Generalized early warning signals in multivariate and gridded data with an application to tropical cyclones

Tipping events in dynamical systems have been studied across many applications, often by measuring changes in variance or autocorrelation in a one-dimensional time series. In this paper, methods for detecting early warning signals of tipping events in multidimensional systems are reviewed and expanded. An analytical justification of the use of dimension-reduction by empirical orthogonal functions, in the context of early warning signals, is provided and the one-dimensional techniques are also extended to spatially separated time series over a 2D field. The challenge of predicting an approaching tropical cyclone by a tipping-point analysis of the sea-level pressure series is used as the primary example, and an analytical model of a moving cyclone is also developed in order to test predictions. We show that the one-dimensional power spectrum indicator may be used following dimension-reduction or over a 2D field. We also show the validity of our moving cyclone model with respect to tipping-point indicators. Many dynamical systems experience sudden shifts in behavior, often referred to as tipping points or critical transitions. A volume of work is dedicated to detecting and predicting these critical transitions, often making use of generic early warning signal (EWS) indicators based on autocorrelation1,2 and increasing variance.3,4 Similar indicators based on other scaling properties of the time series, namely, detrended fluctuation analysis (DFA)5,6 and power spectrum scaling,7 have also been used. Other methods have estimated parameters to fit a model to the data, both for detecting critical transitions8–10 and for predicting future transitions dynamics

Nonlinear softening as a predictive precursor to climate tipping

Approaching a dangerous bifurcation, from which a dynamical system such as the Earth's climate will jump (tip) to a different state, the current stable state lies within a shrinking basin of attraction. Persistence of the state becomes increasingly precarious in the presence of noisy disturbances. We consider an underlying potential, as defined theoretically for a saddle-node fold and (via averaging) for a Hopf bifurcation. Close to a stable state, this potential has a parabolic form; but approaching a jump it becomes increasingly dominated by softening nonlinearities. If we have already detected a decrease in the linear decay rate, nonlinear information allows us to estimate the propensity for early tipping due to noise. We argue that one needs to extract information about the nonlinear features (a "softening") of the underlying potential from the time series to judge the probability and timing of tipping. This analysis is the logical next step if one has detected a decrease of the linear decay rate. If there is no discernable trend in the linear analysis, nonlinear softening is even more important in showing the proximity to tipping. After extensive normal form calibration studies, we check two geological time series from paleo-climate tipping events for softening of the underlying well. For the ending of the last ice age, where we find no convincing linear precursor, we identify a statistically significant nonlinear softening towards increasing temperature. The analysis has thus successfully detected a warning of the imminent tipping event.Comment: 22 pages, 11 figures, changed title back, corrected smaller mistakes, updated reference

Integrating Ecological and Engineering Concepts of Resilience in Microbial Communities

Many definitions of resilience have been proffered for natural and engineered ecosystems, but a conceptual consensus on resilience in microbial communities is still lacking. We argue that the disconnect largely results from the wide variance in microbial community complexity, which range from compositionally simple synthetic consortia to complex natural communities, and divergence between the typical practical outcomes emphasized by ecologists and engineers. Viewing microbial communities as elasto-plastic systems that undergo both recoverable and unrecoverable transitions, we argue that this gap between the engineering and ecological definitions of resilience stems from their respective emphases on elastic and plastic deformation, respectively. We propose that the two concepts may be fundamentally united around the resilience of function rather than state in microbial communities and the regularity in the relationship between environmental variation and a community\u27s functional response. Furthermore, we posit that functional resilience is an intrinsic property of microbial communities and suggest that state changes in response to environmental variation may be a key mechanism driving functional resilience in microbial communities

Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

A complex network perspective on clinical science

Contemporary classification systems for mental disorders assume that abnormal behaviors are expressions of latent disease entities. An alternative to the latent disease model is the complex network approach. Instead of assuming that symptoms arise from an underlying disease entity, the complex network approach holds that disorders exist as systems of interrelated elements of a network. This approach also provides a framework for the understanding of therapeutic change. Depending on the structure of the network, change can occur abruptly once the network reaches a critical threshold (the tipping point). Homogeneous and highly connected networks often recover more slowly from local perturbations when the network approaches the tipping point, potentially making it possible to predict treatment change, relapse, and recovery. In this article, we discuss the complex network approach as an alternative to the latent disease model and its implications for classification, therapy, relapse, and recovery.R34 MH086668 - NIMH NIH HHS; R01 AT007257 - NCCIH NIH HHS; R21 MH101567 - NIMH NIH HHS; R34 MH099311 - NIMH NIH HHS; R21 MH102646 - NIMH NIH HHS; K23 MH100259 - NIMH NIH HHS; R01 MH099021 - NIMH NIH HH

Distance entropy cartography characterises centrality in complex networks

We introduce distance entropy as a measure of homogeneity in the distribution of path lengths between a given node and its neighbours in a complex network. Distance entropy defines a new centrality measure whose properties are investigated for a variety of synthetic network models. By coupling distance entropy information with closeness centrality, we introduce a network cartography which allows one to reduce the degeneracy of ranking based on closeness alone. We apply this methodology to the empirical multiplex lexical network encoding the linguistic relationships known to English speaking toddlers. We show that the distance entropy cartography better predicts how children learn words compared to closeness centrality. Our results highlight the importance of distance entropy for gaining insights from distance patterns in complex networks.Comment: 11 page

Methods for anticipating governance breakdown and violent conflict

In this paper, authors Sarah Bressan, Håvard Mokleiv Nygård, and Dominic Seefeldt present the evolution and state of the art of both quantitative forecasting and scenario-based foresight methods that can be applied to help prevent governance breakdown and violent conflict in Europe’s neighbourhood. In the quantitative section, they describe the different phases of conflict forecasting in political science and outline which methodological gaps EU-LISTCO’s quantitative sub-national prediction tool will address to forecast tipping points for violent conflict and governance breakdown. The qualitative section explains EU-LISTCO’s scenario-based foresight methodology for identifying potential tipping points. After comparing both approaches, the authors discuss opportunities for methodological advancements across the boundaries of quantitative forecasting and scenario-based foresight, as well as how they can inform the design of strategic policy options

