Early warning signals of extinction in deteriorating environments

Reviving collapsed plant-pollinator networks from a single species

Mutualistic ecological networks can suddenly transition to undesirable states due to small changes in environmental conditions. Recovering from such a collapse can be difficult as restoring the original environmental conditions may be infeasible. Additionally, such networks can also exhibit a phenomenon known as hysteresis, whereby the system could exhibit multiple states under the same environmental conditions, implying that ecological networks may not recover. Here, we attempted to revive collapsed mutualistic networks to a high-functioning state from a single species, using concepts from signal propagation theory and an eco-evolutionary model based on network structures of 115 empirical plant-pollinator networks. We found that restoring the environmental conditions rarely aided in recovery of collapsed networks, but a positive relationship between recovering pollinator density and network nestedness emerged, which was qualitatively supported by empirical plant-pollinator restoration data. In contrast, network resurrection from a collapsed state in undesirable environmental conditions where restoration has minimal impacts could be readily achieved by perturbing a single species or a few species that control the response of the dynamical networks. Additionally, nestedness in networks and a moderate amount of trait variation could aid in the revival of networks even in undesirable environmental conditions. Our work suggests that focus should be applied to a few species whose dynamics could be steered to resurrect entire networks from a collapsed state and that network architecture could play a crucial role in reviving collapsed plant-pollinator networks.

Monitoring resilience in bursts

The possibility to anticipate critical transitions through detecting loss of resilience has attracted attention in many fields. Resilience indicators rely on the mathematical concept of critical slowing down, which means that a system recovers more slowly from external perturbations when it gets closer to tipping point. This decrease in recovery rate can be reflected in rising autocorrelation and variance in data. To test whether resilience is changing, resilience indicators are often calculated using a moving window in long, continuous time series of the system. However, for some systems, it may be more feasible to collect several high-resolution time series in short periods of time, i.e., in bursts. Resilience indicators can then be calculated to detect a change of resilience between such bursts. Here, we compare the performance of both methods using simulated data and showcase the possible use of bursts in a case study using mood data to anticipate depression in a patient. With the same number of data points, the burst approach outperformed the moving window method, suggesting that it is possible to downsample the continuous time series and still signal an upcoming transition. We suggest guidelines to design an optimal sampling strategy. Our results imply that using bursts of data instead of continuous time series may improve the capacity to detect changes in resilience. This method is promising for a variety of fields, such as human health, epidemiology, or ecology, where continuous monitoring can be costly or unfeasible.

Triangular Triazine-Triphenylamine Functionalized Hybrid Fluorescent Porous Polymers for Detection and Photodegradation of Tetracycline Hydrochloride

First, an organic semiconductor fluorescent molecule of 4',4″,4"'-(2,4,6-triphenyl-1,3,5-triazine)-4-(N,N-diphenyl-(1,1'-biphenyl)-4-amine (TPTz) is successfully synthesized by the Suzuki-Miyaura coupling reaction of 2,4,6-tris(4-bromophenyl)-1,3,5-triazine with 4-(diphenylamino)phenylboronic acid. TPTz offers as high as 85% fluorescence quantum yield and a strong solvent effect, with fluorescent colors across the visible spectrum in different solvents. Then, an organic-inorganic hybrid fluorescent porous polymer of PCS-TPTz with a surface area of 714 m2 g-1 and pore volume of 0.660 cm3 g-1 is prepared by the Friedel-Crafts reaction of TPTz and octavinylsilsesquioxane; PCS-TPTz showed a high fluorescence quantum yield of 17% with a large Stokes shift of up to 280 nm. The excellent fluorescence properties and insolubility of PCS-TPTz make it to act as a heterophase sensor for tetracycline hydrochloride (TH) with a KSV of 2.39 × 104 M-1. In addition, PCS-TPTz exhibits an excellent photodegradation activity for antibiotic TH without the requirement for additional oxidants or pH adjustments. ESR spectra and free radical trapping experiment indicate that superoxide radical (•O2-) is the active radical for achieving the photodegradation. The simultaneous detection and degradation of TH are achieved by PCS-TPTz.

Early warning indicators capture catastrophic transitions driven by explicit rates of environmental change

In response to external changes, ecosystems can undergo catastrophic transitions. Early warning indicators aim to predict such transitions based on the phenomenon of critical slowing down at bifurcation points found under a constant environment. When an explicit rate of environmental change is considered, catastrophic transitions can become distinct phenomena from bifurcations, and result from a delayed response to noncatastrophic bifurcations. We use a trophic metacommunity model where transitions in time series and bifurcations of the system are distinct phenomena. We calculate early warning indicators from the time series of the continually changing system and show that they predict not the bifurcation of the underlying system but the actual catastrophic transition driven by the explicit rate of change. Predictions based on the bifurcation structure could miss catastrophic transitions that can still be captured by early warning signals calculated from time series. Our results expand the repertoire of mechanistic models used to anticipate catastrophic transitions to nonequilibrium ecological systems exposed to a constant rate of environmental change.

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.

Early warning signals indicate climate change-induced stress in Norway spruce in the Eastern Carpathians

Climate change is affecting forest ecosystems globally, in particular through warming as well as increases in the frequency and intensity of extreme events. Norway spruce (Picea abies (L.) Karst.) is one of the most important coniferous tree species in Europe. In recent extremely dry years in Central Europe, spruce suffered and large dieback has been observed. In parts of Eastern Europe, however, no large-scale decline in spruce has been reported so far, though anticipated changes in climate pose the question how the future of these forests may look like. To assess the current state of spruce forests in Eastern Europe, we established a tree-ring network consisting of 157 Norway spruce chronologies (from >3000 trees) of different ages distributed along elevational transects in the Eastern Carpathians, Romania. We evaluated early warning signals of climate change-induced stress, i.e. (1) growth decline, (2) increased sensitivity of tree growth (assessed over the statistics first-order autocorrelation and standard deviation), and (3) increased growth synchrony. A pronounced growth decline was observed over the last two decades, which was strongest in younger stands and at lower elevations. However, growth sensitivity and synchrony did not show consistent patterns, suggesting that forest decline may not be immediately imminent. Overall, our findings highlight an increased vulnerability of spruce in the Eastern Carpathians. With ongoing climate change, spruce dieback may be expected in this part of Europe as well.

