Heteroskedasticity as a leading indicator of desertification in spatially explicit data

Regime shifts are abrupt transitions between alternate ecosystem states including desertification in arid regions due to drought or overgrazing. Regime shifts may be preceded by statistical anomalies such as increased autocorrelation, indicating declining resilience and warning of an impending shift. Tests for conditional heteroskedasticity, a type of clustered variance, have proven powerful leading indicators for regime shifts in time series data, but an analogous indicator for spatial data has not been evaluated. A spatial analog for conditional heteroskedasticity might be especially useful in arid environments where spatial interactions are critical in structuring ecosystem pattern and process. We tested the efficacy of a test for spatial heteroskedasticity as a leading indicator of regime shifts with simulated data from spatially extended vegetation models with regular and scale‐free patterning. These models simulate shifts from extensive vegetative cover to bare, desert‐like conditions. The magnitude of spatial heteroskedasticity increased consistently as the modeled systems approached a regime shift from vegetated to desert state. Relative spatial autocorrelation, spatial heteroskedasticity increased earlier and more consistently. We conclude that tests for spatial heteroskedasticity can contribute to the growing toolbox of early warning indicators for regime shifts analyzed with spatially explicit data.     

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。     

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.     

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。     

Interdisciplinary knowledge exchange across scales in a globally changing marine environment

The effects of anthropogenic global environmental change on biotic and abiotic processes have been reported in aquatic systems across the world. Complex synergies between concurrent environmental stressors and the resilience of the system to regime shifts, which vary in space and time, determine the capacity for marine systems to maintain structure and function with global environmental change. Consequently, an interdisciplinary approach that facilitates the development of new methods for the exchange of knowledge between scientists across multiple scales is required to effectively understand, quantify and predict climate impacts on marine ecosystem services. We use a literature review to assess the limitations and assumptions of current pathways to exchange interdisciplinary knowledge and the transferability of research findings across spatial and temporal scales and levels of biological organization to advance scientific understanding of global environmental change in marine systems. We found that species‐specific regional scale climate change research is most commonly published, and “supporting” is the ecosystem service most commonly referred to in publications. In addition, our paper outlines a trajectory for the future development of integrated climate change science for sustaining marine ecosystem services such as investment in interdisciplinary education and connectivity between disciplines.     

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.     

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.     

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.     

Spatially heterogeneous pressure raises risk of catastrophic shifts

Ecosystems may exhibit catastrophic shifts, i.e. abrupt and irreversible responses of ecosystem functions and services to continuous changes in external conditions. The search for early warning signs of approaching shifts has so far mainly been conducted on theoretical models assuming spatially-homogeneous external pressures (e.g. climatic). Here, we investigate how a spatially explicit pressure may affect ecosystems’ risk of catastrophic shifts and the associated spatial early-warning signs. As a case study, we studied a dryland vegetation model assuming ‘associational resistance’, i.e. the mutual reduction of local grazing impact by neighboring plants sharing the investment in defensive traits. Consequently, grazing pressure depends on the local density of plants and is thus spatially-explicit. We focus on the distribution of vegetation patch sizes, which can be assessed using remote sensing and are candidate early warning signs of catastrophic shifts in drylands. We found that spatially explicit grazing affected both the resilience and the spatial patterns of the landscape. Grazing impact became self-enhancing in more fragmented landscapes, disrupted patch growth and put apparently ‘healthy’ drylands under high risks of catastrophic shifts. Our study highlights that a spatially explicit pressure may affect the nature of the spatial pattern observed and thereby change the interpretation of the early warning signs. This may generalize to other ecosystems exhibiting self-organized spatial patterns, where a spatially-explicit pressure may interfere with pattern formation.     

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.     

