Conditional Heteroskedasticity Forecasts Regime Shift in a Whole-Ecosystem Experiment

Regime shifts in stochastic ecosystem models are often preceded by early warning signals such as increased variance and increased autocorrelation in time series. There is considerable theoretical support for early warning signals, but there is a critical lack of field observations to test the efficacy of early warning signals at spatial and temporal scales relevant for ecosystem management. Conditional heteroskedasticity is persistent periods of high and low variance that may be a powerful leading indicator of regime shift. We evaluated conditional heteroskedasticity as an early warning indicator by applying moving window conditional heteroskedasticity tests to time series of chlorophyll-a and fish catches derived from a whole-lake experiment designed to create a regime shift. There was significant conditional heteroskedasticity at least a year prior to the regime shift in the manipulated lake but there was no significant conditional heteroskedasticity in an adjacent reference lake. Conditional heteroskedasticity was an effective leading indicator of regime shift for the ecosystem manipulation.     

干旱区生态系统稳态转换及其预警信号——基于景观格局特征的识别方法

在日益加剧的气候变化和土地开垦、放牧等人类活动干扰下,具有多稳态特征的干旱区生态系统可能会经历从相对健康状态到退化状态的稳态转换,导致生态系统的功能下降。早期预警信号的识别是生态系统稳态转换研究的热点,也是管理实践中防止生态系统退化的关键环节。以往预警信号研究聚焦于通用信号如自相关性、方差等统计学指标,然而这些指标对于具有特定机制的干旱区生态系统可能并不适用。基于干旱区景观格局特征所发展起来的空间指标为生态系统稳态转换提供了独特的空间视角,对于理解干旱区生态系统退化过程和机理具有科学意义和实践价值。介绍了干旱区生态系统稳态转换现象及其转换机制;聚焦景观生态学的指标和方法,从空间视角总结基于干旱区景观格局特征的关键预警指标(植被覆盖度、植被斑块形态、植被斑块大小频率分布和水文连通性等),重点剖析这些关键指标的概念、量化方法、识别特征及其实践应用;最后针对指标的优势和局限性对未来的研究方向进行展望,包括发掘潜在景观指标,加强干旱区生态系统变化的多种驱动要素的相互作用机制研究,开展多时空尺度的实证研究,构建生态系统稳态转换预警信号的整体分析框架,以及加强指标阈值的量化研究等方面。     

Conditional heteroscedasticity as a leading indicator of ecological regime shifts

Regime shifts are massive, often irreversible, rearrangements of nonlinear ecological processes that occur when systems pass critical transition points. Ecological regime shifts sometimes have severe consequences for human well-being, including eutrophication in lakes, desertification, and species extinctions. Theoretical and laboratory evidence suggests that statistical anomalies may be detectable leading indicators of regime shifts in ecological time series, making it possible to foresee and potentially avert incipient regime shifts. Conditional heteroscedasticity is persistent variance characteristic of time series with clustered volatility. Here, we analyze conditional heteroscedasticity as a potential leading indicator of regime shifts in ecological time series. We evaluate conditional heteroscedasticity by using ecological models with and without four types of critical transition. On approaching transition points, all time series contain significant conditional heteroscedasticity. This signal is detected hundreds of time steps in advance of the regime shift. Time series without regime shifts do not have significant conditional heteroscedasticity. Because probability values are easily associated with tests for conditional heteroscedasticity, detection of false positives in time series without regime shifts is minimized. This property reduces the need for a reference system to compare with the perturbed system.     

Spatial variance and spatial skewness: leading indicators of regime shifts in spatial ecological systems

Ecosystems can undergo large-scale changes in their states, known as catastrophic regime shifts, leading to substantial losses to services they provide to humans. These shifts occur rapidly and are difficult to predict. Several early warning signals of such transitions have recently been developed using simple models. These studies typically ignore spatial interactions, and the signal provided by these indicators may be ambiguous. We employ a simple model of collapse of vegetation in one and two spatial dimensions and show, using analytic and numerical studies, that increases in spatial variance and changes in spatial skewness occur as one approaches the threshold of vegetation collapse. We identify a novel feature, an increasing spatial variance in conjunction with a peaking of spatial skewness, as an unambiguous indicator of an impending regime shift. Once a signal has been detected, we show that a quick management action reducing the grazing activity is needed to prevent the collapse of vegetated state. Our results show that the difficulties in obtaining the accurate estimates of indicators arising due to lack of long temporal data can be alleviated when high-resolution spatially extended data are available. These results are shown to hold true independent of various details of model or different spatial dispersal kernels such as Gaussian or heavily fat tailed. This study suggests that spatial data and monitoring multiple indicators of regime shifts can play a key role in making reliable predictions on ecosystem stability and resilience. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Spatial early warning signals for impending regime shifts: A practical framework for application in real‐world landscapes

