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.

Managing ecological thresholds of a risky commons

Common resources are often overexploited and appear subject to critical transitions from one stable state to another antagonistic state. Many times resulting in tragedy of the commons (TOC)-exploitation of shared resources for personal gain/payoffs, leading to worse outcomes or extinction. An adequate response would be strategic interaction, such as inspection and punishment by institutions to avoid TOC. This strategic interaction is often coupled with dynamically changing common resources. However, effect of strategic interaction in complex, coupled socio-ecological systems is less studied. Here, we develop replicator equations using evolving games in which strategy and common resources co-evolve. We consider the shared commons as fish dynamics governed by the intrinsic growth rate, predation and harvesting. The joint dynamics exhibit an oscillatory TOC, revealing that institutions need to pay special attention to intrinsic growth rate and nonlinear interaction. Our research shows that the co-evolving system exhibits a broader range of dynamics when predation is present compared to the disengaged fishery system. We conclude that the usefulness, chances and challenges of modelling co-evolutionary games to create sustainable systems merit further research.

Five fundamental ways in which complex food webs may spiral out of control

Theory suggests that increasingly long, negative feedback loops of many interacting species may destabilize food webs as complexity increases. Less attention has, however, been paid to the specific ways in which these 'delayed negative feedbacks' may affect the response of complex ecosystems to global environmental change. Here, we describe five fundamental ways in which these feedbacks might pave the way for abrupt, large-scale transitions and species losses. By combining topological and bioenergetic models, we then proceed by showing that the likelihood of such transitions increases with the number of interacting species and/or when the combined effects of stabilizing network patterns approach the minimum required for stable coexistence. Our findings thus shift the question from the classical question of what makes complex, unaltered ecosystems stable to whether the effects of, known and unknown, stabilizing food-web patterns are sufficient to prevent abrupt, large-scale transitions under global environmental change.

The Potential for Alternative Stable States in Food Webs Depends on Feedback Mechanism and Trait Diversity

AbstractAlternative stable ecosystem states are possible under the same environmental conditions in models of two or three interacting species and an array of feedback loops. However, multispecies food webs might weaken the feedbacks loops that can create alternative stable states. To test how this potential depends on food web properties, we develop a many-species model where consumer Allee effects emerge from consumer-resource interactions. We evaluate the interactive effects of food web connectance, interspecific trait diversity, and two classes of feedbacks: specialized feedbacks, where consumption of individual resources declines at high resource abundance (e.g., from schooling or reaching size refugia), and aggregate feedbacks, where overall resource abundance reduces consumer recruitment (e.g., from resources enhancing competition or mortality experienced by recruits). We find that aggregate feedbacks maintain, and specialized feedbacks reduce, the potential for alternative states. Interspecific trait diversity decreases the prevalence of alternative stable states more for specialized than for aggregate feedbacks. Increasing food web connectance increases the potential for alternative stable states for aggregated feedbacks but decreases it for specialized feedbacks, where losing vulnerable consumers can cascade into food web collapses. Altogether, multispecies food webs can limit the set of processes that create alternative stable states and impede consumer recovery from disturbance.

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.

Non-equilibrium early-warning signals for critical transitions in ecological systems

Complex systems can exhibit sudden transitions or regime shifts from one stable state to another, typically referred to as critical transitions. It becomes a great challenge to identify a robust warning sufficiently early that action can be taken to avert a regime shift. We employ landscape-flux theory from nonequilibrium statistical mechanics as a general framework to quantify the global stability of ecological systems and provide warning signals for critical transitions. We quantify the average flux as the nonequilibrium driving force and the dynamical origin of the nonequilibrium transition while the entropy production rate as the nonequilibrium thermodynamic cost and thermodynamic origin of the nonequilibrium transition. Average flux, entropy production, nonequilibrium free energy, and time irreversibility quantified by the difference in cross-correlation functions forward and backward in time can serve as early warning signals for critical transitions much earlier than other conventional predictors. We utilize a classical shallow lake model as an exemplar for our early warning prediction. Our proposed method is general and can be readily applied to assess the resilience of many other ecological systems. The early warning signals proposed here can potentially predict critical transitions earlier than established methods and perhaps even sufficiently early to avert catastrophic shifts.

Applying early warning indicators to predict critical transitions in a lake undergoing multiple changes

Lakes are dynamic ecosystems that can transition among stable states. Since ecosystem-scale transitions can be detrimental and difficult to reverse, being able to predict impending critical transitions in state variables has become a major area of research. However, not all transitions are detrimental, and there is considerable interest in better evaluating the success of management interventions to support adaptive management strategies. Here, we retrospectively evaluated the agreement between time series statistics (i.e., standard deviation, autocorrelation, skewness, and kurtosis-also known as early warning indicators) and breakpoints in state variables in a lake (Lake Simcoe, Ontario, Canada) that has improved from a state of eutrophication. Long-term (1980 to 2019) monitoring data collected fortnightly throughout the ice-free season were used to evaluate historical changes in 15 state variables (e.g., dissolved organic carbon, phosphorus, chlorophyll a) and multivariate-derived time series at three monitoring stations (shallow, middepth, deep) in Lake Simcoe. Time series results from the two deep-water stations indicate that over this period Lake Simcoe transitioned from an algal-dominated state toward a state with increased water clarity (i.e., Secchi disk depth) and silica and lower nutrient and chlorophyll a concentrations, which coincided with both substantial management intervention and the establishment of invasive species (e.g., Dreissenid mussels). Consistent with improvement, Secchi depth at the deep-water stations demonstrated expected trends in statistical indicators prior to identified breakpoints, whereas total phosphorus and chlorophyll a revealed more nuanced patterns. Overall, state variables were largely found to yield inconsistent trends in statistical indicators, so many breakpoints were likely not reflective of traditional bifurcation critical transitions. Nevertheless, statistical indicators of state variable time series may be a valuable tool for the adaptive management and long-term monitoring of lake ecosystems, but we call for more research within the domain of early warning indicators to establish a better understanding of state variable behavior prior to lake changes.