Finding critical points and correlation length exponents using finite size scaling of Gini index

The order parameter for a continuous transition shows diverging fluctuation near the critical point. Here we show, through numerical simulations and scaling arguments, that the inequality (or variability) between the values of an order parameter, measured near a critical point, is independent of the system size. Quantification of such variability through the Gini index (g) therefore leads to a scaling form g=G[|F-F_{c}|N^{1/dν}], where F denotes the driving parameter for the transition (e.g., temperature T for ferromagnetic to paramagnetic transition, or lattice occupation probability p in percolation), N is the system size, d is the spatial dimension and ν is the correlation length exponent. We demonstrate the scaling for the Ising model in two and three dimensions, site percolation on square lattice, and the fiber bundle model of fracture.

Early warnings of tipping in a non-autonomous turbulent reactive flow system: Efficacy, reliability, and warning times

Real-world complex systems such as the earth's climate, ecosystems, stock markets, and combustion engines are prone to dynamical transitions from one state to another, with catastrophic consequences. State variables of such systems often exhibit aperiodic fluctuations, either chaotic or stochastic in nature. Often, the parameters describing a system vary with time, showing time dependency. Constrained by these effects, it becomes difficult to be warned of an impending critical transition, as such effects contaminate the precursory signals of the transition. Therefore, a need for efficient and reliable early-warning signals (EWSs) in such complex systems is in pressing demand. Motivated by this fact, in the present work, we analyze various EWSs in the context of a non-autonomous turbulent thermoacoustic system. In particular, we investigate the efficacy of different EWS in forecasting the onset of thermoacoustic instability (TAI) and their reliability with respect to the rate of change of the control parameter. This is the first experimental study of tipping points in a non-autonomous turbulent thermoacoustic system. We consider the Reynolds number (Re) as the control parameter, which is varied linearly with time at finite rates. The considered EWSs are derived from critical slowing down, spectral properties, and fractal characteristics of the system variables. The state of TAI is associated with large amplitude acoustic pressure oscillations that could lead thermoacoustic systems to break down. We consider acoustic pressure fluctuations as a potential system variable to perform the analysis. Our analysis shows that irrespective of the rate of variation of the control parameter, the Hurst exponent and variance of autocorrelation coefficients warn of an impending transition well in advance and are more reliable than other EWS measures. Additionally, we show the variation in the warning time to an impending TAI with rates of change of the control parameter. We also investigate the variation in amplitudes of the most significant modes of acoustic pressure oscillations with the Hurst exponent. Such variations lead to scaling laws that could be significant in prediction and devising control actions to mitigate TAI.

Merging trait-based ecology and regime shift theory to anticipate community responses to warming

Anthropogenic warming is altering species abundance, distribution, physiology, and more. How changes observed at the species level alter emergent community properties is an active and urgent area of research. Trait-based ecology and regime shift theory provide complementary ways to understand climate change impacts on communities, but these two bodies of work are only rarely integrated. Lack of integration handicaps our ability to understand community responses to warming, at a time when such understanding is critical. Therefore, we advocate for merging trait-based ecology with regime shift theory. We propose a general set of principles to guide this merger and apply these principles to research on marine communities in the rapidly warming North Atlantic. In our example, combining trait distribution and regime shift analyses at the community level yields greater insight than either alone. Looking forward, we identify a clear need for expanding quantitative approaches to collecting and merging trait-based and resilience metrics in order to advance our understanding of climate-driven community change.

Rate-induced tipping in complex high-dimensional ecological networks

In an ecosystem, environmental changes as a result of natural and human processes can cause some key parameters of the system to change with time. Depending on how fast such a parameter changes, a tipping point can occur. Existing works on rate-induced tipping, or R-tipping, offered a theoretical way to study this phenomenon but from a local dynamical point of view, revealing, e.g., the existence of a critical rate for some specific initial condition above which a tipping point will occur. As ecosystems are subject to constant disturbances and can drift away from their equilibrium point, it is necessary to study R-tipping from a global perspective in terms of the initial conditions in the entire relevant phase space region. In particular, we introduce the notion of the probability of R-tipping defined for initial conditions taken from the whole relevant phase space. Using a number of real-world, complex mutualistic networks as a paradigm, we find a scaling law between this probability and the rate of parameter change and provide a geometric theory to explain the law. The real-world implication is that even a slow parameter change can lead to a system collapse with catastrophic consequences. In fact, to mitigate the environmental changes by merely slowing down the parameter drift may not always be effective: Only when the rate of parameter change is reduced to practically zero would the tipping be avoided. Our global dynamics approach offers a more complete and physically meaningful way to understand the important phenomenon of R-tipping.

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.

Complex nonmonotonic responses of biodiversity to habitat destruction

It has typically been assumed that habitat destruction, characterized by habitat loss and fragmentation, has consistently negative effects on biodiversity. While numerous empirical studies have shown the detrimental effects of habitat loss, debate continues as to whether habitat fragmentation has universally negative effects. To explore the effects of habitat fragmentation, we developed a simple model for site-occupancy dynamics in fragmented landscapes. With the model, we demonstrate that a competition-colonization trade-off can result in nonlinear oscillatory responses in biodiversity to both habitat loss and fragmentation. However, the overall pattern of habitat loss reducing species richness is still established, in line with empirical observations. Interestingly, the existence of localized oscillations in biodiversity can explain the mixed responses of species richness to habitat fragmentation per se observed in nature, thereby reconciling the debate on the fragmentation-diversity relationship. Therefore, this study offers a parsimonious mechanistic explanation for empirically observed biodiversity patterns in response to habitat destruction.

