环境压力的复杂性、非线性、随机性等特征，往往导致状态转变表现为非线性、突变、跃变等特点。准确界定系统状态跃变的拐点或阈值点存在很大的挑战，而捕捉接近临界拐点前的生态系统结构和属性上的变化特征作为早期预警信号是切实可行的。早期预警信号理论经历理论框架构建、方法确立、机理认知等近半个多世纪的探索，已经由最初的通过仅依赖检测临界点恢复力的速率减慢、方差增加、系统自相关增强等统计学信号过度到更加多样化的检测方法，如检测系统组分属性的变化特征，诊断系统组分各属性之间的关系变化，系统组分的性状变化、系统组分网络结构变化等等，并且试图整合多信号提高预警的精确性。利用来自自然生态系统的长时间高密度数据集和空间代替时间的数据集，基于多度及性状信号的早期预警，结合稳定性、临界恢复力的减速、以及统计参数的指示作用对系统跃变进行早期诊断和预警是预测生态学的主旨。早期预警信号的深入研究不仅能够完善已有理论的不足，同时还能够为生态系统的保护和管理提供切实有效的理论指导。     

Phenotypic Plasticity and Repeatability in the Mating Signals of Enchenopa Treehoppers, with Implications for Reduced Gene Flow among Host-Shifted Populations

Mate signaling systems, because of their role in assortative mating, have often been implicated in the origins of evolutionary independence between lineages. We investigated three sources of phenotypic plasticity in mating signals with potential relevance to assortative mating in a species in the Enchenopa binotata complex of treehoppers. This group has been a model for speciation in sympatry through shifts to novel host plants. Host shifts result in partial reproductive isolation in Enchenopa binotata because of their effects on life history timing, but interbreeding is still possible if there is dispersal and some overlap of mating periods. Courtship in these plant‐feeding insects is mediated by plant‐borne vibrational signals. We asked whether variation in male mate signaling behavior is influenced by plant substrate, age, or size, each of which may play a role in interactions among host‐shifted populations. Males produced fewer, shorter signals when on non‐hosts than when on hosts. However, there were no effects of age or size on signal variation. Significant repeatability of some signal features (carrier frequency and the number of signals produced in a signaling bout) is consistent with the presence of genetic variation and thus the potential to respond to selection. Our results suggest that plasticity in mate signaling systems, and in particular in male mate searching behavior on hosts and non‐hosts, may have the potential to reduce interbreeding between populations that use different species of host plant.     

Rate of forcing and the forecastability of critical transitions

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

Robustness of early warning signals of regime shifts in time-delayed ecological models

Various ecological and other complex dynamical systems may exhibit abrupt regime shifts or critical transitions, wherein they reorganize from one stable state to another over relatively short time scales. Because of potential losses to ecosystem services, forecasting such unexpected shifts would be valuable. Using mathematical models of regime shifts, ecologists have proposed various early warning signals of imminent shifts. However, their generality and applicability to real ecosystems remain unclear because these mathematical models are considered too simplistic. Here, we investigate the robustness of recently proposed early warning signals of regime shifts in two well-studied ecological models, but with the inclusion of time-delayed processes. We find that the average variance may either increase or decrease prior to a regime shift and, thus, may not be a robust leading indicator in time-delayed ecological systems. In contrast, changing average skewness, increasing autocorrelation at short time lags, and reddening power spectra of time series of the ecological state variable all show trends consistent with those of models with no time delays. Our results provide insights into the robustness of early warning signals of regime shifts in a broader class of ecological systems.     