Visualizing Invisible Phase Transitions in Blue Phase Liquid Crystals Using Early Warning Indicators

Changes in the statistical properties of data as a system approaches a critical transition is studied intensively as early warning signals, but their application to materials science, where phase transitions-a type of critical transition-are of fundamental importance, are limited. Here, a critical transition analysis is applied to time-series data from a microscopic 3D ordered soft material-blue phase liquid crystals (BPLC)-and demonstrates that phase transitions that are invisible under ambient conditions can be visualized through the choice of appropriate early warning indicators. After discussing how a phase transition affects the statistical properties in a system with a Landau-de Gennes type free energy potential, the predicted changes are experimentally observed at the two types of phase transitions that occur in a BPLC: the isotropic to simple cubic, and simple cubic to body-centered cubic transitions. In particular, it is shown that the skewness of the intensity distribution inverts its sign at the phase transition, enabling temporally and spatially resolved mapping of phase transitions. This approach can be easily adapted to a wide variety of material systems and microscopy techniques, providing a powerful tool for studying complex critical transition phenomena.

A probabilistic framework for windows of opportunity: the role of temporal variability in critical transitions

The establishment of young organisms in harsh environments often requires a window of opportunity (WoO). That is, a short time window in which environmental conditions drop long enough below the hostile average level, giving the organism time to develop tolerance and transition into stable existence. It has been suggested that this kind of establishment dynamics is a noise-induced transition between two alternate states. Understanding how temporal variability (i.e. noise) in environmental conditions affects establishment of organisms is therefore key, yet not well understood or included explicitly in the WoO framework. In this paper, we develop a coherent theoretical framework for understanding when the WoO open or close based on simple dichotomous environmental variation. We reveal that understanding of the intrinsic timescales of both the developing organism and the environment is fundamental to predict if organisms can or cannot establish. These insights have allowed us to develop statistical laws for predicting establishment probabilities based on the period and variance of the fluctuations in naturally variable environments. Based on this framework, we now get a clear understanding of how changes in the timing and magnitude of climate variability or management can mediate establishment chances.

Failures to disagree are essential for environmental science to effectively influence policy development

While environmental science, and ecology in particular, is working to provide better understanding to base sustainable decisions on, the way scientific understanding is developed can at times be detrimental to this cause. Locked‐in debates are often unnecessarily polarised and can compromise any common goals of the opposing camps. The present paper is inspired by a resolved debate from an unrelated field of psychology where Nobel laureate David Kahneman and Garry Klein turned what seemed to be a locked‐in debate into a constructive process for their fields. The present paper is also motivated by previous discourses regarding the role of thresholds in natural systems for management and governance, but its scope of analysis targets the scientific process within complex social‐ecological systems in general. We identified four features of environmental science that appear to predispose for locked‐in debates: (1) The strongly context‐dependent behaviour of ecological systems. (2) The dominant role of single hypothesis testing. (3) The high prominence given to theory demonstration compared investigation. (4) The effect of urgent demands to inform and steer policy. This fertile ground is further cultivated by human psychological aspects as well as the structure of funding and publication systems.

Critical Transitions in Ecosystems and Society. The Contribution of Sociological Systems Theory to the Analysis of Socio-Environmental Transformations

The theory of critical transitions and the theory of self-referential social systems are two well-established theories in the ecosystem and sociological research respectively. A dialogue between them may offer new insights on the complex articulation of the nature and society nexus in socio-environmental transformations. By means of the conceptual reconstruction of both theories and drawing on relevant literature of social-ecological research, in this article, I argue that systems theory can contribute to the theory of critical transitions with a robust concept of communication that accounts for the relevance of semantics and social structures, the production of communicative locks, and the identification of early warning signals of social-ecological transitions in communication. On the other hand, the theory of critical transitions provides systems theory with both a refined concept of crisis as critical transition and the technical tools for empirical research. The article concludes that the dialogue between the science of ecosystems and the science of society is not an intellectual exercise but a form of increasing the correspondence between social-ecological transitions and our explanations and interventions in this domain.