Variation in environmental stochasticity dramatically affects viability and extinction time in a predator-prey system with high prey group cohesion

Understanding how tipping points arise is critical for population protection and ecosystem robustness. This work evaluates the impact of environmental stochasticity on the emergence of tipping points in a predator-prey system subject to the Allee effect and Holling type IV functional response, modeling an environment in which the prey has high group cohesion. We analyze the relationship between stochasticity and the probability and time that predator and prey populations in our model tip between different steady states. We evaluate the safety from extinction of different population values for each species, and accordingly assign extinction warning levels to these population values. Our analysis suggests that the effects of environmental stochasticity on tipping phenomena are scenario-dependent but follow a few interpretable trends. The probability of tipping towards a steady state in which one or both species go extinct generally monotonically increased with noise intensity, while the probability of tipping towards a more favorable steady state (in which more species were viable) usually peaked at intermediate noise intensity. For tipping between two equilibria where a given species was at risk of extinction in one equilibrium but not the other, noise affecting that species had greater impact on tipping probability than noise affecting the other species. Noise in the predator population facilitated quicker tipping to extinction equilibria, whereas prey noise instead often slowed down extinction. Changes in warning level for initial population values due to noise were most apparent near attraction basin boundaries, but noise of sufficient magnitude (especially in the predator population) could alter risk even far away from these boundaries. Our model provides critical theoretical insights for the conservation of population diversity: management criteria and early warning signals can be developed based on our results to keep populations away from destructive critical thresholds.

Dynamic gene regulatory networks improving spike fertility through regulation of floret primordia fate in wheat

The developmental process of spike is critical for spike fertility through affecting floret primordia fate in wheat; however, the genetic regulation of this dynamic and complex developmental process remains unclear. Here, we conducted a high temporal-resolution analysis of spike transcriptomes and monitored the number and morphology of floret primordia within spike. The development of all floret primordia in a spike was clearly separated into three distinct phases: differentiation, pre-dimorphism and dimorphism. Notably, we identified that floret primordia with meiosis ability at the pre-dimorphism phase usually develop into fertile floret primordia in the next dimorphism phase. Compared to control, increasing plant space treatment achieved the maximum increasement range (i.e., 50%) in number of fertile florets by accelerating spike development. The process of spike fertility improvement was directed by a continuous and dynamic regulatory network involved in transcription factor and genes interaction. This was based on the coordination of genes related to heat shock protein and jasmonic acid biosynthesis during differentiation phase, and genes related to lignin, anthocyanin and chlorophyll biosynthesis during dimorphism phase. The multi-dimensional association with high temporal-resolution approach reported here allows rapid identification of genetic resource for future breeding studies to realise the maximum spike fertility potential in more cereal crops.

Critical Scaling through Gini Index

In the systems showing critical behavior, various response functions have a singularity at the critical point. Therefore, as the driving field is tuned toward its critical value, the response functions change drastically, typically diverging with universal critical exponents. In this Letter, we quantify the inequality of response functions with measures traditionally used in economics, namely by constructing a Lorenz curve and calculating the corresponding Gini index. The scaling of such a response function, when written in terms of the Gini index, shows singularity at a point that is at least as universal as the corresponding critical exponent. The critical scaling, therefore, becomes a single parameter fit, which is a considerable simplification from the usual form where the critical point and critical exponents are independent. We also show that another measure of inequality, the Kolkata index, crosses the Gini index at a point just prior to the critical point. Therefore, monitoring these two inequality indices for a system where the critical point is not known can produce a precursory signal for the imminent criticality. This could be useful in many systems, including that in condensed matter, bio- and geophysics to atmospheric physics. The generality and numerical validity of the calculations are shown with the Monte Carlo simulations of the two dimensional Ising model, site percolation on square lattice, and the fiber bundle model of fracture.

Extinction time distributions of populations and genotypes

Ultimately, the eventual extinction of any biological population is an inevitable outcome. While extensive research has focused on the average time it takes for a population to go extinct under various circumstances, there has been limited exploration of the distributions of extinction times and the likelihood of significant fluctuations. Recently, Hathcock and Strogatz [D. Hathcock and S. H. Strogatz, Phys. Rev. Lett. 128, 218301 (2022)0031-900710.1103/PhysRevLett.128.218301] identified Gumbel statistics as a universal asymptotic distribution for extinction-prone dynamics in a stable environment. In this study we aim to provide a comprehensive survey of this problem by examining a range of plausible scenarios, including extinction-prone, marginal (neutral), and stable dynamics. We consider the influence of demographic stochasticity, which arises from the inherent randomness of the birth-death process, as well as cases where stochasticity originates from the more pronounced effect of random environmental variations. Our work proposes several generic criteria that can be used for the classification of experimental and empirical systems, thereby enhancing our ability to discern the mechanisms governing extinction dynamics. Employing these criteria can help clarify the underlying mechanisms driving extinction processes.

Resilience of hybrid herbivore-plant-pollinator networks

The concept of network resilience has gained increasing attention in the last few decades owing to its great potential in strengthening and maintaining complex systems. From network-based approaches, researchers have explored resilience of real ecological systems comprising diverse types of interactions, such as mutualism, antagonist, and predation, or mixtures of them. In this paper, we propose a dimension-reduction method for analyzing the resilience of hybrid herbivore-plant-pollinator networks. We qualitatively evaluate the contribution of species toward maintaining resilience of networked systems, as well as the distinct roles played by different categories of species. Our findings demonstrate that the strong contributors to network resilience within each category are more vulnerable to extinction. Notably, among the three types of species in consideration, plants exhibit a higher likelihood of extinction, compared to pollinators and herbivores.

Effects of triadimefon fungicide on Daphnia magna: Multigenerational effect and population-level ecological risk

Triadimefon is ubiquitous in various environmental media. Although toxicity of triadimefon to individual of aquatic organisms has been confirmed, its effect on organisms at population level remain poorly understood. In this study the long-term effect of triadimefon on individual and population of Daphnia magna were studied using multi-generational experiments and matrix model. Development and reproduction of three generations of F1 and F2 were significantly inhibited with the triadimefon concentration of 0.1 mg/L (p < 0.01). Toxicity of triadimefon to the offspring was stronger than to the parent (p < 0.05). When triadimefon concentration was higher than 0.1 mg/L, both population number and intrinsic rate of increase showed a decreasing trend with the increasing exposure concentration. Age structure of the population also tended to decline. Toxicity threshold derived on population-level was between mortality-based LC₅₀ and reproduction-based NOEC of Daphnia magna, and also between acute toxicity and chronic toxicity derived from species sensitivity distribution (SSD). The risk of population level derived from risk quotient was low for most areas, and the results derived from probability risk showed that the expected loss of intrinsic rate of increase of population was 0.0039 without considering other factors. Compared to the individual-level, the ecological risks at the population level were closer to the actual situation of the ecosystem response to the chemical pollution.