能源预测预警理论与方法研究进展

能源作为一种稀缺性的战略资源是国民经济增长和社会进步的物质基础,但是随着化石能源耗竭及能源使用造成的环境问题日趋严重,能源安全问题逐渐成为关注的焦点,而能源预测预警也成为能源系统科学领域的新兴学科,其内容包含能源安全理论、基于模型的能源供需预测和基于安全评价指标体系的能源预警等方面内容。通过系统回顾能源安全的理论及其演变的历程,重点综述了自上而下、自下而上和混合建模3种建模思路的能源预测模型,探讨了三类模型的优点和局限性,并根据能源安全预警评价指标浓缩信息的程度,将现有预警评价体系划分单个型指标评价体系和聚合型指标评价体系两大类。通过对以上研究内容的总结分析,明确了当前能源预测预警研究各领域的研究进展,及其在理论和应用方面的优势与不足。在未来研究中,建议从供应链的角度出发,考虑能源系统内部各因素及与外部因素的相互作用,构建基于链式的预警体系,以有效弥补现有研究中的不足。     

Protein aggregation/crystallization and minor structural changes: universal versus specific aspects

Protein association covers wide interests in biophysics, protein science, and biotechnologies, and it is often viewed as governed by conformation details. More recently, the existence of a universal physical principle governing aggregation/crystallization processes has been suggested by a series of experiments and shown to be linked to the universal scaling properties of concentration fluctuations occurring in the proximity of a phase transition (spinodal demixing in the specific case). Such properties have provided a quantitative basis for capturing kinetic association data on a universal master curve, ruled by the normalized distance of the state of the system from its instability region. Here we report new data on lysozyme crystal nucleation. They strengthen the evidence in favor of universality and show that the system enters the region of universal behavior in a stepwise manner as a result of minor conformation changes. Results also show that the link between conformation details and universal behavior is actuated by interactions mediated by the solvent. Outside the region of universal behavior, nucleation rates become unpredictable and undetectably long.     

Sudden Shifts in Ecological Systems: Intermittency and Transients in the Coupled Ricker Population Model

Many real ecological systems show sudden changes in behavior, phenomena sometimes categorized as regime shifts in the literature. The relative importance of exogenous versus endogenous forces producing regime shifts is an important question. These forces’ role in generating variability over time in ecological systems has been explored using tools from dynamical systems. We use similar ideas to look at transients in simple ecological models as a way of understanding regime shifts. Based in part on the theory of crises, we carefully analyze a simple two patch spatial model and begin to understand from a mathematical point of view what produces transient behavior in ecological systems. In particular, since the tools are essentially qualitative, we are able to suggest that transient behavior should be ubiquitous in systems with overcompensatory local dynamics, and thus should be typical of many ecological systems. This work has been supported by NSF Grant EF-0434266.     

From morphology to neural information: the electric sense of the skate

Morphology typically enhances the fidelity of sensory systems. Sharks, skates, and rays have a well-developed electrosense that presents strikingly unique morphologies. Here, we model the dynamics of the peripheral electrosensory system of the skate, a dorsally flattened batoid, moving near an electric dipole source (e.g., a prey organism). We compute the coincident electric signals that develop across an array of the skate's electrosensors, using electrodynamics married to precise morphological measurements of sensor location, infrastructure, and vector projection. Our results demonstrate that skate morphology enhances electrosensory information. Not only could the skate locate prey using a simple population vector algorithm, but its morphology also specifically leads to quick shifts in firing rates that are well-suited to the demonstrated bandwidth of the electrosensory system. Finally, we propose electrophysiology trials to test the modeling scheme.     

Histogram-based scoring schemes for protein NMR resonance assignment

In NMR protein structure determination, after the resonance peaks have been identified and chemical shifts from peaks across multiple spectra have been grouped into spin systems, associating these spin systems to their host residues is the key toward the success of structural information extraction and thus the key to the success of the structure calculation. To achieve accurate enough structure calculation, a near complete and accurate assignment is a prerequisite. There are two pieces of information that can be used into the assignment, one of which is the adjacency information among the spin systems and the other is the signature information of the spin systems. The signature information reflects the fact that, generally speaking, for one type of amino acid residing in a specific local structural environment, the chemical shifts for the atoms inside the amino acid fall into some very narrow distinct ranges. In most of the existing work, normal distributions are assumed with means and standard deviations statistically collected from the available data. In this paper, we followed a simple yet effective histogram-based way to estimate for every spin system the probability that its host is a certain type of amino acid residing in a certain type of secondary structure. We used two combinations of chemical shifts to demonstrate the effectiveness of this type of histogram-based scoring schemes.