Prediction of ecosystem response to global environmental change is a pressing scientific challenge of major societal relevance. Many ecosystems display nonlinear responses to environmental change, and may even undergo practically irreversible ‘regime shifts’ that initiate ecosystem collapse. Recently, early warning signals based on spatiotemporal metrics have been proposed for the identification of impending regime shifts. The rapidly increasing availability of remotely sensed data provides excellent opportunities to apply such model‐based spatial early warning signals in the real world, to assess ecosystem resilience and identify impending regime shifts induced by global change. Such information would allow land‐managers and policy makers to interfere and avoid catastrophic shifts, but also to induce regime shifts that move ecosystems to a desired state. Here, we show that the application of spatial early warning signals in real‐world landscapes presents unique and unexpected challenges, and may result in misleading conclusions when employed without careful consideration of the spatial data and processes at hand. We identify key practical and theoretical issues and provide guidelines for applying spatial early warning signals in heterogeneous, real‐world landscapes based on literature review and examples from real‐world data. Major identified issues include (1) spatial heterogeneity in real‐world landscapes may enhance reversibility of regime shifts and boost landscape‐level resilience to environmental change (2) ecosystem states are often difficult to define, while these definitions have great impact on spatial early warning signals and (3) spatial environmental variability and socio‐economic factors may affect spatial patterns, spatial early warning signals and associated regime shift predictions. We propose a novel framework, shifting from an ecosystem perspective towards a landscape approach. The framework can be used to identify conditions under which resilience assessment with spatial remotely sensed data may be successful, to support well‐informed application of spatial early warning signals, and to improve predictions of ecosystem responses to global environmental change.     

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.     

浅水湖泊生态系统稳态转换的阈值判定方法

浅水湖泊生态系统对人类干扰的反应会随着干扰力度的改变或增强而出现突然的变化,即发生稳态转换;对其机理和驱动机制的揭示将有助于对湖泊富营养化的控制及恢复.基于“多稳态”理论的稳态转换研究已广泛开展,但对浅水湖泊生态系统稳态转换的驱动机制结论各异,采用的阈值判定方法相差很大,主要有实验观测、模型模拟和统计分析3种.实验观测多关注少数特定指标,指标筛选过程复杂且工作量大;模型模拟虽能从较为全面的尺度上理解生态系统稳态变化的特征和主要机理过程,但在模型误差和不确定性的处理等问题上尚存在不足;统计分析方法基于对长时间序列数据的统计变化规律分析,用以判断或者预警稳态转换现象的发生,是目前最为常用的方法.目前稳态转换领域的研究大都是对已发生的稳态转换进行机制分析或过程反演,对未来预测与预警的问题仍然亟需加强.     

Leading indicators of trophic cascades

Regime shifts are large, long-lasting changes in ecosystems. They are often hard to predict but may have leading indicators which are detectable in advance. Potential leading indicators include wider swings in dynamics of key ecosystem variables, slower return rates after perturbation and shift of variance towards lower frequencies. We evaluated these indicators using a food web model calibrated to long-term whole-lake experiments. We investigated whether impending regime shifts driven by gradual increase in exploitation of the top predator can create signals that cascade through food webs and be discerned in phytoplankton. Substantial changes in standard deviations, return rates and spectra occurred near the switch point, even two trophic levels removed from the regime shift in fishes. Signals of regime shift can be detected well in advance, if the driver of the regime shift changes much more slowly than the dynamics of key ecosystem variables which can be sampled frequently enough to measure the indicators. However, the regime shift may occur long after the driver has passed the critical point, because of very slow transient dynamics near the critical point. Thus, the ecosystem can be poised for regime shift by the time the signal is discernible. Field tests are needed to evaluate these indicators.     

Shifts in the dynamics of productivity signal ecosystem state transitions at the biome‐scale

Understanding ecosystem dynamics and predicting directional changes in ecosystem in response to global changes are ongoing challenges in ecology. Here we present a framework that links productivity dynamics and ecosystem state transitions based on a spatially continuous dataset of aboveground net primary productivity (ANPP) from the temperate grassland of China. Across a regional precipitation gradient, we quantified spatial patterns in ANPP dynamics (variability, asymmetry and sensitivity to rainfall) and related these to transitions from desert to semi‐arid to mesic steppe. We show that these three indices of ANPP dynamics displayed distinct spatial patterns, with peaks signalling transitions between grassland types. Thus, monitoring shifts in ANPP dynamics has the potential for predicting ecosystem state transitions in the future. Current ecosystem models fail to capture these dynamics, highlighting the need to incorporate more nuanced ecological controls of productivity in models to forecast future ecosystem shifts.     