Structure-based identification of sensor species for anticipating critical transitions

Ecological systems can undergo sudden, catastrophic changes known as critical transitions. Anticipating these critical transitions remains challenging in systems with many species because the associated early warning signals can be weakly present or even absent in some species, depending on the system dynamics. Therefore, our limited knowledge of ecological dynamics may suggest that it is hard to identify those species in the system that display early warning signals. Here, we show that, in mutualistic ecological systems, it is possible to identify species that early anticipate critical transitions by knowing only the system structure-that is, the network topology of plant-animal interactions. Specifically, we leverage the mathematical theory of structural observability of dynamical systems to identify a minimum set of "sensor species," whose measurement guarantees that we can infer changes in the abundance of all other species. Importantly, such a minimum set of sensor species can be identified by using the system structure only. We analyzed the performance of such minimum sets of sensor species for detecting early warnings using a large dataset of empirical plant-pollinator and seed-dispersal networks. We found that species that are more likely to be sensors tend to anticipate earlier critical transitions than other species. Our results underscore how knowing the structure of multispecies systems can improve our ability to anticipate critical transitions.

Resilience dynamics and productivity-driven shifts in the marine communities of the Western Mediterranean Sea

Ecological resilience has become a conceptual cornerstone bridging ecological processes to conservation needs. Global change is increasingly associated with local changes in environmental conditions that can cause abrupt ecosystem reorganizations attending to system‐specific resilience fluctuations with time (i.e. resilience dynamics).

Here we assess resilience dynamics associated with climate‐driven ecosystems transitions, expressed as changes in the relevant contribution of species with different life‐history strategies, in two benthopelagic systems.

We analysed data from 1994 to 2019 coming from a scientific bottom trawl survey in two environmentally contrasting ecosystems in the Western Mediterranean Sea—Northern Spain and Alboran Sea. Benthopelagic species were categorized according to their life‐history strategies (opportunistic, periodic and equilibrium), ecosystem functions and habitats. We implemented an Integrated Resilience Assessment (IRA) to elucidate the response mechanism of the studied ecosystems to several candidate environmental stressors and quantify the ecosystems’ resilience. We demonstrate that both ecosystems responded discontinuously to changes in chlorophyll‐a concentration more than any other stressor. The response in Northern Spain indicated a more overarching regime shift than in the Alboran Sea. Opportunistic fish were unfavoured in both ecosystems in the recent periods, while invertebrate species of short life cycle were generally favoured, particularly benthic species in the Alboran Sea.

The study illustrates that the resilience dynamics of the two ecosystems were mostly associated with fluctuating productivity, but subtle and long‐term effects from sea warming and fishing reduction were also discernible. Such dynamics are typical of systems with wide environmental gradient such as the Northern Spain, as well as systems with highly hydrodynamic and of biogeographical complexity such as the Alboran Sea. We stress that management should become more adaptive by utilizing the knowledge on the systems’ productivity thresholds and underlying shifts to help anticipate both short‐term/less predictable events and long‐term/expected effects of climate change.

Early warning signals of infectious disease transitions: a review

Early warning signals (EWSs) are a group of statistical time-series signals which could be used to anticipate a critical transition before it is reached. EWSs are model-independent methods that have grown in popularity to support evidence of disease emergence and disease elimination. Theoretical work has demonstrated their capability of detecting disease transitions in simple epidemic models, where elimination is reached through vaccination, to more complex vector transmission, age-structured and metapopulation models. However, the exact time evolution of EWSs depends on the transition; here we review the literature to provide guidance on what trends to expect and when. Recent advances include methods which detect when an EWS becomes significant; the earlier an upcoming disease transition is detected, the more valuable an EWS will be in practice. We suggest that future work should firstly validate detection methods with synthetic and historical datasets, before addressing their performance with real-time data which is accruing. A major challenge to overcome for the use of EWSs with disease transitions is to maintain the accuracy of EWSs in data-poor settings. We demonstrate how EWSs behave on reported cases for pertussis in the USA, to highlight some limitations when detecting disease transitions with real-world data.

Emergence of hierarchy in networked endorsement dynamics

Many social and biological systems are characterized by enduring hierarchies, including those organized around prestige in academia, dominance in animal groups, and desirability in online dating. Despite their ubiquity, the general mechanisms that explain the creation and endurance of such hierarchies are not well understood. We introduce a generative model for the dynamics of hierarchies using time-varying networks, in which new links are formed based on the preferences of nodes in the current network and old links are forgotten over time. The model produces a range of hierarchical structures, ranging from egalitarianism to bistable hierarchies, and we derive critical points that separate these regimes in the limit of long system memory. Importantly, our model supports statistical inference, allowing for a principled comparison of generative mechanisms using data. We apply the model to study hierarchical structures in empirical data on hiring patterns among mathematicians, dominance relations among parakeets, and friendships among members of a fraternity, observing several persistent patterns as well as interpretable differences in the generative mechanisms favored by each. Our work contributes to the growing literature on statistically grounded models of time-varying networks.

No warning for slow transitions

A rise in fragility as a system approaches a tipping point may be sometimes estimated using dynamical indicators of resilience (DIORs) that measure the characteristic slowing down of recovery rates before a tipping point. A change in DIORs could be interpreted as an early warning signal for an upcoming critical transition. However, in order to be able to estimate the DIORs, observational records need to be long enough to capture the response rate of the system. As we show here, the required length of the time series depends on the response rates of the system. For instance, the current rate of anthropogenic climate forcing is fast relative to the response rate of some parts of the climate system. Therefore, we may expect difficulties estimating the resilience from modern time series. So far, there have been no systematic studies of the effects of the response rates of the dynamical systems and the rates of forcing on the detectability trends in the DIORs prior to critical transitions. Here, we quantify the performance of the resilience indicators variance and temporal autocorrelation, in systems with different response rates and for different rates of forcing. Our results show that the rapid rise of anthropogenic forcing to the Earth may make it difficult to detect changes in the resilience of ecosystems and climate elements from time series. These findings suggest that in order to determine with models whether the use of the DIORs is appropriate, we need to use realistic models that incorporate the key processes with the appropriate time constants.