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.

Distance to Criticality Undergoes Critical Transition Before Epileptic Seizure Attacks

Epilepsy is a common neurological disorder characterized by recurring seizures, but its underlying mechanisms remain poorly understood. Despite extensive research, there are still gaps in our knowledge about the relationship between brain dynamics and seizures. In this study, our aim is to address these gaps by proposing a novel approach to assess the role of brain network dynamics in the onset of seizures. Specifically, we investigate the relationship between brain dynamics and seizures by tracking the distance to criticality. Our hypothesis is that this distance plays a crucial role in brain state changes and that seizures may be related to critical transitions of this distance. To test this hypothesis, we develop a method to measure the evolution of the brain network's distance to the critical dynamic systems (i.e., the distance to the tipping point, DTP) using dynamic network biomarker theory and random matrix theory. The results show that the DTP of the brain decreases significantly immediately after onset of an epileptic seizure, suggesting that the brain loses its well-defined quasi-critical state during seizures. We refer to this phenomenon as the "criticality of the criticality" (COC). Furthermore, we observe that DTP exhibits a shape transition before and after the onset of the seizures. This phenomenon suggests the possibility of early warning signal (EWS) identification in the dynamic sequence of DTP, which could be utilized for seizure prediction. Our results show that the Hurst exponent, skewness, kurtosis, autocorrelation, and variance of the DTP sequence are potential EWS features. This study advances our understanding of the relationship between brain dynamics and seizures and highlights the potential for using criticality-based measures to predict and prevent seizures.

Gene co-expression network analysis for the selection of candidate early warning indicators of heat and nutrient stress in Posidonia oceanica

The continuous worldwide seagrasses decline calls for immediate actions in order to preserve this precious marine ecosystem. The main stressors that have been linked with decline in seagrasses are 1) the increasing ocean temperature due to climate change and 2) the continuous inputs of nutrients (eutrophication) associated with coastal human activities. To avoid the loss of seagrass populations, an "early warning" system is needed. We used Weighed Gene Co-expression Network Analysis (WGCNA), a systems biology approach, to identify potential candidate genes that can provide an early warning signal of stress in the Mediterranean iconic seagrass Posidonia oceanica, anticipating plant mortality. Plants were collected from both eutrophic (EU) and oligotrophic (OL) environments and were exposed to thermal and nutrient stress in a dedicated mesocosm. By correlating the whole-genome gene expression after 2-weeks exposure with the shoot survival percentage after 5-weeks exposure to stressors, we were able to identify several transcripts that indicated an early activation of several biological processes (BP) including: protein metabolic process, RNA metabolic process, organonitrogen compound biosynthetic process, catabolic process and response to stimulus, which were shared among OL and EU plants and among leaf and shoot apical meristem (SAM), in response to excessive heat and nutrients. Our results suggest a more dynamic and specific response of the SAM compared to the leaf, especially the SAM from plants coming from a stressful environment appeared more dynamic than the SAM from a pristine environment. A vast list of potential molecular markers is also provided that can be used as targets to assess field samples.

Managing aquatic habitat structure for resilient trophic interactions

Structural habitat (the three-dimensional arrangement of physical matter, abiotic and biotic, at a location) is a foundational element for the resilience and maintenance of biodiversity, yet anthropogenic development is driving the global simplification of aquatic environments. Resource managers regularly seek to conserve aquatic food webs by increasing structural habitat complexity with expected benefits to fisheries; however, the global effectiveness of such actions is unclear. Our synthesis and theoretical analyses found that the response of a consumer-resource interaction (predatory sportfish and forage fish prey) to the addition of prey refuge habitat differed among systems with low and high rates of biomass transfer from resource to consumer (i.e., biomass potential); stabilization was not the rule. Greater prey refuge habitat availability tended to stabilize systems characterized by high biomass potential while simultaneously increasing consumer densities. In contrast, increasing prey refuge habitat availability in systems characterized by low biomass potential tended to mute energy transfer and moved consumer densities toward local extinction. Importantly, biomass potential and prey refuge can have antagonistic effects on stability and relative consumer densities, and it is therefore important to consider the local conditions of a system when using habitat manipulation as a management measure. Further development of our context-dependent perspective to whole food webs, and across different environments, may help to guide structural habitat management to better restore and protect aquatic ecosystems.

Experimental evidence of size-selective harvest and environmental stochasticity effects on population demography, fluctuations and non-linearity

Theory and analyses of fisheries data sets indicate that harvesting can alter population structure and destabilise non-linear processes, which increases population fluctuations. We conducted a factorial experiment on the population dynamics of Daphnia magna in relation to size-selective harvesting and stochasticity of food supply. Harvesting and stochasticity treatments both increased population fluctuations. Timeseries analysis indicated that fluctuations in control populations were non-linear, and non-linearity increased substantially in response to harvesting. Both harvesting and stochasticity induced population juvenescence, but harvesting did so via the depletion of adults, whereas stochasticity increased the abundance of juveniles. A fitted fisheries model indicated that harvesting shifted populations towards higher reproductive rates and larger-magnitude damped oscillations that amplify demographic noise. These findings provide experimental evidence that harvesting increases the non-linearity of population fluctuations and that both harvesting and stochasticity increase population variability and juvenescence.

