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.

Background: Chronic stress increases chronic disease risk and may underlie the association between exposure to adverse socioeconomic conditions and adverse health outcomes. The relationship between exposure to such conditions and chronic stress is complex due to feedback loops between stressor exposure and psychological processes, encompassing different temporal (acute stress response to repeated exposure over the life course) and spatial (biological/psychological/social) scales. We examined the mechanisms underlying the relationship between exposure to adverse socioeconomic conditions and chronic stress from a complexity science perspective, focusing on amplifying feedback loops across different scales. Methods: We developed a causal loop diagram (CLD) to interpret available evidence from this perspective. The CLD was drafted by an interdisciplinary group of researchers. Evidence from literature was used to confirm/contest the variables and causal links included in the conceptual framework and refine their conceptualisation. Our findings were evaluated by eight independent researchers. Results: Adverse socioeconomic conditions imply an accumulation of stressors and increase the likelihood of exposure to uncontrollable childhood and life course stressors. Repetition of such stressors may activate mechanisms that can affect coping resources and coping strategies and stimulate appraisal of subsequent stressors as uncontrollable. We identified five feedback loops describing these mechanisms: (1) progressive deterioration of access to coping resources because of repeated insolvability of stressors; (2) perception of stressors as uncontrollable due to learned helplessness; (3) tax on cognitive bandwidth caused by stress; (4) stimulation of problem avoidance to provide relief from the stress response and free up cognitive bandwidth; and (5) susceptibility to appraising stimuli as stressors against a background of stress. Conclusions: Taking a complexity science perspective reveals that exposure to adverse socioeconomic conditions implies recurrent stressor exposure which impacts chronic stress via amplifying feedback loops that together could be conceptualised as one vicious cycle. This means that in order for individual-level psychological interventions to be effective, the context of exposure to adverse socioeconomic conditions also needs to be addressed.

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. Conclusions: Formalizing idiographic theories is promising in bridging the gap between complexity science and clinical practice and can help foster more rigorous scientific practices in psychotherapy, through enhancing theory development. More precise case conceptualizations could potentially improve intervention planning and treatment outcomes. We discuss applications in psychotherapy and future directions, amongst others barriers for systematic theory evaluation and extending the framework to incorporate interactions between individual systems, relevant for modeling social learning processes. With this report, we hope to stimulate future efforts in formalizing clinical frameworks.

Quantifying synergy among stochastic variables is an important open problem in information theory. Information synergy occurs when multiple sources together predict an outcome variable better than the sum of single-source predictions. It is an essential phenomenon in biology such as in neuronal networks and cellular regulatory processes, where different information flows integrate to produce a single response, but also in social cooperation processes as well as in statistical inference tasks in machine learning. Here we propose a metric of synergistic entropy and synergistic information from first principles. The proposed measure relies on so-called synergistic random variables (SRVs) which are constructed to have zero mutual information about individual source variables but non-zero mutual information about the complete set of source variables. We prove several basic and desired properties of our measure, including bounds and additivity properties. In addition, we prove several important consequences of our measure, including the fact that different types of synergistic information may co-exist between the same sets of variables. A numerical implementation is provided, which we use to demonstrate that synergy is associated with resilience to noise. Our measure may be a marked step forward in the study of multivariate information theory and its numerous applications.

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.