Flickering body temperature anticipates criticality in hibernation dynamics

Hibernation has been selected for increasing survival in harsh climatic environments. Seasonal variability in temperature may push the body temperatures of hibernating animals across boundaries of alternative states between euthermic temperature and torpor temperature, typical of either hibernation or summer dormancy. Nowadays, wearable electronics present a promising avenue to assess the occurrence of criticality in physiological systems, such as body temperature fluctuating between attractors of activity and hibernation. For this purpose, we deployed temperature loggers on two hibernating edible dormice for an entire year and under Mediterranean climate conditions. Highly stochastic body temperatures with sudden switches over time allowed us to assess the reliability of statistical leading indicators to anticipate tipping points when approaching a critical transition. Hibernation dynamics showed flickering, a phenomenon occurring when a system rapidly moves back and forth between two alternative attractors preceding the upcoming major regime shift. Flickering of body temperature increased when the system approached bifurcations, which were also anticipated by several metric- and model-based statistical indicators. Nevertheless, some indicators did not show a pattern in their response, which suggests that their performance varies with the dynamics of the biological system studied. Gradual changes in air temperature drove transient between states of hibernation and activity, and also drove hysteresis. For hibernating animals, hysteresis may increase resilience when ending hibernation earlier than the optimal time, which may occur in regions where temperatures are sharply rising, especially during winter. Temporal changes in early indicators of critical transitions in hibernation dynamics may help to understand the effects of climate on evolutionary life histories and the plasticity of hibernating organisms to cope with shortened hibernation due to global warming.

Anticipating the Novel Coronavirus Disease (COVID-19) Pandemic

The COVID-19 outbreak was first declared an international public health, and it was later deemed a pandemic. In most countries, the COVID-19 incidence curve rises sharply over a short period of time, suggesting a transition from a disease-free (or low-burden disease) equilibrium state to a sustained infected (or high-burden disease) state. Such a transition is often known to exhibit characteristics of "critical slowing down." Critical slowing down can be, in general, successfully detected using many statistical measures, such as variance, lag-1 autocorrelation, density ratio, and skewness. Here, we report an empirical test of this phenomena on the COVID-19 datasets of nine countries, including India, China, and the United States. For most of the datasets, increases in variance and autocorrelation predict the onset of a critical transition. Our analysis suggests two key features in predicting the COVID-19 incidence curve for a specific country: (a) the timing of strict social distancing and/or lockdown interventions implemented and (b) the fraction of a nation's population being affected by COVID-19 at that time. Furthermore, using satellite data of nitrogen dioxide as an indicator of lockdown efficacy, we found that countries where lockdown was implemented early and firmly have been successful in reducing COVID-19 spread. These results are essential for designing effective strategies to control the spread/resurgence of infectious pandemics.

Data-driven identification of reliable sensor species to predict regime shifts in ecological networks

Signals of critical slowing down are useful for predicting impending transitions in ecosystems. However, in a system with complex interacting components not all components provide the same quality of information to detect system-wide transitions. Identifying the best indicator species in complex ecosystems is a challenging task when a model of the system is not available. In this paper, we propose a data-driven approach to rank the elements of a spatially distributed ecosystem based on their reliability in providing early-warning signals of critical transitions. The proposed method is rooted in experimental modal analysis techniques traditionally used to identify structural dynamical systems. We show that one could use natural system fluctuations and the system responses to small perturbations to reveal the slowest direction of the system dynamics and identify indicator regions that are best suited for detecting abrupt transitions in a network of interacting components. The approach is applied to several ecosystems to demonstrate how it successfully ranks regions based on their reliability to provide early-warning signals of regime shifts. The significance of identifying the indicator species and the challenges associated with ranking nodes in networks of interacting components are also discussed.

Critical transitions in malaria transmission models are consistently generated by superinfection

The history of modelling vector-borne infections essentially begins with the papers by Ross on malaria. His models assume that the dynamics of malaria can most simply be characterized by two equations that describe the prevalence of malaria in the human and mosquito hosts. This structure has formed the central core of models for malaria and most other vector-borne diseases for the past century, with additions acknowledging important aetiological details. We partially add to this tradition by describing a malaria model that provides for vital dynamics in the vector and the possibility of super-infection in the human host: reinfection of asymptomatic hosts before they have cleared a prior infection. These key features of malaria aetiology create the potential for break points in the prevalence of infected hosts, sudden transitions that seem to characterize malaria's response to control in different locations. We show that this potential for critical transitions is a general and underappreciated feature of any model for vector-borne diseases with incomplete immunity, including the canonical Ross-McDonald model. Ignoring these details of the host's immune response to infection can potentially lead to serious misunderstanding in the interpretation of malaria distribution patterns and the design of control schemes for other vector-borne diseases. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'. This issue is linked with the subsequent theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'.

