The rapid prosperity of China's Pearl River Delta from the perspective of social-ecological coupling: implications for sustainable management

Systems theory and complex science, especially knowledge of social-ecological interdependencies, are urgently needed in planning and decision-making on sustainable urban development due to the intensification of the contradiction between human development and nature conservation. Here, we present an analytical framework, the "social-ecological coupling trajectory", that integrates the social-ecological coupling, multi-stability, causal feedbacks and sustainable management through understanding the evolution of the urban social-ecological system (SES). This framework is applied to a typical urban SES, i.e., China's rapidly prosperous Pearl River Delta (PRD). Our results indicate that the SES evolution in the PRD is a phased process, which is accompanied by a continuous decline in major ecosystem services (ESs) and the disproportionate decline of ecological management performance. Further analysis shows that social and economic policies have a decisive role in driving the evolution of SES and the cumulative effect of sustained human interference is directly linked to the disproportionate increase in sustainability challenges. The findings of critical slowing down and evolution patterns of SES in the PRD may provide evidence for the threshold recognition and regime shift prediction in SES. In sum, this study expands the theoretical framework and empirical knowledge of SES evolution and provides a pathway for sustainable development of regions seeking prosperity from the social-ecological coupling perspective.

Optimal sampling of spatial patterns improves deep learning-based early warning signals of critical transitions

Complex spatio-temporal systems like lakes, forests and climate systems exhibit alternative stable states. In such systems, as the threshold value of the driver is crossed, the system may experience a sudden (discontinuous) transition or smooth (continuous) transition to an undesired steady state. Theories predict that changes in the structure of the underlying spatial patterns precede such transitions. While there has been a large body of research on identifying early warning signals of critical transitions, the problem of forecasting the type of transitions (sudden versus smooth) remains an open challenge. We address this gap by developing an advanced machine learning (ML) toolkit that serves as an early warning indicator of spatio-temporal critical transitions, Spatial Early Warning Signal Network (S-EWSNet). ML models typically resemble a black box and do not allow envisioning what the model learns in discerning the labels. Here, instead of naively relying upon the deep learning model, we let the deep neural network learn the latent features characteristic of transitions via an optimal sampling strategy (OSS) of spatial patterns. The S-EWSNet is trained on data from a stochastic cellular automata model deploying the OSS, providing an early warning indicator of transitions while detecting its type in simulated and empirical samples.

Systematic analysis and optimization of early warning signals for critical transitions using distribution data

Abrupt shifts between alternative regimes occur in complex systems, from cell regulation to brain functions to ecosystems. Several model-free early warning signals (EWS) have been proposed to detect impending transitions, but failure or poor performance in some systems have called for better investigation of their generic applicability. Notably, there are still ongoing debates whether such signals can be successfully extracted from data in particular from biological experiments. In this work, we systematically investigate properties and performance of dynamical EWS in different deteriorating conditions, and we propose an optimized combination to trigger warnings as early as possible, eventually verified on experimental data from microbiological populations. Our results explain discrepancies observed in the literature between warning signs extracted from simulated models and from real data, provide guidance for EWS selection based on desired systems and suggest an optimized composite indicator to alert for impending critical transitions using distribution data.

Using functional indicators to detect state changes in terrestrial ecosystems

Indicators to predict ecosystem state change are urgently needed to cope with the degradation of ecosystem services caused by global change. With the development of new technologies for measuring ecosystem function with fine spatiotemporal resolution over broad areas, we are in the era of 'big data'. However, it is unclear how large, emerging datasets can be used to anticipate ecosystem state change. We propose the construction of indicators based on functional variables (flows) and state variables (pools) to predict future ecosystem state changes. The indicators identified here may be useful signals for doing so. In addition, functional indicators have explicit ecological meanings that can identify the ecological mechanism that is causing state changes, and can thus be used to improve ecosystem models.