Ecological indicators for abandoned mines, Phase 1: Review of the literature

Mine waters have been identified as a significant issue in the majority of Environment Agency draft River Basin Management Plans. They are one of the largest drivers for chemical pollution in the draft Impact Assessment for the Water Framework Directive (WFD), with significant failures of environmental quality standards (EQS) for metals (particularly Cd, Pb, Zn, Cu, Fe) in many rivers linked to abandoned mines. Existing EQS may be overprotective of aquatic life which may have adapted over centuries of exposure. This study forms part of a larger project to investigate the ecological impact of metals in rivers, to develop water quality targets (alternative objectives for the WFD) for aquatic ecosystems impacted by long-term mining pollution. The report reviews literature on EQS failures, metal effects on aquatic biota and effects of water chemistry, and uses this information to consider further work. A preliminary assessment of water quality and biology data for 87 sites across Gwynedd and Ceredigion (Wales) shows that existing Environment Agency water quality and biology data could be used to establish statistical relations between chemical variables and metrics of ecological quality. Visual representation and preliminary statistical analyses show that invertebrate diversity declines with increasing zinc concentration. However, the situation is more complex because the effects of other metals are not readily apparent. Furthermore, pH and aluminium also affect streamwater invertebrates, making it difficult to tease out toxicity due to individual mine-derived metals. The most characteristic feature of the plant communities of metal-impacted systems is a reduction in diversity, compared to that found in comparable unimpacted streams. Some species thrive in the presence of heavy metals, presumably because they are able to develop metal tolerance, whilst others consistently disappear. Effects are, however, confounded by water chemistry, particularly pH. Tolerant species are spread across a number of divisions of photosynthetic organisms, though green algae, diatoms and blue-green algae are usually most abundant, often thriving in the absence of competition and/or grazing. Current UK monitoring techniques focus on community composition and, whilst these provide a sampling and analytical framework for studies of metal impacts, the metrics are not sensitive to these impacts. There is scope for developing new metrics, based on community-level analyses and for looking at morphological variations common in some taxa at elevated metal concentrations. On the whole, community-based metrics are recommended, as these are easier to relate to ecological status definitions. With respect to invertebrates and fish, metals affect individuals, population and communities but sensitivity varies among species, life stages, sexes, trophic groups and with body condition. Acclimation or adaptation may cause varying sensitivity even within species. Ecosystem-scale effects, for example on ecological function, are poorly understood. Effects vary between metals such as cadmium, copper, lead, chromium, zinc and nickel in order of decreasing toxicity. Aluminium is important in acidified headwaters. Biological effects depend on speciation, toxicity, availability, mixtures, complexation and exposure conditions, for example discharge (flow). Current water quality monitoring is unlikely to detect short-term episodic increases in metal concentrations or evaluate the bioavailability of elevated metal concentrations in sediments. These factors create uncertainty in detecting ecological impairment in metal-impacted ecosystems. Moreover, most widely used biological indicators for UK freshwaters were developed for other pressures and none distinguishes metal impacts from other causes of impairment. Key ecological needs for better regulation and management of metals in rivers include: i) models relating metal data to ecological data that better represent influences on metal toxicity; ii) biodiagnostic indices to reflect metal effects; iii) better methods to identify metal acclimation or adaptation among sensitive taxa; iv) better investigative procedures to isolate metal effects from other pressures. Laboratory data on the effects of water chemistry on cationic metal toxicity and bioaccumulation show that a number of chemical parameters, particularly pH, dissolved organic carbon (DOC) and major cations (Na, Mg, K, Ca) exert a major influence on the toxicity and/or bioaccumulation of cationic metals. The biotic ligand model (BLM) provides a conceptual framework for understanding these water chemistry effects as a combination of the influence of chemical speciation, and metal uptake by organisms in competition with H+ and other cations. In some cases where the BLM cannot describe effects, empirical bioavailable models have been successfully used. Laboratory data on the effects of metal mixtures across different water chemistries are sparse, with implications for transferring understanding to mining-impacted sites in the field where mixture effects are likely. The available field data, although relatively sparse, indicate that water chemistry influences metal effects on aquatic ecosystems. This occurs through complexation reactions, notably involving dissolved organic matter and metals such as Al, Cu and Pb. Secondly, because bioaccumulation and toxicity are partly governed by complexation reactions, competition effects among metals, and between metals and H+, give rise to dependences upon water chemistry. There is evidence that combinations of metals are active in the field; the main study conducted so far demonstrated the combined effects of Al and Zn, and suggested, less certainly, that Cu and H+ can also contribute. Chemical speciation is essential to interpret and predict observed effects in the field. Speciation results need to be combined with a model that relates free ion concentrations to toxic effect. Understanding the toxic effects of heavy metals derived from abandoned mines requires the simultaneous consideration of the acidity-related components Al and H+. There are a number of reasons why organisms in waters affected by abandoned mines may experience different levels of metal toxicity than in the laboratory. This could lead to discrepancies between actual field behaviour and that predicted by EQS derived from laboratory experiments, as would be applied within the WFD. The main factors to consider are adaptation/acclimation, water chemistry, and the effects of combinations of metals. Secondary effects are metals in food, metals supplied by sediments, and variability in stream flows. Two of the most prominent factors, namely adaptation/ acclimation and bioavailability, could justify changes in EQS or the adoption of an alternative measure of toxic effects in the field. Given that abandoned mines are widespread in England and Wales, and the high cost of their remediation to meet proposed WFD EQS criteria, further research into the question is clearly justified. Although ecological communities of mine-affected streamwaters might be over-protected by proposed WFD EQS, there are some conditions under which metals emanating from abandoned mines definitely exert toxic effects on biota. The main issue is therefore the reliable identification of chemical conditions that are unacceptable and comparison of those conditions with those predicted by WFD EQS. If significant differences can convincingly be demonstrated, the argument could be made for alternative standards for waters affected by abandoned mines. Therefore in our view, the immediate research priority is to improve the quantification of metal effects under field circumstances. Demonstration of dose-response relationships, based on metal mixtures and their chemical speciation, and the use of better biological tools to detect and diagnose community-level impairment, would provide the necessary scientific information