Critical transitions in rainfall manipulation experiments on grasslands

As a result of climate and land-use changes, grasslands have been subjected to intensifying drought regimes. Extreme droughts could interfere in the positive feedbacks between grasses and soil water content, pushing grasslands across critical thresholds of productivity and leading them to collapse. If this happens, systems may show hysteresis and costly management interventions might be necessary to restore predrought productivity. Thus, neglecting critical transitions may lead to mismanagement of grasslands and to irreversible loss of ecosystem services. Rainfall manipulation experiments constitute a powerful approach to investigate the risk of such critical transitions. However, experiments performed to date have rarely applied extreme droughts and have used resilience indices that disregard the existence of hysteresis. Here, we suggest how to incorporate critical transitions when designing rainfall manipulation experiments on grasslands and when measuring their resilience to drought. The ideas presented here have the potential to trigger a perspective shift among experimental researchers, into a new state where the existence of critical transitions will be discussed, experimentally tested, and largely considered when assessing and managing vegetation resilience to global changes.

The effect of climate change on the resilience of ecosystems with adaptive spatial pattern formation

In a rapidly changing world, quantifying ecosystem resilience is an important challenge. Historically, resilience has been defined via models that do not take spatial effects into account. These systems can only adapt via uniform adjustments. In reality, however, the response is not necessarily uniform, and can lead to the formation of (self-organised) spatial patterns - typically localised vegetation patches. Classical measures of resilience cannot capture the emerging dynamics in spatially self-organised systems, including transitions between patterned states that have limited impact on ecosystem structure and productivity. We present a framework of interlinked phase portraits that appropriately quantifies the resilience of patterned states, which depends on the number of patches, the distances between them and environmental conditions. We show how classical resilience concepts fail to distinguish between small and large pattern transitions, and find that the variance in interpatch distances provides a suitable indicator for the type of imminent transition. Subsequently, we describe the dependency of ecosystem degradation based on the rate of climatic change: slow change leads to sporadic, large transitions, whereas fast change causes a rapid sequence of smaller transitions. Finally, we discuss how pre-emptive removal of patches can minimise productivity losses during pattern transitions, constituting a viable conservation strategy.

Anticipating critical transitions in epithelial-hybrid-mesenchymal cell-fate determination

In the vicinity of a tipping point, critical transitions occur when small changes in an input condition cause sudden, large, and often irreversible changes in the state of a system. Many natural systems ranging from ecosystems to molecular biosystems are known to exhibit critical transitions in their response to stochastic perturbations. In diseases, an early prediction of upcoming critical transitions from a healthy to a disease state by using early-warning signals is of prime interest due to potential application in forecasting disease onset. Here, we analyze cell-fate transitions between different phenotypes (epithelial, hybrid-epithelial/mesenchymal [E/M], and mesenchymal states) that are implicated in cancer metastasis and chemoresistance. These transitions are mediated by a mutually inhibitory feedback loop-microRNA-200/ZEB-driven by the levels of transcription factor SNAIL. We find that the proximity to tipping points enabling these transitions among different phenotypes can be captured by critical slowing down-based early-warning signals, calculated from the trajectory of ZEB messenger RNA level. Further, the basin stability analysis reveals the unexpectedly large basin of attraction for a hybrid-E/M phenotype. Finally, we identified mechanisms that can potentially elude the transition to a hybrid-E/M phenotype. Overall, our results unravel the early-warning signals that can be used to anticipate upcoming epithelial-hybrid-mesenchymal transitions. With the emerging evidence about the hybrid-E/M phenotype being a key driver of metastasis, drug resistance, and tumor relapse, our results suggest ways to potentially evade these transitions, reducing the fitness of cancer cells and restricting tumor aggressiveness.

Superorganisms or loose collections of species? A unifying theory of community patterns along environmental gradients

The question whether communities should be viewed as superorganisms or loose collections of individual species has been the subject of a long-standing debate in ecology. Each view implies different spatiotemporal community patterns. Along spatial environmental gradients, the organismic view predicts that species turnover is discontinuous, with sharp boundaries between communities, while the individualistic view predicts gradual changes in species composition. Using a spatially explicit multispecies competition model, we show that organismic and individualistic forms of community organisation are two limiting cases along a continuum of outcomes. A high variance of competition strength leads to the emergence of organism-like communities due to the presence of alternative stable states, while weak and uniform interactions induce gradual changes in species composition. Dispersal can play a confounding role in these patterns. Our work highlights the critical importance of considering species interactions to understand and predict the responses of species and communities to environmental changes.

