Evaluating the performance of multivariate indicators of resilience loss

Environmental changes in river chemistry: A compositional approach for effective monitoring and management

River ecosystems are fundamental to sustaining global water and biogeochemical cycles, as well as supporting biodiversity. However, increasing pressures from human activities and climate change pose significant challenges to the stability of these systems. This study examines the sources of geochemical variability in the river waters of the Tiber River Basin (central Italy) to assess the system's sensitivity to environmental changes, with a special focus on seasonal variations. The proposed methods combine the exploration of multivariate parameters, known as Principal Balances (PBs), within the Compositional Data Analysis framework, with the interpretation of basins of attraction in their density distributions. Results indicate that NO3-, largely influenced by human activity, drives higher variability in water chemistry, overshadowing the natural geochemical processes such as water-rock interactions, which manifest at lower variability levels. Additionally, seasonal effects were explored highlighting greater sensitivity during dry periods and relevant changes in the proportions of some solutes (i.e. Cl-/Na+). The PBs approach offers valuable insights into system functioning principles compared to Principal Component Analysis, demonstrating a wider applicability, particularly when combined with the interpretation of the distributions. These findings emphasize the dominant role of anthropogenic factors in shaping river water chemistry, highlighting the importance of identifying key parameters for monitoring environmental changes and informing water resource management and policy decisions. However, much work remains to improve the understanding of the link between basins of attraction and distribution parameters, in order to explore their role in monitoring the system's sensitivity to global environmental changes.

Examining the research methods of early warning signals in clinical psychology through a theoretical lens

BACKGROUND

The past few years have seen a rapid growth in research on early warning signals (EWSs) in the psychopathology domain. Whereas early studies found EWSs to be associated with sudden changes in clinical change trajectories, later findings showed that EWSs may not be general across variables and cases and have low predictive power. These mixed results may be explained by the diverse methods employed in clinical EWS studies, with some of these approaches and practices potentially misaligned with the underlying theory of EWSs.

METHODS

This article employs a variety of methods, such as a narrative review, mathematical derivations, simulations, and visual illustrations, to support our claims, explain specific assumptions, and guide future empirical research. This multitude of methods serves our aim to provide theoretical as well as methodological contributions to the field.

RESULTS

We identify the following key assumptions for EWS validation studies: the system departs from a point attractor, EWSs appear before the critical transition, and EWS variables align with system destabilization. The literature review shows that the common research practices in the field are often not in line with those assumptions, and we provide specific suggestions corresponding to each of the assumptions.

CONCLUSIONS

More rigorous empirical evidence is needed to better validate the existence of EWSs in clinical sudden changes and fully realize their clinical potential. As theory-based prediction tools, EWSs require stronger alignment between theory and practice to enhance both theoretical understanding and predictive accuracy.

CLINICAL TRIAL NUMBER

Not applicable.

Toward a resilience selection index with indicator traits in German Holstein dairy cattle

Resilience expresses the ability of an individual to cope with short-term disturbances and to recover quickly by returning to the original level of performance. It can be measured by variance-based parameters and by the autocorrelation of daily milk yields in dairy cows. The design of resilience indicator traits and their heritabilities and genetic correlations have been studied in detail in recent years. There is a need to combine different resilience indicators in an index. The relevance of resilience indicator traits for incorporation into selection indices arises from their correlations with health traits and longevity. The correlations of diverse resilience indicator traits with health traits and longevity were analyzed. The resilience indicator traits were identified that would lead to the highest correlated selection response in the German selection index for health, and appropriate weights of the resilience indicator traits in a selection index for resilience were derived. Certain variance-based indicators were significantly positively correlated with most of the established health and functional traits, whereas the autocorrelation had a negligible correlation with these traits. A resilience selection index composed of 2 different variance-based resilience indicator traits was most likely to be recommended. Its correlation with overall performance was positive but moderately small. Incorporating more than 2 resilience indicator traits into the index improved the correlated response in health traits only slightly.

Application of early warning signs to physiological contexts: a comparison of multivariate indices in patients on long-term hemodialysis

Early warnings signs (EWSs) can anticipate abrupt changes in system state, known as "critical transitions," by detecting dynamic variations, including increases in variance, autocorrelation (AC), and cross-correlation. Numerous EWSs have been proposed; yet no consensus on which perform best exists. Here, we compared 15 multivariate EWSs in time series of 763 hemodialyzed patients, previously shown to present relevant critical transition dynamics. We calculated five EWSs based on AC, six on variance, one on cross-correlation, and three on AC and variance. We assessed their pairwise correlations, trends before death, and mortality predictive power, alone and in combination. Variance-based EWSs showed stronger correlations (r = 0.663 ± 0.222 vs. 0.170 ± 0.205 for AC-based indices) and a steeper increase before death. Two variance-based EWSs yielded HR95 > 9 (HR95 standing for a scale-invariant metric of hazard ratio), but combining them did not improve the area under the receiver-operating curve (AUC) much compared to using them alone (AUC = 0.798 vs. 0.796 and 0.791). Nevertheless, the AUC reached 0.825 when combining 13 indices. While some indicators did not perform overly well alone, their addition to the best performing EWSs increased the predictive power, suggesting that indices combination captures a broader range of dynamic changes occurring within the system. It is unclear whether this added benefit reflects measurement error of a unified phenomenon or heterogeneity in the nature of signals preceding critical transitions. Finally, the modest predictive performance and weak correlations among some indices call into question their validity, at least in this context.