Universal early warning signals of phase transitions in climate systems

The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and often irreversible shift is well established, but prediction of these events using standard forecast modelling techniques is quite difficult. This has led to the development of an alternative suite of methods that seek to identify signatures of critical phenomena in data, which are expected to occur in advance of many classes of dynamical bifurcation. Crucially, the manifestations of these critical phenomena are generic across a variety of systems, meaning that data-intensive deep learning methods can be trained on (abundant) synthetic data and plausibly prove effective when transferred to (more limited) empirical datasets. This paper provides a proof of concept for this approach as applied to lattice phase transitions: a deep neural network trained exclusively on two-dimensional Ising model phase transitions is tested on a number of real and simulated climate systems with considerable success. Its accuracy frequently surpasses that of conventional statistical indicators, with performance shown to be consistently improved by the inclusion of spatial indicators. Tools such as this may offer valuable insight into climate tipping events, as remote sensing measurements provide increasingly abundant data on complex geospatially resolved Earth systems.

Simple methods for early warnings of COVID-19 surges: Lessons learned from 21 months of wastewater and clinical data collection in Detroit, Michigan, United States

Wastewater-based epidemiology (WBE) has drawn great attention since the Coronavirus disease 2019 (COVID-19) pandemic, not only due to its capability to circumvent the limitations of traditional clinical surveillance, but also due to its potential to forewarn fluctuations of disease incidences in communities. One critical application of WBE is to provide "early warnings" for upcoming fluctuations of disease incidences in communities which traditional clinical testing is incapable to achieve. While intricate models have been developed to determine early warnings based on wastewater surveillance data, there is an exigent need for straightforward, rapid, broadly applicable methods for health departments and partner agencies to implement. Our purpose in this study is to develop and evaluate such early-warning methods and clinical-case peak-detection methods based on WBE data to mount an informed public health response. Throughout an extended wastewater surveillance period across Detroit, MI metropolitan area (the entire study period is from September 2020 to May 2022) we designed eight early-warning methods (three real-time and five post-factum). Additionally, we designed three peak-detection methods based on clinical epidemiological data. We demonstrated the utility of these methods for providing early warnings for COVID-19 incidences, with their counterpart accuracies evaluated by hit rates. "Hit rates" were defined as the number of early warning dates (using wastewater surveillance data) that captured defined peaks (using clinical epidemiological data) divided by the total number of early warning dates. Hit rates demonstrated that the accuracy of both real-time and post-factum methods could reach 100 %. Furthermore, the results indicate that the accuracy was influenced by approaches to defining peaks of disease incidence. The proposed methods herein can assist health departments capitalizing on WBE data to assess trends and implement quick public health responses to future epidemics. Besides, this study elucidated critical factors affecting early warnings based on WBE amid the COVID-19 pandemic.

A predictive timeline of wildlife population collapse

Contemporary rates of biodiversity decline emphasize the need for reliable ecological forecasting, but current methods vary in their ability to predict the declines of real-world populations. Acknowledging that stressor effects start at the individual level, and that it is the sum of these individual-level effects that drives populations to collapse, shifts the focus of predictive ecology away from using predominantly abundance data. Doing so opens new opportunities to develop predictive frameworks that utilize increasingly available multi-dimensional data, which have previously been overlooked for ecological forecasting. Here, we propose that stressed populations will exhibit a predictable sequence of observable changes through time: changes in individuals' behaviour will occur as the first sign of increasing stress, followed by changes in fitness-related morphological traits, shifts in the dynamics (for example, birth rates) of populations and finally abundance declines. We discuss how monitoring the sequential appearance of these signals may allow us to discern whether a population is increasingly at risk of collapse, or is adapting in the face of environmental change, providing a conceptual framework to develop new forecasting methods that combine multi-dimensional (for example, behaviour, morphology, life history and abundance) data.

Multiple phase transitions shape biodiversity of a migrating population

In a wide variety of natural systems, closely related microbial strains coexist stably, resulting in high levels of fine-scale biodiversity. However, the mechanisms that stabilize this coexistence are not fully understood. Spatial heterogeneity is one common stabilizing mechanism, but the rate at which organisms disperse throughout the heterogeneous environment may strongly impact the stabilizing effect that heterogeneity can provide. An intriguing example is the gut microbiome, where active mechanisms affect the movement of microbes and potentially maintain diversity. We investigate how biodiversity is affected by migration rate using a simple evolutionary model with heterogeneous selection pressure. We find that the biodiversity-migration rate relationship is shaped by multiple phase transitions, including a reentrant phase transition to coexistence. At each transition, an ecotype goes extinct and dynamics exhibit critical slowing down (CSD). CSD is encoded in the statistics of fluctuations due to demographic noise-this may provide an experimental means for detecting and altering impending extinction.

Predicting critical transitions in assortative spin-shifting networks

Methods to forecast critical transitions, i.e. abrupt changes in systems' equilibrium states have relevance in scientific fields such as ecology, seismology, finance and medicine among others. So far, the bulk of investigations on forecasting methods builds on equation-based modeling methods, which consider system states as aggregates and thus do not account for the different connection strengths in each part of the system. This seems inadequate against the background of studies that insinuate that critical transitions can originate in sparsely connected parts of systems. Here we use agent-based spin-shifting models with assortative network representations to distinguish different interaction densities. Our investigations confirm that signals of imminent critical transitions can indeed be detected significantly earlier in network parts with low link degrees. We discuss the reason for this circumstance on the basis of the free energy principle.

Rising temperature drives tipping points in mutualistic networks

The effect of climate warming on species' physiological parameters, including growth rate, mortality rate and handling time, is well established from empirical data. However, with an alarming rise in global temperature more than ever, predicting the interactive influence of these changes on mutualistic communities remains uncertain. Using 139 real plant-pollinator networks sampled across the globe and a modelling approach, we study the impact of species' individual thermal responses on mutualistic communities. We show that at low mutualistic strength plant-pollinator networks are at potential risk of rapid transitions at higher temperatures. Evidently, generalist species play a critical role in guiding tipping points in mutualistic networks. Further, we derive stability criteria for the networks in a range of temperatures using a two-dimensional reduced model. We identify network structures that can ascertain the delay of a community collapse. Until the end of this century, on account of increasing climate warming many real mutualistic networks are likely to be under the threat of sudden collapse, and we frame strategies to mitigate this. Together, our results indicate that knowing individual species' thermal responses and network structure can improve predictions for communities facing rapid transitions.