Rising variance: a leading indicator of ecological transition

Regime shifts are substantial, long-lasting reorganizations of complex systems, such as ecosystems. Large ecosystem changes such as eutrophication, shifts among vegetation types, degradation of coral reefs and regional climate change often come as surprises because we lack leading indicators for regime shifts. Increases in variability of ecosystems have been suggested to foreshadow ecological regime shifts. However, it may be difficult to discern variability due to impending regime shift from that of exogenous drivers that affect the ecosystem. We addressed this problem using a model of lake eutrophication. Lakes are subject to fluctuations in recycling associated with regime shifts, as well as fluctuating nutrient inputs. Despite the complications of noisy inputs, increasing variability of lake-water phosphorus was discernible prior to the shift to eutrophic conditions. Simulations show that rising standard deviation (SD) could signal impending shifts about a decade in advance. The rising SD was detected by studying variability around predictions of a simple time-series model, and did not depend on detailed knowledge of the actual ecosystem dynamics.     

浅水湖泊稳态转换预警识别方法局限与展望

浅水湖泊水体底泥交换强烈,极易受人类活动干扰,超过一定阈值即可能发生灾难性的稳态转换,对其有效识别有助于湖泊富营养化的及时防控与修复。浅水湖泊稳态转换可通过系统关键变量(叶绿素、溶解氧、浮游动物、鱼类等)的时间序列(判别不同稳态)、预警信号及阈值等进行识别,其中预警识别可为湖泊生态系统稳态转换提供预判信息,有利于早预警早行动。目前,浅水湖泊稳态转换预警识别因子(方差及自相关性等)主要用于"临界慢化"现象,但在强大外力作用、强烈随机扰动及极端事件下,这些"临界慢化"因子则可能出现误用或错用。基于浅水湖泊基本特征,针对稳态转换的不同驱动机制,探讨"临界慢化"因子的适用性与局限性,并展望其未来发展方向,旨在为湖泊生态系统稳态转换预警识别提供科学参考。     

沉积物记录揭示的深圳湾红树林生态系统稳态转变

稳态转换作为滨海生态系统的一种灾变现象,其过程伴随着生态系统质量下降和功能退化。深圳湾位于粤港澳大湾区的核心区域,深入理解其生态系统演化过程是进行适应性管理的重要前提。2014年于深圳湾福田红树林湿地获得4根岩芯沉积柱,通过分析沉积和生物地球化学指标（包括金属元素、营养盐、粒度和有机质指标）,重建半个世纪以来深圳湾环境的历史变迁,揭示其生态系统发生的稳态转变过程。结果表明：稳态转换发生前（1954-1980）,福田红树林沉积物中重金属、无机营养和有机物含量稳定增加,但处于较低水平;稳态转换发生后（1990-2014）,深圳湾中污染输入增加,沉积物中重金属和营养盐含量发生明显变化,深圳湾生态系统质量持续下降。通过揭示深圳湾生态系统演变过程及其稳态转变的发生规律,为粤港澳大湾区生态系统修复和管理提供重要的理论依据和参考。     

Evidence of alternate attractors from a whole-ecosystem regime shift experiment

Ecosystems sometimes shift between different states or dynamic regimes. Theory attributes these shifts to multiple ecosystem attractors. However, documenting multiple ecosystem attractors is difficult, particularly at spatial and temporal scales relevant to ecosystem management. We manipulated the fish community of a lake with the goal of causing trophic cascades and shifting the food web from a planktivore-dominated state to an alternate piscivore-dominated state. We evaluated evidence that the shifts in the fish community comprise alternate attractors using two complementary approaches. First, we calculated phase space trajectories to visualize the shift between attractors. Second, we computed generalized autoregressive conditional heteroskedasticity (GARCH) models and the Brock–Dechert–Scheinkman (BDS) test for linearity. The reconstructed phase space trajectories show the system departing a point attractor, entering a limit cycle, and then shifting to a new point attractor. The GARCH and BDS results indicate that linear explanations are not sufficient to explain the observed patterns. The results provide evidence for alternate attractors based on high-frequency time series of field measurements.     