Variance reflects resilience to disturbance along a stress gradient: Experimental evidence from coastal marshes

Quantifying ecosystem resilience to disturbance is important for understanding the effects of disturbances on ecosystems, especially in an era of rapid global change. However, there are few studies that have used standardized experimental disturbances to compare resilience patterns across abiotic gradients in real-world ecosystems. Theoretical studies have suggested that increased return times are associated with increasing variance during recovery from disturbance. However, this notion has rarely been explicitly tested in field, in part due to the challenges involved in obtaining long-term experimental data. In this study, we examined resilience to disturbance of 12 coastal marsh sites (five low-salinity and seven polyhaline [=salt] marshes) along a salinity gradient in Georgia, USA. We found that recovery times after experimental disturbance ranged from 7 to >127 months, and differed among response variables (vegetation height, cover and composition). Recovery rates decreased along the stress gradient of increasing salinity, presumably due to stress reducing plant vigor, but only when low-salinity and polyhaline sites were analyzed separately, indicating a strong role for traits of dominant plant species. The coefficient of variation of vegetation cover and height in control plots did not vary with salinity. In disturbed plots, however, the coefficient of variation (CV) was consistently elevated during the recovery period and increased with salinity. Moreover, higher CV values during recovery were correlated with slower recovery rates. Our results deepen our understanding of resilience to disturbance in natural ecosystems, and point to novel ways that variance can be used either to infer recent disturbance, or, if measured in areas with a known disturbance history, to predict recovery patterns.

Anticipating regime shifts by mixing early warning signals from different nodes

Real systems showing regime shifts, such as ecosystems, are often composed of many dynamical elements interacting on a network. Various early warning signals have been proposed for anticipating regime shifts from observed data. However, it is unclear how one should combine early warning signals from different nodes for better performance. Based on theory of stochastic differential equations, we propose a method to optimize the node set from which to construct an early warning signal. The proposed method takes into account that uncertainty as well as the magnitude of the signal affects its predictive performance, that a large magnitude or small uncertainty of the signal in one situation does not imply the signal's high performance, and that combining early warning signals from different nodes is often but not always beneficial. The method performs well particularly when different nodes are subjected to different amounts of dynamical noise and stress.

Early warning signals have limited applicability to empirical lake data

Research aimed at identifying indicators of persistent abrupt shifts in ecological communities, a.k.a regime shifts, has led to the development of a suite of early warning signals (EWSs). As these often perform inaccurately when applied to real-world observational data, it remains unclear whether critical transitions are the dominant mechanism of regime shifts and, if so, which EWS methods can predict them. Here, using multi-trophic planktonic data on multiple lakes from around the world, we classify both lake dynamics and the reliability of classic and second generation EWSs methods to predict whole-ecosystem change. We find few instances of critical transitions, with different trophic levels often expressing different forms of abrupt change. The ability to predict this change is highly processing dependant, with most indicators not performing better than chance, multivariate EWSs being weakly superior to univariate, and a recent machine learning model performing poorly. Our results suggest that predictive ecology should start to move away from the concept of critical transitions, developing methods suitable for predicting resilience loss not limited to the strict bounds of bifurcation theory.

Understanding the complexity of individual developmental pathways: A primer on metaphors, models, and methods to study resilience in development

The modern study of resilience in development is conceptually based on a complex adaptive system ontology in which many (intersystem) factors are involved in the emergence of resilient developmental pathways. However, the methods and models developed to study complex dynamical systems have not been widely adopted, and it has recently been noted this may constitute a problem moving the field forward. In the present paper, I argue that an ontological commitment to complex adaptive systems is not only possible, but highly recommended for the study of resilience in development. Such a commitment, however, also comes with a commitment to a different causal ontology and different research methods. In the first part of the paper, I discuss the extent to which current research on resilience in development conceptually adheres to the complex systems perspective. In the second part, I introduce conceptual tools that may help researchers conceptualize causality in complex systems. The third part discusses idiographic methods that could be used in a research program that embraces the interaction dominant causal ontology and idiosyncratic nature of the dynamics of complex systems. The conclusion is that a strong ontological commitment is warranted, but will require a radical departure from nomothetic science.

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.

Early warnings for multi-stage transitions in dynamics on networks

Successfully anticipating sudden major changes in complex systems is a practical concern. Such complex systems often form a heterogeneous network, which may show multi-stage transitions in which some nodes experience a regime shift earlier than others as an environment gradually changes. Here we investigate early warning signals for networked systems undergoing a multi-stage transition. We found that knowledge of both the ongoing multi-stage transition and network structure enables us to calculate effective early warning signals for multi-stage transitions. Furthermore, we found that small subsets of nodes could anticipate transitions as well as or even better than using all the nodes. Even if we fix the network and dynamical system, no single best subset of nodes provides good early warning signals, and a good choice of sentinel nodes depends on the tipping direction and the current stage of the dynamics within a multi-stage transition, which we systematically characterize.

