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The heart of the scientific enterprise is a rational effort to understand the causes behind the phenomena we observe. In large-scale complex dynamical systems such as the Earth system, real experiments are rarely feasible. However, a rapidly increasing amount of observational and simulated data opens up the use of novel data-driven causal methods beyond the commonly adopted correlation techniques. Here, we give an overview of causal inference frameworks and identify promising generic application cases common in Earth system sciences and beyond. We discuss challenges and initiate the benchmark platform causeme.net to close the gap between method users and developers. Questions of causality are ubiquitous in Earth system sciences and beyond, yet correlation techniques still prevail. This Perspective provides an overview of causal inference methods, identifies promising applications and methodological challenges, and initiates a causality benchmark platform.

Tropical forests modify the conditions they depend on through feedbacks at different spatial scales. These feedbacks shape the hysteresis (history-dependence) of tropical forests, thus controlling their resilience to deforestation and response to climate change. Here, we determine the emergent hysteresis from local-scale tipping points and regional-scale forest-rainfall feedbacks across the tropics under the recent climate and a severe climate-change scenario. By integrating remote sensing, a global hydrological model, and detailed atmospheric moisture tracking simulations, we find that forest-rainfall feedback expands the geographic range of possible forest distributions, especially in the Amazon. The Amazon forest could partially recover from complete deforestation, but may lose that resilience later this century. The Congo forest currently lacks resilience, but is predicted to gain it under climate change, whereas forests in Australasia are resilient under both current and future climates. Our results show how tropical forests shape their own distributions and create the climatic conditions that enable them. Tropical rainforests partly create their own climatic conditions by promoting precipitation, therefore rainforest losses may trigger dramatic shifts. Here the authors combine remote sensing, hydrological modelling, and atmospheric moisture tracking simulations to assess forest-rainfall feedbacks in three major tropical rainforest regions on Earth and simulate potential changes under a severe climate change scenario.

Tipping points in complex systems may imply risks of unwanted collapse, but also opportunities for positive change. Our capacity to navigate such risks and opportunities can be boosted by combining emerging insights from two unconnected fields of research. One line of work is revealing fundamental architectural features that may cause ecological networks, financial markets, and other complex systems to have tipping points. Another field of research is uncovering generic empirical indicators of the proximity to such critical thresholds. Although sudden shifts in complex systems will inevitably continue to surprise us, work at the crossroads of these emerging fields offers new approaches for anticipating critical transitions.

Tip-offs for tipping points Many complex systems, ranging from ecosystems to financial markets and the climate, can have critical thresholds or tipping points where a sudden shift from one stable state to a contrasting regime may occur. Predicting such critical points before they are reached is extremely difficult, but work in different fields of science is now suggesting the existence of generic early warning signals that may indicate for a wide class of systems if a critical threshold is approaching. Scheffer et al . conclude their review of this work optimistically: in situations where the existence of a critical transition is suspected, the generic character of the warning signs suggests that they may provide valuable information on whether the probability of a major event is increasing. Complex dynamical systems, ranging from ecosystems to financial markets and the climate, can have tipping points at which a sudden shift to a contrasting dynamical regime may occur. Although predicting such critical points before they are reached is extremely difficult, work in different scientific fields is now suggesting the existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching.

All life requires the capacity to recover from challenges that are as inevitable as they are unpredictable. Understanding this resilience is essential for managing the health of humans and their livestock. It has long been difficult to quantify resilience directly, forcing practitioners to rely on indirect static indicators of health. However, measurements from wearable electronics and other sources now allow us to analyze the dynamics of physiology and behavior with unsurpassed resolution. The resulting flood of data coincides with the emergence of novel analytical tools for estimating resilience from the pattern of microrecoveries observed in natural time series. Such dynamic indicators of resilience may be used to monitor the risk of systemic failure across systems ranging from organs to entire organisms. These tools invite a fundamental rethinking of our approach to the adaptive management of health and resilience.

Many dynamical systems, including lakes, organisms, ocean circulation patterns, or financial markets, are now thought to have tipping points where critical transitions to a contrasting state can happen. Because critical transitions can occur unexpectedly and are difficult to manage, there is a need for methods that can be used to identify when a critical transition is approaching. Recent theory shows that we can identify the proximity of a system to a critical transition using a variety of so-called 'early warning signals', and successful empirical examples suggest a potential for practical applicability. However, while the range of proposed methods for predicting critical transitions is rapidly expanding, opinions on their practical use differ widely, and there is no comparative study that tests the limitations of the different methods to identify approaching critical transitions using time-series data. Here, we summarize a range of currently available early warning methods and apply them to two simulated time series that are typical of systems undergoing a critical transition. In addition to a methodological guide, our work offers a practical toolbox that may be used in a wide range of fields to help detect early warning signals of critical transitions in time series data.