The absence of alternative stable states in vegetation cover of northeastern India

Globally, forests and savannah are shown to be alternative stable states for intermediate rainfall regimes. This has implications for how these ecosystems respond to changing rainfall conditions. However, we know little about the occurrence of alternative stable states in forest ecosystems in India. In this study, we investigate the possibility of alternative stable states in the vegetation cover of northeastern India, which is a part of the Eastern Himalaya and the Indo-Burma biodiversity hotspots. To do so, we construct the so-called state diagram, by plotting frequency distributions of vegetation cover as a function of mean annual precipitation (MAP). We use remotely sensed satellite data of the enhanced vegetation index (EVI) as a proxy for vegetation cover (at 1 km resolution). We find that EVI exhibits unimodal distribution across a wide range of MAP. Specifically, EVI increases monotonically in the range 1000-2000 mm of MAP, after which it plateaus. This range of MAP corresponds to the vegetation transitional zone (1200-3700 m), whereas MAP greater than 2000 mm covers the larger extent of the tropical forest (less than or equal to 1200 m) of northeast India. In other words, we find no evidence for alternative stable states in vegetation cover or forest states at coarser scales in northeast India.

Machine learning methods trained on simple models can predict critical transitions in complex natural systems

Forecasting sudden changes in complex systems is a critical but challenging task, with previously developed methods varying widely in their reliability. Here we develop a novel detection method, using simple theoretical models to train a deep neural network to detect critical transitions-the Early Warning Signal Network (EWSNet). We then demonstrate that this network, trained on simulated data, can reliably predict observed real-world transitions in systems ranging from rapid climatic change to the collapse of ecological populations. Importantly, our model appears to capture latent properties in time series missed by previous warning signals approaches, allowing us to not only detect if a transition is approaching, but critically whether the collapse will be catastrophic or non-catastrophic. These novel properties mean EWSNet has the potential to serve as an indicator of transitions across a broad spectrum of complex systems, without requiring information on the structure of the system being monitored. Our work highlights the practicality of deep learning for addressing further questions pertaining to ecosystem collapse and has much broader management implications.

Divergent responses of primary production to increasing precipitation variability in global drylands

Interannual variability in precipitation has increased globally as climate warming intensifies. The increased variability impacts both terrestrial plant production and carbon (C) sequestration. However, mechanisms driving these changes are largely unknown. Here, we examined mechanisms underlying the response of aboveground net primary production (ANPP) to interannual precipitation variability in global drylands with mean annual precipitation (MAP) <500 mm year^-1 , using a combined approach of data synthesis and process-based modeling. We found a hump-shaped response of ANPP to precipitation variability along the MAP gradient. The response was positive when MAP < ~300 mm year^-1 and negative when MAP was higher than this threshold, with a positive peak at 140 mm year^-1 . Transpiration and subsoil water content mirrored the response of ANPP to precipitation variability; evaporation responded negatively and water loss through runoff and drainage responded positively to precipitation variability. Mean annual temperature, soil type, and plant physiological traits all altered the magnitude but not the pattern of the response of ANPP to precipitation variability along the MAP gradient. By extrapolating to global drylands (<500 mm year^-1  MAP), we estimated that ANPP would increase by 15.2 ± 6.0 Tg C year^-1 in arid and hyper-arid lands and decrease by 2.1 ± 0.5 Tg C year^-1 in dry sub-humid lands under future changes in interannual precipitation variability. Thus, increases in precipitation variability will enhance primary production in many drylands in the future.

Forecasting semi-arid biome shifts in the Anthropocene

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.

Phylogenetic and biogeographic controls of plant nighttime stomatal conductance

The widely documented phenomenon of nighttime stomatal conductance g_sn could lead to substantial water loss with no carbon gain, and thus it remains unclear whether nighttime stomatal conductance confers a functional advantage. Given that studies of g_sn have focused on controlled environments or small numbers of species in natural environments, a broad phylogenetic and biogeographic context could provide insights into potential adaptive benefits of g_sn . We measured g_sn on a diverse suite of species (n = 73) across various functional groups and climates-of-origin in a common garden to study the phylogenetic and biogeographic/climatic controls on g_sn and further assessed the degree to which g_sn co-varied with leaf functional traits and daytime gas-exchange rates. Closely related species were more similar in g_sn than expected by chance. Herbaceous species had higher g_sn than woody species. Species that typically grow in climates with lower mean annual precipitation - where the fitness cost of water loss should be the highest - generally had higher g_sn . Our results reveal the highest g_sn rates in species from environments where neighboring plants compete most strongly for water, suggesting a possible role for the competitive advantage of g_sn .