The Resilience of Plant-Pollinator Networks

There is growing awareness of pollinator declines worldwide. Conservation efforts have mainly focused on finding the direct causes, while paying less attention to building a systemic understanding of the fragility of these communities of pollinators. To fill this gap, we need operational measures of network resilience that integrate two different approaches in theoretical ecology. First, we should consider the range of conditions compatible with the stable coexistence of all of the species in a community. Second, we should address the rate and shape of network collapse once this safe operational space is exited. In this review, we describe this integrative approach and consider several mechanisms that may enhance the resilience of pollinator communities, chiefly rewiring the network of interactions, increasing heterogeneity, allowing variance, and enhancing coevolution. The most pressing need is to develop ways to reduce the gap between these theoretical recommendations and practical applications. This perspective shifts the emphasis from traditional approaches focusing on the equilibrium states to strategies that allow pollination networks to cope with global environmental change.

Quantifying resilience and the risk of regime shifts under strong correlated noise

Early warning indicators often suffer from the shortness and coarse-graining of real-world time series. Furthermore, the typically strong and correlated noise contributions in real applications are severe drawbacks for statistical measures. Even under favourable simulation conditions the measures are of limited capacity due to their qualitative nature and sometimes ambiguous trend-to-noise ratio. In order to solve these shortcomings, we analyze the stability of the system via the slope of the deterministic term of a Langevin equation, which is hypothesized to underlie the system dynamics close to the fixed point. The open-source available method is applied to a previously studied seasonal ecological model under noise levels and correlation scenarios commonly observed in real world data. We compare the results to autocorrelation, standard deviation, skewness, and kurtosis as leading indicator candidates by a Bayesian model comparison with a linear and a constant model. We show that the slope of the deterministic term is a promising alternative due to its quantitative nature and high robustness against noise levels and types. The commonly computed indicators apart from the autocorrelation with deseasonalization fail to provide reliable insights into the stability of the system in contrast to a previously performed study in which the standard deviation was found to perform best. In addition, we discuss the significant influence of the seasonal nature of the data to the robust computation of the various indicators, before we determine approximately the minimal amount of data per time window that leads to significant trends for the drift slope estimations.

Exploring the role of the potential surface in the behaviour of early warning signals

The theory of critical slowing down states that a system displays increasing relaxation times as it approaches a critical transition. These changes can be seen in statistics generated from timeseries data, which can be used as early warning signals of a transition. Such early warning signals would be of value for emerging infectious diseases or to understand when an endemic disease is close to elimination. However, in applications to a variety of epidemiological models there is frequent disagreement with the general theory of critical slowing down, with some indicators performing well on prevalence data but not when applied to incidence data. Furthermore, the alternative theory of critical speeding up predicts contradictory behaviour of early warning signals prior to some stochastic transitions. To investigate the possibility of observing critical speeding up in epidemiological models we characterise the behaviour of common early warning signals in terms of a system's potential surface and noise around a quasi-steady state. We then describe a method to obtain these key features from timeseries data, taking as a case study a version of the SIS model, adapted to demonstrate either critical slowing down or critical speeding up. We show this method accurately reproduces the analytic potential surface and diffusion function, and that these results can be used to determine the behaviour of early warning signals and correctly identify signs of both critical slowing down and critical speeding up.

The fundamental benefits of multiplexity in ecological networks

A tipping point presents perhaps the single most significant threat to an ecological system as it can lead to abrupt species extinction on a massive scale. Climate changes leading to the species decay parameter drifts can drive various ecological systems towards a tipping point. We investigate the tipping-point dynamics in multi-layer ecological networks supported by mutualism. We unveil a natural mechanism by which the occurrence of tipping points can be delayed by multiplexity that broadly describes the diversity of the species abundances, the complexity of the interspecific relationships, and the topology of linkages in ecological networks. For a double-layer system of pollinators and plants, coupling between the network layers occurs when there is dispersal of pollinator species. Multiplexity emerges as the dispersing species establish their presence in the destination layer and have a simultaneous presence in both. We demonstrate that the new mutualistic links induced by the dispersing species with the residence species have fundamental benefits to the well-being of the ecosystem in delaying the tipping point and facilitating species recovery. Articulating and implementing control mechanisms to induce multiplexity can thus help sustain certain types of ecosystems that are in danger of extinction as the result of environmental changes.

When and where to protect forests

Ongoing deforestation poses a major threat to biodiversity^1,2. With limited resources and imminent threats, deciding when as well as where to conserve is a fundamental question. Here we use a dynamic optimization approach to identify an optimal sequence for the conservation of plant species in 458 forested ecoregions globally over the next 50 years. The optimization approach includes species richness in each forested ecoregion, complementarity of species across ecoregions, costs of conservation that rise with cumulative protection in an ecoregion, the existing degree of protection, the rate of deforestation and the potential for reforestation in each ecoregion. The optimal conservation strategy for this formulation initially targets a small number of ecoregions where further deforestation leads to large reductions in species and where the costs of conservation are low. In later years, conservation efforts spread to more ecoregions, and invest in both expanded protection of primary forest and reforestation. The largest gains in species conservation come in Melanesia, South and Southeast Asia, the Anatolian peninsula, northern South America and Central America. The results highlight the potentially large gains in conservation that can be made with carefully targeted investments.

Scaling up our understanding of tipping points

Anthropogenic activities are increasingly affecting ecosystems across the globe. Meanwhile, empirical and theoretical evidence suggest that natural systems can exhibit abrupt collapses in response to incremental increases in the stressors, sometimes with dramatic ecological and economic consequences. These catastrophic shifts are faster and larger than expected from the changes in the stressors and happen once a tipping point is crossed. The primary mechanisms that drive ecosystem responses to perturbations lie in their architecture of relationships, i.e. how species interact with each other and with the physical environment and the spatial structure of the environment. Nonetheless, existing theoretical work on catastrophic shifts has so far largely focused on relatively simple systems that have either few species and/or no spatial structure. This work has laid a critical foundation for understanding how abrupt responses to incremental stressors are possible, but it remains difficult to predict (let alone manage) where or when they are most likely to occur in more complex real-world settings. Here, we discuss how scaling up our investigations of catastrophic shifts from simple to more complex-species rich and spatially structured-systems could contribute to expanding our understanding of how nature works and improve our ability to anticipate the effects of global change on ecological systems. This article is part of the theme issue 'Ecological complexity and the biosphere: the next 30 years'.