Inferring critical thresholds of ecosystem transitions from spatial data

Ecosystems can undergo abrupt transitions between alternative stable states when the driver crosses a critical threshold. Dynamical systems theory shows that when ecosystems approach the point of loss of stability associated with these transitions, they take a long time to recover from perturbations, a phenomenon known as critical slowing down. This generic feature of dynamical systems can offer early warning signals of abrupt transitions. However, these signals are qualitative and cannot quantify the thresholds of drivers at which transition may occur. Here, we propose a method to estimate critical thresholds from spatial data. We show that two spatial metrics, spatial variance and autocorrelation of ecosystem state variable, computed along driver gradients can be used to estimate critical thresholds. First, we investigate cellular-automaton models of ecosystem dynamics that show a transition from a high-density state to a bare state. Our models show that critical thresholds can be estimated as the ecosystem state and the driver values at which spatial variance and spatial autocorrelation of the ecosystem state are maximum. Next, to demonstrate the application of the method, we choose remotely sensed vegetation data (Enhanced Vegetation Index, EVI) from regions in central Africa and northeast Australia that exhibit alternative states in woody cover. We draw transects (8 × 90 km) that span alternative stable states along rainfall gradients. Our analyses of spatial variance and autocorrelation of EVI along transects yield estimates of critical thresholds. These estimates match reasonably well with those obtained by an independent method that uses large-scale (250 × 200 km) spatial data sets. Given the generality of the principles that underlie our method, our method can be applied to a variety of ecosystems that exhibit alternative stable states.

Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation

Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the effect of the rate of change of the bifurcation parameter on the tipping points. In this work, we consider a subcritical stochastic Hopf bifurcation under two scenarios: the bifurcation parameter is first changed in a quasi-steady manner and then, with a finite ramping rate. In the latter case, a rate-dependent bifurcation delay is observed and exemplified experimentally using a thermoacoustic instability in a combustion chamber. This delay increases with the rate of change. This leads to a state transition of larger amplitude compared with the one that would be experienced by the system with a quasi-steady change of the parameter. We also bring experimental evidence of a dynamic hysteresis caused by the bifurcation delay when the parameter is ramped back. A surrogate model is derived in order to predict the statistic of these delays and to scrutinize the underlying stochastic dynamics. Our study highlights the dramatic influence of a finite rate of change of bifurcation parameters upon tipping points, and it pinpoints the crucial need of considering this effect when investigating critical transitions.

On the complex dynamics of savanna landscapes

Simple mathematical models can exhibit rich and complex behaviors. Prototypical examples of these drawn from biology and other disciplines have provided insights that extend well beyond the situations that inspired them. Here, we explore a set of simple, yet realistic, models for savanna-forest vegetation dynamics based on minimal ecological assumptions. These models are aimed at understanding how vegetation interacts with both climate (a primary global determinant of vegetation structure) and feedbacks with chronic disturbances from fire. The model includes three plant functional types-grasses, savanna trees, and forest trees. Grass and (when they allow grass to persist in their subcanopy) savanna trees promote the spread of fires, which in turn, demographically limit trees. The model exhibits a spectacular range of behaviors. In addition to bistability, analysis reveals (i) that diverse cyclic behaviors (including limit and homo- and heteroclinic cycles) occur for broad ranges of parameter space, (ii) that large shifts in landscape structure can result from endogenous dynamics and not just from external drivers or from noise, and (iii) that introducing noise into this system induces resonant and inverse resonant phenomena, some of which have never been previously observed in ecological models. Ecologically, these results raise questions about how to evaluate complicated dynamics with data. Mathematically, they lead to classes of behaviors that are likely to occur in other models with similar structure.

Dynamical Resilience Indicators in Time Series of Self-Rated Health Correspond to Frailty Levels in Older Adults

Background

We currently still lack valid methods to dynamically measure resilience for stressors before the appearance of adverse health outcomes that hamper well-being. Quantifying an older adult's resilience in an early stage would aid complex decision-making in health care. Translating complex dynamical systems theory to humans, we hypothesized that three dynamical indicators of resilience (variance, temporal autocorrelation, and cross-correlation) in time series of self-rated physical, mental, and social health were associated with frailty levels in older adults.

Methods

We monitored self-rated physical, mental, and social health during 100 days using daily visual analogue scale questions in 22 institutionalized older adults (mean age 84.0, SD: 5.9 years). Frailty was determined by the Survey of Health, Ageing and Retirement in Europe (SHARE) frailty index. The resilience indicators (variance, temporal autocorrelation, and cross-correlation) were calculated using multilevel models.

Results

The self-rated health time series of frail elderly exhibited significantly elevated variance in the physical, mental, and social domain, as well as significantly stronger cross-correlations between all three domains, as compared to the nonfrail group (all P < 0.001). Temporal autocorrelation was not significantly associated with frailty.

Conclusions

We found supporting evidence for two out of three hypothesized resilience indicators to be related to frailty levels in older adults. By mirroring the dynamical resilience indicators to a frailty index, we delivered a first empirical base to validate and quantify the construct of systemic resilience in older adults in a dynamic way.

Early warning signals of regime shifts in coupled human-environment systems

In complex systems, a critical transition is a shift in a system's dynamical regime from its current state to a strongly contrasting state as external conditions move beyond a tipping point. These transitions are often preceded by characteristic early warning signals such as increased system variability. However, early warning signals in complex, coupled human-environment systems (HESs) remain little studied. Here, we compare critical transitions and their early warning signals in a coupled HES model to an equivalent environment model uncoupled from the human system. We parameterize the HES model, using social and ecological data from old-growth forests in Oregon. We find that the coupled HES exhibits a richer variety of dynamics and regime shifts than the uncoupled environment system. Moreover, the early warning signals in the coupled HES can be ambiguous, heralding either an era of ecosystem conservationism or collapse of both forest ecosystems and conservationism. The presence of human feedback in the coupled HES can also mitigate the early warning signal, making it more difficult to detect the oncoming regime shift. We furthermore show how the coupled HES can be "doomed to criticality": Strategic human interactions cause the system to remain perpetually in the vicinity of a collapse threshold, as humans become complacent when the resource seems protected but respond rapidly when it is under immediate threat. We conclude that the opportunities, benefits, and challenges of modeling regime shifts and early warning signals in coupled HESs merit further research.