Abrupt changes in Great Britain vegetation carbon projected under climate change

Past abrupt ‘regime shifts’ have been observed in a range of ecosystems due to various forcing factors. Large‐scale abrupt shifts are projected for some terrestrial ecosystems under climate change, particularly in tropical and high‐latitude regions. However, there is very little high‐resolution modelling of smaller‐scale future projected abrupt shifts in ecosystems, and relatively less focus on the potential for abrupt shifts in temperate terrestrial ecosystems. Here, we show that numerous climate‐driven abrupt shifts in vegetation carbon are projected in a high‐resolution model of Great Britain's land surface driven by two different climate change scenarios. In each scenario, the effects of climate and CO₂ combined are isolated from the effects of climate change alone. We use a new algorithm to detect and classify abrupt shifts in model time series, assessing the sign and strength of the non‐linear responses. The abrupt ecosystem changes projected are non‐linear responses to climate change, not simply driven by abrupt shifts in climate. Depending on the scenario, 374–1,144 grid cells of 1.5 km × 1.5 km each, comprising 0.5%–1.5% of Great Britain's land area show abrupt shifts in vegetation carbon. We find that abrupt ecosystem shifts associated with increases (rather than decreases) in vegetation carbon, show the greatest potential for early warning signals (rising autocorrelation and variance beforehand). In one scenario, 89% of abrupt increases in vegetation carbon show increasing autocorrelation and variance beforehand. Across the scenarios, 81% of abrupt increases in vegetation carbon have increasing autocorrelation and 74% increasing variance beforehand, whereas for decreases in vegetation carbon these figures are 56% and 47% respectively. Our results should not be taken as specific spatial or temporal predictions of abrupt ecosystem change. However, they serve to illustrate that numerous abrupt shifts in temperate terrestrial ecosystems could occur in a changing climate, with some early warning signals detectable beforehand.     

Robustness of early warning signals for catastrophic and non‐catastrophic transitions

Early warning signals (EWS) are statistical indicators that a rapid regime shift may be forthcoming. Their development has given ecologists hope of predicting rapid regime shifts before they occur. Accurate predictions, however, rely on the signals being appropriate to the system in question. Most of the EWS commonly applied in ecology have been studied in the context of one specific type of regime shift (the type brought on by a saddle‐node bifurcation, at which one stable equilibrium point collides with an unstable equilibrium and disappears) under one particular perturbation scheme (temporally uncorrelated noise that perturbs the net population growth rate in a density independent way). Whether and when these EWS can be applied to other ecological situations remains relatively unknown, and certainly underappreciated. We study a range of models with different types of dynamical transitions (including rapid regime shifts) and several perturbation schemes (density‐dependent uncorrelated or temporally‐correlated noise) and test the ability of EWS to warn of an approaching transition. We also test the sensitivity of our results to the amount of available pre‐transition data and various decisions that must be made in the analysis (i.e. the rolling window size and smoothing bandwidth used to compute the EWS). We find that EWS generally work well to signal an impending saddle‐node bifurcation, regardless of the autocorrelation or intensity of the noise. However, EWS do not reliably appear as expected for other types of transition. EWS were often very sensitive to the length of the pre‐transition time series analyzed, and usually less sensitive to other decisions. We conclude that the EWS perform well for saddle‐node bifurcation in a range of noise environments, but different methods should be used to predict other types of regime shifts. As a consequence, knowledge of the mechanism behind a possible regime shift is needed before EWS can be used to predict it.     

Incorporating spatial autocorrelation into species distribution models alters forecasts of climate‐mediated range shifts

Species distribution models (SDMs) are widely used to forecast changes in the spatial distributions of species and communities in response to climate change. However, spatial autocorrelation (SA) is rarely accounted for in these models, despite its ubiquity in broad‐scale ecological data. While spatial autocorrelation in model residuals is known to result in biased parameter estimates and the inflation of type I errors, the influence of unmodeled SA on species' range forecasts is poorly understood. Here we quantify how accounting for SA in SDMs influences the magnitude of range shift forecasts produced by SDMs for multiple climate change scenarios. SDMs were fitted to simulated data with a known autocorrelation structure, and to field observations of three mangrove communities from northern Australia displaying strong spatial autocorrelation. Three modeling approaches were implemented: environment‐only models (most frequently applied in species' range forecasts), and two approaches that incorporate SA; autologistic models and residuals autocovariate (RAC) models. Differences in forecasts among modeling approaches and climate scenarios were quantified. While all model predictions at the current time closely matched that of the actual current distribution of the mangrove communities, under the climate change scenarios environment‐only models forecast substantially greater range shifts than models incorporating SA. Furthermore, the magnitude of these differences intensified with increasing increments of climate change across the scenarios. When models do not account for SA, forecasts of species' range shifts indicate more extreme impacts of climate change, compared to models that explicitly account for SA. Therefore, where biological or population processes induce substantial autocorrelation in the distribution of organisms, and this is not modeled, model predictions will be inaccurate. These results have global importance for conservation efforts as inaccurate forecasts lead to ineffective prioritization of conservation activities and potentially to avoidable species extinctions.     