Data-driven prediction in dynamical systems: recent developments

In recent years, we have witnessed a significant shift toward ever-more complex and ever-larger-scale systems in the majority of the grand societal challenges tackled in applied sciences. The need to comprehend and predict the dynamics of complex systems have spurred developments in large-scale simulations and a multitude of methods across several disciplines. The goals of understanding and prediction in complex dynamical systems, however, have been hindered by high dimensionality, complexity and chaotic behaviours. Recent advances in data-driven techniques and machine-learning approaches have revolutionized how we model and analyse complex systems. The integration of these techniques with dynamical systems theory opens up opportunities to tackle previously unattainable challenges in modelling and prediction of dynamical systems. While data-driven prediction methods have made great strides in recent years, it is still necessary to develop new techniques to improve their applicability to a wider range of complex systems in science and engineering. This focus issue shares recent developments in the field of complex dynamical systems with emphasis on data-driven, data-assisted and artificial intelligence-based discovery of dynamical systems. This article is part of the theme issue 'Data-driven prediction in dynamical systems'.

Evaluating the performance of temporal and spatial early warning statistics of algal blooms

Regime shifts have large consequences for ecosystems and the services they provide. However, understanding the potential for, causes of, proximity to, and thresholds for regime shifts in nearly all settings is difficult. Generic statistical indicators of resilience have been proposed and studied in a wide range of ecosystems as a method to detect when regime shifts are becoming more likely without direct knowledge of underlying system dynamics or thresholds. These early warning statistics (EWS) have been studied separately but there have been few examples that directly compare temporal and spatial EWS in ecosystem-scale empirical data. To test these methods, we collected high-frequency time series and high-resolution spatial data during a whole-lake fertilization experiment while also monitoring an adjacent reference lake. We calculated two common EWS, standard deviation and autocorrelation, in both time series and spatial data to evaluate their performance prior to the resulting algal bloom. We also applied the quickest detection method to generate binary alarms of resilience change from temporal EWS. One temporal EWS, rolling window standard deviation, provided advanced warning in most variables prior to the bloom, showing trends and between-lake patterns consistent with theory. In contrast, temporal autocorrelation and both measures of spatial EWS (spatial SD, Moran's  I) provided little or no warning. By compiling time series data from this and past experiments with and without nutrient additions, we were able to evaluate temporal EWS performance for both constant and changing resilience conditions. True positive alarm rates were 2.5-8.3 times higher for rolling window standard deviation when a lake was being pushed towards a bloom than the rate of false positives when it was not. For rolling window autocorrelation, alarm rates were much lower and no variable had a higher true positive than false positive alarm rate. Our findings suggest temporal EWS provide advanced warning of algal blooms and that this approach could help managers prepare for and/or minimize negative bloom impacts.

Practical guide to using Kendall's τ in the context of forecasting critical transitions

Recent studies demonstrate that trends in indicators extracted from measured time series can indicate an approach of an impending transition. Kendall's τ coefficient is often used to study the trend of statistics related to the critical slowing down phenomenon and other methods to forecast critical transitions. Because statistics are estimated from time series, the values of Kendall's τ are affected by parameters such as window size, sample rate and length of the time series, resulting in challenges and uncertainties in interpreting results. In this study, we examine the effects of different parameters on the distribution of the trend obtained from Kendall's τ, and provide insights into how to choose these parameters. We also suggest the use of the non-parametric Mann-Kendall test to evaluate the significance of a Kendall's τ value. The non-parametric test is computationally much faster compared with the traditional parametric auto-regressive, moving-average model test.

The toxic effects of combined exposure of chlorpyrifos and p, p'-DDE to zebrafish (Danio rerio) and tissue bioaccumulation

Pesticides are widely used and frequently detected in the environment. The evaluation on the toxic effects of the co-exposure of two or more pesticides or related metabolites could reflect the real situation of the exposing risks. In this study, zebrafish was used as a model to investigate the potential toxic interactions of chlorpyrifos and 1,1-dichloro-2,2-bis(p-chlorophenyl)ethylene (p,p'-DDE) on the survival rate, oxidative stress response and neurotoxicity, as well as their bioaccumulation and distribution in tissues. Co-exposure of chlorpyrifos and p,p'-DDE resulted in significant additive acute toxic effects on adult zebrafish with model deviation ratio (MDR) = 1.64. Both 7-day short-term at 1% LC₅₀ and 35-day long-term at 0.5% LC₅₀ co-exposure of chlorpyrifos with p,p'-DDE (50 and 100 µg/L) significantly reduced the survival rate of zebrafish colony to 75 and 82.5%. Co-exposure of chlorpyrifos and p,p'-DDE contributed to increased activity of antioxidant enzyme CAT, SOD and GST and excessive MDA generation, and decreased activity of CarE, CYP450 and AChE, compared with either single exposure of them. In co-exposure, the bioaccumulation of chlorpyrifos and p,p'-DDE was significantly different from the single exposure group. Overall, this study unraveled the potential toxic interaction of chlorpyrifos and p,p'-DDE on zebrafish and provided reference for environmental risk assessment of pesticide mixture.

Practical guide to using Kendall's τ in the context of forecasting critical transitions

Recent studies demonstrate that trends in indicators extracted from measured time series can indicate an approach of an impending transition. Kendall's τ coefficient is often used to study the trend of statistics related to the critical slowing down phenomenon and other methods to forecast critical transitions. Because statistics are estimated from time series, the values of Kendall's τ are affected by parameters such as window size, sample rate and length of the time series, resulting in challenges and uncertainties in interpreting results. In this study, we examine the effects of different parameters on the distribution of the trend obtained from Kendall's τ, and provide insights into how to choose these parameters. We also suggest the use of the non-parametric Mann-Kendall test to evaluate the significance of a Kendall's τ value. The non-parametric test is computationally much faster compared with the traditional parametric auto-regressive, moving-average model test.