What Do You Mean, 'Tipping Point'?

Over the past 10 years the use of the term 'tipping point' in the scientific literature has exploded. It was originally used loosely as a metaphor for the phenomenon that, beyond a certain threshold, runaway change propels a system to a new state. Although several specific mathematical definitions have since been proposed, we argue that these are too narrow and that it is better to retain the original definition.

Seizures Start without Common Signatures of Critical Transition

Complex dynamical systems may exhibit sudden autonomous changes from one state to another. Such changes that occur rapidly in comparison to the regular dynamics have been termed critical transitions. Examples of such phenomena can be found in many complex systems: changes in climate and ocean circulation, changes in wildlife populations, financial crashes, as well as in medical conditions like asthma attacks and depression. It has been recognized that critical transitions, even if they arise in completely different contexts and situations, share several common attributes and also generic early-warning signals that indicate that a critical transition is approaching. In the present study, we review briefly the general characteristics that have been observed in systems prior to critical transitions and apply these general indicators to nearly 300 epileptic seizures collected from human subjects using invasive EEG. Only in about 8% of the patients was evidence of critical transitions found. In the remaining majority of cases no early warning signals that behaved consistently prior to seizures were observed. These results do not rule out the possibility of critical transitions to seizure but point to limited relevance of their early warning signals in the context of human epilepsy observed using intracranial EEG recordings.

Catalogue of abrupt shifts in Intergovernmental Panel on Climate Change climate models

Abrupt transitions of regional climate in response to the gradual rise in atmospheric greenhouse gas concentrations are notoriously difficult to foresee. However, such events could be particularly challenging in view of the capacity required for society and ecosystems to adapt to them. We present, to our knowledge, the first systematic screening of the massive climate model ensemble informing the recent Intergovernmental Panel on Climate Change report, and reveal evidence of 37 forced regional abrupt changes in the ocean, sea ice, snow cover, permafrost, and terrestrial biosphere that arise after a certain global temperature increase. Eighteen out of 37 events occur for global warming levels of less than 2°, a threshold sometimes presented as a safe limit. Although most models predict one or more such events, any specific occurrence typically appears in only a few models. We find no compelling evidence for a general relation between the overall number of abrupt shifts and the level of global warming. However, we do note that abrupt changes in ocean circulation occur more often for moderate warming (less than 2°), whereas over land they occur more often for warming larger than 2°. Using a basic proportion test, however, we find that the number of abrupt shifts identified in Representative Concentration Pathway (RCP) 8.5 scenarios is significantly larger than in other scenarios of lower radiative forcing. This suggests the potential for a gradual trend of destabilization of the climate with respect to such shifts, due to increasing global mean temperature change.

Phenotypic states become increasingly sensitive to perturbations near a bifurcation in a synthetic gene network

Microorganisms often exhibit a history-dependent phenotypic response after exposure to a stimulus which can be imperative for proper function. However, cells frequently experience unexpected environmental perturbations that might induce phenotypic switching. How cells maintain phenotypic states in the face of environmental fluctuations remains an open question. Here, we use environmental perturbations to characterize the resilience of phenotypic states in a synthetic gene network near a critical transition. We find that far from the critical transition an environmental perturbation may induce little to no phenotypic switching, whereas close to the critical transition the same perturbation can cause many cells to switch phenotypic states. This loss of resilience was observed for perturbations that interact directly with the gene circuit as well as for a variety of generic perturbations-such as salt, ethanol, or temperature shocks-that alter the state of the cell more broadly. We obtain qualitatively similar findings in natural gene circuits, such as the yeast GAL network. Our findings illustrate how phenotypic memory can become destabilized by environmental variability near a critical transition.

DOI:http://dx.doi.org/10.7554/eLife.07935.001

All organisms need to be able to react to the challenges thrown at them by their changing environment. Yeast, bacteria and other microbes have networks of genes that can give rise to many different traits and characteristics, which can also be referred to as phenotypes. A change in the environment can alter the activities' of the genes so that the microbes display a different phenotype. The point at which a small change in the environment can lead to a sudden switch in the phenotype is called a ‘critical transition’.

An individual microbe's history can influence the phenotype that it presents. However, it is not clear how microbes ‘remember’ their history, or how fluctuations in the environment might cause the microbe to lose the ability to store this memory and present a different phenotype instead. Here, Axelrod et al. studied phenotype memory in yeast cells grown in the laboratory. The experiments used cells that had been genetically modified to glow red in the presence of a molecule called anhydrotetracycline (or ATc) and to glow green in the absence of the molecule.

