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.

Alzheimer's disease (AD) is a complex, multicausal disorder involving several spatiotemporal scales and scientific domains. While many studies focus on specific parts of this system, the complexity Electronic supplementary material The online version of this article (

Background: The past decades of research have seen an increase in statistical tools to explore the complex dynamics of mental health from patient data, yet the application of these tools in clinical practice remains uncommon. This is surprising, given that clinical reasoning, e.g., case conceptualizations, largely coincides with the dynamical system approach. We argue that the gap between statistical tools and clinical practice can partly be explained by the fact that current estimation techniques disregard theoretical and practical considerations relevant to psychotherapy. To address this issue, we propose that case conceptualizations should be formalized. We illustrate this approach by introducing a computational model of functional analysis, a framework commonly used by practitioners to formulate case conceptualizations and design patient-tailored treatment. Methods: We outline the general approach of formalizing idiographic theories, drawing on the example of a functional analysis for a patient suffering from panic disorder. We specified the system using a series of differential equations and simulated different scenarios; first, we simulated data without intervening in the system to examine the effects of avoidant coping on the development of panic symptomatic. Second, we formalized two interventions commonly used in cognitive behavioral therapy (CBT; exposure and cognitive reappraisal) and subsequently simulated their effects on the system. Results: The first simulation showed that the specified system could recover several aspects of the phenomenon (panic disorder), however, also showed some incongruency with the nature of panic attacks (e.g., rapid decreases were not observed). The second simulation study illustrated differential effects of CBT interventions for this patient. All tested interventions could decrease panic levels in the system.

Changing conditions may lead to sudden shifts in the state of ecosystems when critical thresholds are passed. Some well‐studied drivers of such transitions lead to predictable outcomes such as a turbid lake or a degraded landscape. Many ecosystems are, however, complex systems of many interacting species. While detecting upcoming transitions in such systems is challenging, predicting what comes after a critical transition is terra incognita altogether. The problem is that complex ecosystems may shift to many different, alternative states. Whether an impending transition has minor, positive or catastrophic effects is thus unclear. Some systems may, however, behave more predictably than others. The dynamics of mutualistic communities can be expected to be relatively simple, because delayed negative feedbacks leading to oscillatory or other complex dynamics are weak. Here, we address the question of whether this relative simplicity allows us to foresee a community's future state. As a case study, we use a model of a bipartite mutualistic network and show that a network's post‐transition state is indicated by the way in which a system recovers from minor disturbances. Similar results obtained with a unipartite model of facilitation suggest that our results are of relevance to a wide range of mutualistic systems.

In financial markets, participants locally optimize their profit which can result in a globally unstable state leading to a catastrophic change. The largest crash in the past decades is the bankruptcy of Lehman Brothers which was followed by a trust-based crisis between banks due to high-risk trading in complex products. We introduce information dissipation length (IDL) as a leading indicator of global instability of dynamical systems based on the transmission of Shannon information, and apply it to the time series of USD and EUR interest rate swaps (IRS). We find in both markets that the IDL steadily increases toward the bankruptcy, then peaks at the time of bankruptcy, and decreases afterwards. Previously introduced indicators such as ‘critical slowing down' do not provide a clear leading indicator. Our results suggest that the IDL may be used as an early-warning signal for critical transitions even in the absence of a predictive model.

We characterized the annual luminescent and skeletal density banding patterns in 51 massive Porites corals from 15 reefs from six locations around the Thai‐Malay Peninsula in Southeast Asia, and explored the seasonal environmental cues/drivers of band formation. Location‐specific recurrent annual luminescent banding patterns were found at all study locations with a brighter band occurring toward the end of the year (∼October/November/December) (at five locations) and in ∼June (one location). Annual density banding patterns could only be discerned at four locations, and were categorized into those that formed a dense band commencing ∼November/December, and those starting ∼May/June. Overall, compared to luminescence, variations in skeletal density provided a less clear signal for demarcation of annual growth increments. Seasonal variations in luminescence showed clearest relationships with salinity, as a proxy for freshwater/river runoff. No convincing relationship between intra‐annual luminescence intensity and density variations was found, which supports the notion that luminescent banding is due to inclusions of fluorophores into the coral skeleton rather than variations in skeletal architecture. The relationships between seasonal density variations and significant wave height and rainfall suggest density banding in this region is likely related to wave energy, or some other correlated environmental parameter/s. The large variability in skeletal banding patterns not only highlights the current relatively poor understanding of their nature and causes, but also the need for replication in their interpretation, especially in settings with complex seasonal hydrodynamic/hydrological patterns such as those found around the Thai‐Malay Peninsula.

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.

Summary Group‐level obesity can be seen as an emergent property of a complex system, consisting of feedback loops between individual body weight perception, individual weight‐related behaviour and group‐level social norms (a product of group‐level ‘normal' body mass index (BMI) and sociocultural ‘ideal' BMI). As overweight becomes normal, the norm might be counteracting health awareness in shaping individual weight‐related behaviour. System dynamics modelling facilitates understanding and simulating this system's emergent behaviour. We constructed six system dynamics models (SDMs) based on an expert‐informed causal loop diagram and data from six sociocultural groups (Dutch, Moroccan and South‐Asian Surinamese men and women). The SDMs served to explore the effect of three scenarios on group‐level BMI: ‘what if' weight‐related behaviour were driven by (1) health awareness, (2) norms or (3) a combination of the two. Median BMI decreased approximately 50% and 30% less in scenarios 2 and 3, respectively, than in 1. In men, the drop in BMI was approximately two times larger in scenario 1 versus 3, whereas in women, the drop was approximately equal in these scenarios. This study indicates that the overweight norm in men holds group‐level BMI close to overweight despite health awareness. Since norms are counteracting health awareness less strongly in women, other drivers of obesity must be more relevant.