Decadal community structure shifts with cold pool variability in the eastern Bering Sea shelf

A characteristic feature of the eastern Bering Sea (EBS) is a subsurface layer linked to seasonal sea ice (SSI) and defined by bottom temperatures less than 2 °C, which is termed the cold pool. Cold pool variability is directly tied to regional zooplankton and fish dynamics. Multifrequency (200 and 460 kHz) acoustic backscatter data were collected remotely using upward looking echosounders along the EBS shelf from 2008 and 2018 and used as a proxy of biological abundance. Acoustic data were coupled with bottom temperature and regional SSI data from the cold (2006-2013) and warm (2014-2018) regimes to assess the relationship between biological scattering communities and cold pool variation. Acoustic backscatter was 2 orders of magnitude greater during the cold regime than during the warm regime, with multifrequency analysis indicating a shift in the warm regime frequency-dependent scattering communities. Cold pool proxy SSI was a stronger predictor for biological scattering than bottom temperature in the cold regime, while warm regime bottom temperature and SSI were equal in predictive power and resulted in improved predictive model performance. Results suggest coupled cold pool and frequency-dependent scattering dynamics are a potential regime shift indicator and may be useful for management practices in surrounding Arctic ecosystems.

Community structure determines the predictability of population collapse

Early warning signals (EWS) are phenomenological tools that have been proposed as predictors of the collapse of biological systems. Although a growing body of work has shown the utility of EWS based on either statistics derived from abundance data or shifts in phenotypic traits such as body size, so far this work has largely focused on single species populations.

However, to predict reliably the future state of ecological systems, which inherently could consist of multiple species, understanding how reliable such signals are in a community context is critical.

Here, reconciling quantitative trait evolution and Lotka–Volterra equations, which allow us to track both abundance and mean traits, we simulate the collapse of populations embedded in mutualistic and multi‐trophic predator–prey communities. Using these simulations and warning signals derived from both population‐ and community‐level data, we showed the utility of abundance‐based EWS, as well as metrics derived from stability‐landscape theory (e.g. width and depth of the basin of attraction), were fundamentally linked. Thus, the depth and width of such stability‐landscape curves could be used to identify which species should exhibit the strongest EWS of collapse.

The probability a species displays both trait and abundance‐based EWS was dependent on its position in a community, with some species able to act as indicator species. In addition, our results also demonstrated that in general trait‐based EWS were less reliable in comparison with abundance‐based EWS in forecasting species collapses in our simulated communities. Furthermore, community‐level abundance‐based EWS were fairly reliable in comparison with their species‐level counterparts in forecasting species‐level collapses.

Our study suggests a holistic framework that combines abundance‐based EWS and metrics derived from stability‐landscape theory that may help in forecasting species loss in a community context.

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.

Anticipating manic and depressive transitions in patients with bipolar disorder using early warning signals

Background

In bipolar disorder treatment, accurate episode prediction is paramount but remains difficult. A novel idiographic approach to prediction is to monitor generic early warning signals (EWS), which may manifest in symptom dynamics. EWS could thus form personalized alerts in clinical care. The present study investigated whether EWS can anticipate manic and depressive transitions in individual patients with bipolar disorder.

Methods

Twenty bipolar type I/II patients (with ≥ 2 episodes in the previous year) participated in ecological momentary assessment (EMA), completing five questionnaires a day for four months (Mean = 491 observations per person). Transitions were determined by weekly completed questionnaires on depressive (Quick Inventory for Depressive Symptomatology Self-Report) and manic (Altman Self-Rating Mania Scale) symptoms. EWS (rises in autocorrelation at lag-1 and standard deviation) were calculated in moving windows over 17 affective and symptomatic EMA states. Positive and negative predictive values were calculated to determine clinical utility.

Results

Eleven patients reported 1–2 transitions. The presence of EWS increased the probability of impending depressive and manic transitions from 32-36% to 46–48% (autocorrelation) and 29–41% (standard deviation). However, the absence of EWS could not be taken as a sign that no transition would occur in the near future. The momentary states that indicated nearby transitions most accurately (predictive values: 65–100%) were full of ideas, worry, and agitation. Large individual differences in the utility of EWS were found.

Conclusions

EWS show theoretical promise in anticipating manic and depressive transitions in bipolar disorder, but the level of false positives and negatives, as well as the heterogeneity within and between individuals and preprocessing methods currently limit clinical utility.

Supplementary Information

The online version contains supplementary material available at 10.1186/s40345-022-00258-4.

Warning signs for non-Markovian bifurcations: colour blindness and scaling laws

Warning signs for tipping points (or critical transitions) have been very actively studied. Although the theory has been applied successfully in models and in experiments for many complex systems such as for tipping in climate systems, there are ongoing debates as to when warning signs can be extracted from data. In this work, we shed light on this debate by considering different types of underlying noise. Thereby, we significantly advance the general theory of warning signs for nonlinear stochastic dynamics. A key scenario deals with stochastic systems approaching a bifurcation point dynamically upon slow parameter variation. The stochastic fluctuations are generically able to probe the dynamics near a deterministic attractor to reveal critical slowing down. Using scaling laws near bifurcations, one can then anticipate the distance to a bifurcation. Previous warning signs results assume that the noise is Markovian, most often even white. Here, we study warning signs for non-Markovian systems including coloured noise and α -regular Volterra processes (of which fractional Brownian motion and the Rosenblatt process are special cases). We prove that early warning scaling laws can disappear completely or drastically change their exponent based upon the parameters controlling the noise process. This provides a clear explanation as to why applying standard warning signs results to reduced models of complex systems may not agree with data-driven studies. We demonstrate our results numerically in the context of a box model of the Atlantic Meridional Overturning Circulation.