Macroecological scale effects of biodiversity on ecosystem functions under environmental change

Conserving different spatial and temporal dimensions of biological diversity is considered necessary for maintaining ecosystem functions under predicted global change scenarios. Recent work has shifted the focus from spatially local (α‐diversity) to macroecological scales (β‐ and γ‐diversity), emphasizing links between macroecological biodiversity and ecosystem functions (MB–EF relationships). However, before the outcomes of MB–EF analyses can be useful to real‐world decisions, empirical modeling needs to be developed for natural ecosystems, incorporating a broader range of data inputs, environmental change scenarios, underlying mechanisms, and predictions. We outline the key conceptual and technical challenges currently faced in developing such models and in testing and calibrating the relationships assumed in these models using data from real ecosystems. These challenges are explored in relation to two potential MB–EF mechanisms: “macroecological complementarity” and “spatiotemporal compensation.” Several regions have been sufficiently well studied over space and time to robustly test these mechanisms by combining cutting‐edge spatiotemporal methods with remotely sensed data, including plant community data sets in Australia, Europe, and North America. Assessing empirical MB–EF relationships at broad spatiotemporal scales will be crucial in ensuring these macroecological processes can be adequately considered in the management of biodiversity and ecosystem functions under global change.     

Hydrologic variability in dryland regions: impacts on ecosystem dynamics and food security

Research on ecosystem and societal response to global environmental change typically considers the effects of shifts in mean climate conditions. There is, however, some evidence of ongoing changes also in the variance of hydrologic and climate fluctuations. A relatively high interannual variability is a distinctive feature of the hydrologic regime of dryland regions, particularly at the desert margins. Hydrologic variability has an important impact on ecosystem dynamics, food security and societal reliance on ecosystem services in water-limited environments. Here, we investigate some of the current patterns of hydrologic variability in drylands around the world and review the major effects of hydrologic fluctuations on ecosystem resilience, maintenance of biodiversity and food security. We show that random hydrologic fluctuations may enhance the resilience of dryland ecosystems by obliterating bistable deterministic behaviours and threshold-like responses to external drivers. Moreover, by increasing biodiversity and the associated ecosystem redundancy, hydrologic variability can indirectly enhance post-disturbance recovery, i.e. ecosystem resilience.     

A comprehensive landscape genomics approach for seed sourcing strategies in landscapes under varying degrees of habitat disturbance

As most ecosystems around the world are threatened by anthropogenic degradation and climate change, there is an increasing urgency to implement restoration strategies aiming at ensuring ecosystem self‐sustainability and resilience. An initial step towards that goal relies on selecting the most suitable seed sources for a successful revegetation, which can be extremely challenging in highly degraded landscapes. The most common seed sourcing strategy is to select local seeds because it is assumed that plants experience strong adaptations to their natal sites. An alternative strategy is the selection of climate‐adapted genotypes to future conditions. While considering future climatic projections is important to account for spatial shifts in climate to inform assisted gene flow and translocations, to restore highly degraded landscapes we need a comprehensive approach that first accounts for species adaptations to current at‐site environmental conditions. In this issue of Molecular Ecology Resources, Carvalho et al. present a novel landscape genomics framework to identify the most appropriate seed sourcing strategy for moderately and highly degraded sites by integrating genotype, phenotype and environmental data in a spatially explicit context for two native plant species with potential to help restore iron‐rich Amazonian savannas. This framework is amenable to be applicable and adapted to a broad range of restoration initiatives, as the dichotomy between focusing on the current or future climatic conditions should depend on the goals and environmental circumstances of each restoration site.     

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.     

Linking remotely sensed ecosystem resilience with forest mortality across the continental United States

Episodes of forest mortality have been observed worldwide associated with climate change, impacting species composition and ecosystem services such as water resources and carbon sequestration. Yet our ability to predict forest mortality remains limited, especially across large scales. Time series of satellite imagery has been used to document ecosystem resilience globally, but it is not clear how well remotely sensed resilience can inform the prediction of forest mortality across continental, multi-biome scales. Here, we leverage forest inventories across the continental United States to systematically assess the potential of ecosystem resilience derived using different data sets and methods to predict forest mortality. We found high resilience was associated with low mortality in eastern forests but was associated with high mortality in western regions. The unexpected resilience–mortality relation in western United States may be due to several factors including plant trait acclimation, insect population dynamics, or resource competition. Overall, our results not only supported the opportunity to use remotely sensed ecosystem resilience to predict forest mortality but also highlighted that ecological factors may have crucial influences because they can reverse the sign of the resilience–mortality relationships.     

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.     

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.     