Anticipating the occurrence and type of critical transitions

Critical transition can occur in many real-world systems. The ability to forecast the occurrence of transition is of major interest in a range of contexts. Various early warning signals (EWSs) have been developed to anticipate the coming critical transition or distinguish types of transition. However, no effective method allows to establish practical threshold indicating the condition when the critical transition is most likely to occur. Here, we introduce a powerful EWS, named dynamical eigenvalue (DEV), that is rooted in bifurcation theory of dynamical systems to estimate the dominant eigenvalue of the system. Theoretically, the absolute value of DEV approaches 1 when the system approaches bifurcation, while its position in the complex plane indicates the type of transition. We demonstrate the efficacy of the DEV approach in model systems with known bifurcation types and also test the DEV approach on various critical transitions in real-world systems.

Synchrony of biomarker variability indicates a critical transition: Application to mortality prediction in hemodialysis

Critical transition theory suggests that complex systems should experience increased temporal variability just before abrupt state changes. We tested this hypothesis in 763 patients on long-term hemodialysis, using 11 biomarkers collected every two weeks and all-cause mortality as a proxy for critical transitions. We find that variability-measured by coefficients of variation (CVs)-increases before death for all 11 clinical biomarkers, and is strikingly synchronized across all biomarkers: the first axis of a principal component analysis on all CVs explains 49% of the variance. This axis then generates powerful predictions of mortality (HR95 = 9.7, p < 0.0001, where HR95 is a scale-invariant metric of hazard ratio; AUC up to 0.82) and starts to increase markedly ∼3 months prior to death. Our results provide an early warning sign of physiological collapse and, more broadly, a quantification of joint system dynamics that opens questions of how system modularity may break down before critical transitions.

Early Warning Signals in Phase Space: Geometric Resilience Loss Indicators From Multiplex Cumulative Recurrence Networks

The detection of Early Warning Signals (EWS) of imminent phase transitions, such as sudden changes in symptom severity could be an important innovation in the treatment or prevention of disease or psychopathology. Recurrence-based analyses are known for their ability to detect differences in behavioral modes and order transitions in extremely noisy data. As a proof of principle, the present paper provides an example of a recurrence network based analysis strategy which can be implemented in a clinical setting in which data from an individual is continuously monitored for the purpose of making decisions about diagnosis and intervention. Specifically, it is demonstrated that measures based on the geometry of the phase space can serve as Early Warning Signals of imminent phase transitions. A publicly available multivariate time series is analyzed using so-called cumulative Recurrence Networks (cRN), which are recurrence networks with edges weighted by recurrence time and directed towards previously observed data points. The results are compared to previous analyses of the same data set, benefits, limitations and future directions of the analysis approach are discussed.

Towards a Data-Driven Estimation of Resilience in Networked Dynamical Systems: Designing a Versatile Testbed

Estimating resilience of adaptive, networked dynamical systems remains a challenge. Resilience refers to a system's capacity "to absorb exogenous and/or endogenous disturbances and to reorganize while undergoing change so as to still retain essentially the same functioning, structure, and feedbacks." The majority of approaches to estimate resilience requires exact knowledge of the underlying equations of motion; the few data-driven approaches so far either lack appropriate strategies to verify their suitability or remain subject of considerable debate. We develop a testbed that allows one to modify resilience of a multistable networked dynamical system in a controlled manner. The testbed also enables generation of multivariate time series of system observables to evaluate the suitability of data-driven estimators of resilience. We report first findings for such an estimator.

Anticipating the direction of symptom progression using critical slowing down: a proof-of-concept study

BACKGROUND

As complex dynamic systems approach a transition, their dynamics change. This process, called critical slowing down (CSD), may precede transitions in psychopathology as well. This study investigated whether CSD may also indicate the direction of future symptom transitions, i.e., whether they involve an increase or decrease in symptoms.

METHODS

In study 1, a patient with a history of major depression monitored their mental states ten times a day for almost eight months. Study 2 used data from the TRAILS TRANS-ID study, where 122 young adults at increased risk of psychopathology (mean age 23.64±0.67 years, 56.6% males) monitored their mental states daily for six consecutive months. Symptom transitions were inferred from semi-structured diagnostic interviews. In both studies, CSD direction was estimated using moving-window principal component analyses.

RESULTS

In study 1, CSD was directed towards an increase in negative mental states. In study 2, the CSD direction matched the direction of symptom shifts in 34 individuals. The accuracy of the indicator was higher in subsets of individuals with larger absolute symptom transitions. The indicator's accuracy exceeded chance levels in sensitivity analyses (accuracy 22.92% vs. 11.76%, z=-2.04, P=.02) but not in main analyses (accuracy 27.87% vs. 20.63%, z=-1.32, P=.09).

CONCLUSIONS

The CSD direction may predict whether upcoming symptom transitions involve remission or worsening. However, this may only hold for specific individuals, namely those with large symptom transitions. Future research is needed to replicate these findings and to delineate for whom CSD reliably forecasts the direction of impending symptom transitions.