Inferring critical thresholds of ecosystem transitions from spatial data

Ecosystems can undergo abrupt transitions between alternative stable states when the driver crosses a critical threshold. Dynamical systems theory shows that when ecosystems approach the point of loss of stability associated with these transitions, they take a long time to recover from perturbations, a phenomenon known as critical slowing down. This generic feature of dynamical systems can offer early warning signals of abrupt transitions. However, these signals are qualitative and cannot quantify the thresholds of drivers at which transition may occur. Here, we propose a method to estimate critical thresholds from spatial data. We show that two spatial metrics, spatial variance and autocorrelation of ecosystem state variable, computed along driver gradients can be used to estimate critical thresholds. First, we investigate cellular-automaton models of ecosystem dynamics that show a transition from a high-density state to a bare state. Our models show that critical thresholds can be estimated as the ecosystem state and the driver values at which spatial variance and spatial autocorrelation of the ecosystem state are maximum. Next, to demonstrate the application of the method, we choose remotely sensed vegetation data (Enhanced Vegetation Index, EVI) from regions in central Africa and northeast Australia that exhibit alternative states in woody cover. We draw transects (8 × 90 km) that span alternative stable states along rainfall gradients. Our analyses of spatial variance and autocorrelation of EVI along transects yield estimates of critical thresholds. These estimates match reasonably well with those obtained by an independent method that uses large-scale (250 × 200 km) spatial data sets. Given the generality of the principles that underlie our method, our method can be applied to a variety of ecosystems that exhibit alternative stable states.

Divergent evapotranspiration partition dynamics between shrubs and grasses in a shrub-encroached steppe ecosystem

Previous evapotranspiration (ET) partitioning studies have usually neglected competitions and interactions between antagonistic plant functional types. This study investigated whether shrubs and grasses have divergent ET partition dynamics impacted by different water-use patterns, canopy structures, and physiological properties in a shrub-encroached steppe ecosystem in Inner Mongolia, China. The soil water-use patterns of shrubs and grasses have been quantified by an isotopic tracing approach and coupled into an improved multisource energy balance model to partition ET fluxes into soil evaporation, grass transpiration, and shrub transpiration. The mean fractional contributions to total ET were 24 ± 13%, 20 ± 4%, and 56 ± 16% for shrub transpiration, grass transpiration, and soil evaporation respectively during the growing season. Difference in ecohydrological connectivity and leaf development both contributed to divergent transpiration partitioning between shrubs and grasses. Shrub-encroachment processes result in larger changes in the ET components than in total ET flux, which could be well explained by changes in canopy resistance, an ecosystem function dominated by the interaction of soil water-use patterns and ecosystem structure. The analyses presented here highlight the crucial effects of vegetation structural changes on the processes of land-atmosphere interaction and climate feedback.

Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation

Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the effect of the rate of change of the bifurcation parameter on the tipping points. In this work, we consider a subcritical stochastic Hopf bifurcation under two scenarios: the bifurcation parameter is first changed in a quasi-steady manner and then, with a finite ramping rate. In the latter case, a rate-dependent bifurcation delay is observed and exemplified experimentally using a thermoacoustic instability in a combustion chamber. This delay increases with the rate of change. This leads to a state transition of larger amplitude compared with the one that would be experienced by the system with a quasi-steady change of the parameter. We also bring experimental evidence of a dynamic hysteresis caused by the bifurcation delay when the parameter is ramped back. A surrogate model is derived in order to predict the statistic of these delays and to scrutinize the underlying stochastic dynamics. Our study highlights the dramatic influence of a finite rate of change of bifurcation parameters upon tipping points, and it pinpoints the crucial need of considering this effect when investigating critical transitions.