A number of ecosystems can exhibit abrupt shifts between alternative stable states. Because of their important ecological and economic consequences, recent research has focused on devising early warning signals for anticipating such abrupt ecological transitions. In particular, theoretical studies show that changes in spatial characteristics of the system could provide early warnings of approaching transitions. However, the empirical validation of these indicators lag behind their theoretical developments. Here, we summarize a range of currently available spatial early warning signals, suggest potential null models to interpret their trends, and apply them to three simulated spatial data sets of systems undergoing an abrupt transition. In addition to providing a step-by-step methodology for applying these signals to spatial data sets, we propose a statistical toolbox that may be used to help detect approaching transitions in a wide range of spatial data. We hope that our methodology together with the computer codes will stimulate the application and testing of spatial early warning signals on real spatial data.

The size of the basin of attraction in ecosystems with alternative stable states is often referred to as “ecological resilience.” Ecosystems with a low ecological resilience may easily be tipped into an alternative basin of attraction by a stochastic event. Unfortunately, it is very difficult to measure ecological resilience in practice. Here we show that the rate of recovery from small perturbations (sometimes called “engineering resilience”) is a remarkably good indicator of ecological resilience. Such recovery rates decrease as a catastrophic regime shift is approached, a phenomenon known in physics as “critical slowing down.” We demonstrate the robust occurrence of critical slowing down in six ecological models and outline a possible experimental approach to quantify differences in recovery rates. In all the models we analyzed, critical slowing down becomes apparent quite far from a threshold point, suggesting that it may indeed be of practical use as an early warning signal. Despite the fact that critical slowing down could also indicate other critical transitions, such as a stable system becoming oscillatory, the robustness of the phenomenon makes it a promising indicator of loss of resilience and the risk of upcoming regime shifts in a system.

Various complex systems, such as the climate, ecosystems, and physical and mental health can show large shifts in response to small changes in their environment. These ‘tipping points’ are notoriously hard to predict based on trends. However, in the past 20 years several indicators pointing to a loss of resilience have been developed. These indicators use fluctuations in time series to detect critical slowing down preceding a tipping point. Most of the existing indicators are based on models of one-dimensional systems. However, complex systems generally consist of multiple interacting entities. Moreover, because of technological developments and wearables, multivariate time series are becoming increasingly available in different fields of science. In order to apply the framework of resilience indicators to multivariate time series, various extensions have been proposed. Not all multivariate indicators have been tested for the same types of systems and therefore a systematic comparison between the methods is lacking. Here, we evaluate the performance of the different multivariate indicators of resilience loss in different scenarios. We show that there is not one method outperforming the others. Instead, which method is best to use depends on the type of scenario the system is subject to. We propose a set of guidelines to help future users choose which multivariate indicator of resilience is best to use for their particular system.

Recent work has indicated that tropical forest and savanna can be alternative stable states under a range of climatic conditions. However, dynamical systems theory suggests that in case of strong spatial interactions between patches of forest and savanna, a boundary between both states is only possible at conditions in which forest and savanna are equally stable, called the ‘Maxwell point.’ Frequency distributions of MODIS tree-cover data at 250 m resolution were used to estimate such Maxwell points with respect to the amount and seasonality of rainfall in both South America and Africa. We tested on a 0.5° scale whether there is a larger probability of local coexistence of forests and savannas near the estimated Maxwell points. Maxwell points for South America and Africa were estimated at 1760 and 1580 mm mean annual precipitation and at Markham’s Seasonality Index values of 50 and 24 %. Although the probability of local coexistence was indeed highest around these Maxwell points, local coexistence was not limited to the Maxwell points. We conclude that critical transitions between forest and savanna may occur when climatic changes exceed a critical value. However, we also conclude that spatial interactions between patches of forest and savanna may reduce the hysteresis that can be observed in isolated patches, causing more predictable forest-savanna boundaries than continental-scale analyses of tree cover indicate. This effect could be less pronounced in Africa than in South America, where the forestsavanna boundary is substantially affected by rainfall seasonality.