Ecosystems off track: rate‐induced critical transitions in ecological models

Theory suggests that gradual environmental change may erode the resilience of ecosystems and increase their susceptibility to critical transitions. This notion has received a lot of attention in ecology in recent decades. An important question receiving far less attention is whether ecosystems can cope with the rapid environmental changes currently imposed. The importance of this question was recently highlighted by model studies showing that elevated rates of change may trigger critical transitions, whereas slow environmental change would not. This paper aims to provide a mechanistic understanding of these rate‐induced critical transitions to facilitate identification of rate sensitive ecosystems. Analysis of rate sensitive ecological models is challenging, but we demonstrate how rate‐induced transitions in an elementary model can still be understood. Our analyses reveal that rate‐induced transitions 1) occur if the rate of environmental change is high compared to the response rate of ecosystems, 2) are driven by rates, rather than magnitudes, of change and 3) occur once a critical rate of change is exceeded. Disentangling rate‐induced transitions from classical transitions in observations would be challenging. However, common features of rate‐sensitive models suggest that ecosystems with coupled fast–slow dynamics, exhibiting repetitive catastrophic shifts or displaying periodic spatial patterns are more likely to be rate sensitive. Our findings are supported by experimental studies showing rate‐dependent outcomes. Rate sensitivity of models suggests that the common definition of ecological resilience is not suitable for a subset of real ecosystems and that formulating limits to magnitudes of change may not always safeguard against ecosystem degradation. Synthesis Understanding and predicting ecosystem response to environmental change is one of the key challenges in ecology. Model studies have suggested that slow, gradual environmental change beyond some critical threshold can trigger so‐called critical transitions and abrupt ecosystem degradation. An important question remains however whether ecosystems can cope with the ongoing rapid anthropogenic environmental changes to which they are currently imposed. In this study we demonstrate that in some ecological models elevated rates of change can trigger critical transitions even if slow environmental change of the same magnitude would not. Such rateinduced critical transitions in models suggest that concepts like resilience and planetary boundaries may not always be sufficient to explain and prevent ecosystem degradation.     

Tracking unstable states: ecosystem dynamics in a changing world

Ecological systems can show complex and sometimes abrupt responses to environmental change, with important implications for their resilience. Theories of alternate stable states have been used to predict regime shifts of ecosystems as equilibrium responses to sufficiently slow environmental change. The actual rate of environmental change is a key factor affecting the response, yet we are still lacking a non-equilibrium theory that explicitly considers the influence of this rate of environmental change. We present a metacommunity model of predator–prey interactions displaying multiple stable states, and we impose an explicit rate of environmental change in habitat quality (carrying capacity) and connectivity (dispersal rate). We study how regime shifts depend on the rate of environmental change and compare the outcome with a stability analysis in the corresponding constant environment. Our results reveal that in a changing environment, the community can track states that are unstable in the constant environment. This tracking can lead to regime shifts, including local extinctions, that are not predicted by alternative stable state theory. In our metacommunity, tracking unstable states also controls the maintenance of spatial heterogeneity and spatial synchrony. Tracking unstable states can also lead to regime shifts that may be reversible or irreversible. Our study extends current regime shift theories to integrate rate-dependent responses to environmental change. It reveals the key role of unstable states for predicting transient dynamics and long-term resilience of ecological systems to climate change.     

Stoichiometric distribution models: ecological stoichiometry at the landscape extent

Human activities are altering the fundamental geography of biogeochemicals. Yet we lack an understanding of how the spatial patterns in organismal stoichiometry affect biogeochemical processes and the tools to predict the impacts of global changes on biogeochemical processes. In this contribution we develop stoichiometric distribution models (StDMs), which allow us to map spatial structure in resource elemental composition across a landscape and evaluate spatial responses of consumers. We parameterise StDMs for a consumer‐resource (moose‐white birch) system and demonstrate that we can develop predictive models of resource stoichiometry across a landscape and that such models could improve our predictions of consumer space use. With results from our study system application, we argue that explicit consideration of the spatial patterns in organismal elemental composition may uncover emergent individual, population, community and ecosystem properties that are not revealed at the local extents routinely used in ecological stoichiometry. We discuss perspectives for further developments and application of StDMs to advance three emerging frameworks for spatial ecosystem ecology in an era of global change; meta‐ecosystem theory, macroecological stoichiometry and remotely sensed biogeochemistry. Progress on these emerging frameworks will allow for the integration of ecological stoichiometry and individual space use and fitness.