Red herrings revisited: spatial autocorrelation and parameter estimation in geographical ecology

There have been numerous claims in the ecological literature that spatial autocorrelation in the residuals of ordinary least squares (OLS) regression models results in shifts in the partial coefficients, which bias the interpretation of factors influencing geographical patterns. We evaluate the validity of these claims using gridded species richness data for the birds of North America, South America, Europe, Africa, the ex‐USSR, and Australia. We used richness in 110×110 km cells and environmental predictor variables to generate OLS and simultaneous autoregressive (SAR) multiple regression models for each region. Spatial correlograms of the residuals from each OLS model were then used to identify the minimum distance between cells necessary to avoid short‐distance residual spatial autocorrelation in each data set. This distance was used to subsample cells to generate spatially independent data. The partial OLS coefficients estimated with the full dataset were then compared to the distributions of coefficients created with the subsamples. We found that OLS coefficients generated from data containing residual spatial autocorrelation were statistically indistinguishable from coefficients generated from the same data sets in which short‐distance spatial autocorrelation was not present in all 22 coefficients tested. Consistent with the statistical literature on this subject, we conclude that coefficients estimated from OLS regression are not seriously affected by the presence of spatial autocorrelation in gridded geographical data. Further, shifts in coefficients that occurred when using SAR tended to be correlated with levels of uncertainty in the OLS coefficients. Thus, shifts in the relative importance of the predictors between OLS and SAR models are expected when small‐scale patterns for these predictors create weaker and more unstable broad‐scale coefficients. Our results indicate both that OLS regression is unbiased and that differences between spatial and nonspatial regression models should be interpreted with an explicit awareness of spatial scale.     

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.     

Region‐wide changes in marine ecosystem dynamics: state‐space models to distinguish trends from step changes

Regime shifts are sudden changes in ecosystem structure that can be detected across several ecosystem components. The concept that regime shifts are common in marine ecosystems has gained popularity in recent years. Many studies have searched for the step‐like changes in ecosystem state expected under a simple interpretation of this idea. However, other kinds of change, such as pervasive trends, have often been ignored. We assembled over 300 ecological time series from seven UK marine regions, covering two to three decades. We developed state‐space models for the first principal component of the time series in each region, a common measure of ecosystem state. Our models allowed both trends and step changes, possibly in combination. We found trends in three of seven regions and step changes in two of seven regions. Gradual and sudden changes are therefore important trajectories to consider in marine ecosystems.     

Land-cover data improve bioclimatic models for anurans and turtles at a regional scale

Aim We investigated whether accounting for land cover could improve bioclimatic models for eight species of anurans and three species of turtles at a regional scale. We then tested whether accounting for spatial autocorrelation could significantly improve bioclimatic models after statistically controlling for the effects of land cover. Location Nova Scotia, eastern Canada. Methods Species distribution data were taken from a recent (1999–2003) herpetofaunal atlas. Generalized linear models were used to relate the presence or absence of each species to climate and land‐cover variables at a 10‐km resolution. We then accounted for spatial autocorrelation using an autocovariate or third‐order trend surface of the geographical coordinates of each grid square. Finally, variance partitioning was used to explore the independent and joint contributions of climate, land cover and spatial autocorrelation. Results The inclusion of land cover significantly increased the explanatory power of bioclimatic models for 10 of the 11 species. Furthermore, including land cover significantly increased predictive performance for eight of the 11 species. Accounting for spatial autocorrelation improved model fit for rare species but generally did not improve prediction success. Variance partitioning demonstrated that this lack of improvement was a result of the high correlation between climate and trend‐surface variables. Main conclusions The results of this study suggest that accounting for the effects of land cover can significantly improve the explanatory and predictive power of bioclimatic models for anurans and turtles at a regional scale. We argue that the integration of climate and land‐cover data is likely to produce more accurate spatial predictions of contemporary herpetofaunal diversity. However, the use of land‐cover simulations in climate‐induced range‐shift projections introduces additional uncertainty into the predictions of bioclimatic models. Further research is therefore needed to determine whether accounting for the effects of land cover in range‐shift projections is merited.