Axelrod et al. examined what effect altering the levels of this molecule would have on the phenotype produced by the cells. First, the cells were grown with no ATc present for several generations so that the cells glowed green. Next, Axelrod et al. added different amounts of ATc were added. For moderate levels of ATc the cells continued to glow green, illustrating that they ‘remembered’ their prior growth condition. However, cells exposed to higher levels of ATc lost this memory and changed color.

Next, Axelrod et al. carried out further experiments on cells exposed to ATc levels that were close to, or further away from the critical transition. At high levels of ATc (that is, close to the critical transition), many cells switched from green to red when exposed to high temperatures, salt and other changes in the environment. On the other hand, very few of the cells grown in low levels of ATc—and therefore further away from the critical transition—changed color in response to the same fluctuations in their environment.

These finding reveal that phenotype memory is less stable when yeast experience fluctuations in their environment close to a critical transition. Future work will seek to find out how salt or high temperatures can abolish phenotype memory.

DOI:http://dx.doi.org/10.7554/eLife.07935.002

Eluding catastrophic shifts

Transitions between regimes with radically different properties are ubiquitous in nature. Such transitions can occur either smoothly or in an abrupt and catastrophic fashion. Important examples of the latter can be found in ecology, climate sciences, and economics, to name a few, where regime shifts have catastrophic consequences that are mostly irreversible (e.g., desertification, coral reef collapses, and market crashes). Predicting and preventing these abrupt transitions remains a challenging and important task. Usually, simple deterministic equations are used to model and rationalize these complex situations. However, stochastic effects might have a profound effect. Here we use 1D and 2D spatially explicit models to show that intrinsic (demographic) stochasticity can alter deterministic predictions dramatically, especially in the presence of other realistic features such as limited mobility or spatial heterogeneity. In particular, these ingredients can alter the possibility of catastrophic shifts by giving rise to much smoother and easily reversible continuous ones. The ideas presented here can help further understand catastrophic shifts and contribute to the discussion about the possibility of preventing such shifts to minimize their disruptive ecological, economic, and societal consequences.

Marine regime shifts: drivers and impacts on ecosystems services

Marine ecosystems can experience regime shifts, in which they shift from being organized around one set of mutually reinforcing structures and processes to another. Anthropogenic global change has broadly increased a wide variety of processes that can drive regime shifts. To assess the vulnerability of marine ecosystems to such shifts and their potential consequences, we reviewed the scientific literature for 13 types of marine regime shifts and used networks to conduct an analysis of co-occurrence of drivers and ecosystem service impacts. We found that regime shifts are caused by multiple drivers and have multiple consequences that co-occur in a non-random pattern. Drivers related to food production, climate change and coastal development are the most common co-occurring causes of regime shifts, while cultural services, biodiversity and primary production are the most common cluster of ecosystem services affected. These clusters prioritize sets of drivers for management and highlight the need for coordinated actions across multiple drivers and scales to reduce the risk of marine regime shifts. Managerial strategies are likely to fail if they only address well-understood or data-rich variables, and international cooperation and polycentric institutions will be critical to implement and coordinate action across the scales at which different drivers operate. By better understanding these underlying patterns, we hope to inform the development of managerial strategies to reduce the risk of high-impact marine regime shifts, especially for areas of the world where data are not available or monitoring programmes are not in place.

Human-aided admixture may fuel ecosystem transformation during biological invasions: theoretical and experimental evidence

Biological invasions can transform our understanding of how the interplay of historical isolation and contemporary (human-aided) dispersal affects the structure of intraspecific diversity in functional traits, and in turn, how changes in functional traits affect other scales of biological organization such as communities and ecosystems. Because biological invasions frequently involve the admixture of previously isolated lineages as a result of human-aided dispersal, studies of invasive populations can reveal how admixture results in novel genotypes and shifts in functional trait variation within populations. Further, because invasive species can be ecosystem engineers within invaded ecosystems, admixture-induced shifts in the functional traits of invaders can affect the composition of native biodiversity and alter the flow of resources through the system. Thus, invasions represent promising yet under-investigated examples of how the effects of short-term evolutionary changes can cascade across biological scales of diversity. Here, we propose a conceptual framework that admixture between divergent source populations during biological invasions can reorganize the genetic variation underlying key functional traits, leading to shifts in the mean and variance of functional traits within invasive populations. Changes in the mean or variance of key traits can initiate new ecological feedback mechanisms that result in a critical transition from a native ecosystem to a novel invasive ecosystem. We illustrate the application of this framework with reference to a well-studied plant model system in invasion biology and show how a combination of quantitative genetic experiments, functional trait studies, whole ecosystem field studies and modeling can be used to explore the dynamics predicted to trigger these critical transitions.

Critical slowing down as early warning for the onset and termination of depression

About 17% of humanity goes through an episode of major depression at some point in their lifetime. Despite the enormous societal costs of this incapacitating disorder, it is largely unknown how the likelihood of falling into a depressive episode can be assessed. Here, we show for a large group of healthy individuals and patients that the probability of an upcoming shift between a depressed and a normal state is related to elevated temporal autocorrelation, variance, and correlation between emotions in fluctuations of autorecorded emotions. These are indicators of the general phenomenon of critical slowing down, which is expected to occur when a system approaches a tipping point. Our results support the hypothesis that mood may have alternative stable states separated by tipping points, and suggest an approach for assessing the likelihood of transitions into and out of depression.