Vishwesha Guttal

Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data

Many dynamical systems, including lakes, organisms, ocean circulation patterns, or financial markets, are now thought to have tipping points where critical transitions to a contrasting state can happen. Because critical transitions can occur unexpectedly and are difficult to manage, there is a need for methods that can be used to identify when a critical transition is approaching. Recent theory shows that we can identify the proximity of a system to a critical transition using a variety of so-called ‘early warning signals’, and successful empirical examples suggest a potential for practical applicability. However, while the range of proposed methods for predicting critical transitions is rapidly expanding, opinions on their practical use differ widely, and there is no comparative study that tests the limitations of the different methods to identify approaching critical transitions using time-series data. Here, we summarize a range of currently available early warning methods and apply them to two simulated time series that are typical of systems undergoing a critical transition. In addition to a methodological guide, our work offers a practical toolbox that may be used in a wide range of fields to help detect early warning signals of critical transitions in time series data.

Social interactions, information use, and the evolution of collective migration

Migration of organisms (or cells) is typically an adaptive response to spatiotemporal variation in resources that requires individuals to detect and respond to long-range and noisy environmental gradients. Many organisms, from wildebeest to bacteria, migrate en masse in a process that can involve a vast number of individuals. Despite the ubiquity of collective migration, and the key function it plays in the ecology of many species, it is still unclear what role social interactions play in the evolution of migratory strategies. Here, we explore the evolution of migratory behavior using an individual-based spatially explicit model that incorporates the costs and benefits of obtaining directional cues from the environment and evolvable social interactions among migrating individuals. We demonstrate that collective migratory strategies evolve under a wide range of ecological scenarios, even when social encounters are rare. Although collective migration appears to be a shared navigational process, populations typically consist of small proportions of individuals actively acquiring directional information from their environment, whereas the majorities use a socially facilitated movement behavior. Because many migratory species face severe threat through anthropogenic influences, we also explore the microevolutionary response of migratory strategies to environmental pressures. We predict a gradual decline of migration due to increasing habitat destruction and argue that much greater restoration is required to recover lost behaviors (i.e., a strong hysteresis effect). Our results provide insights into both the proximate and ultimate factors that underlie evolved migratory behavior in nature.

Predatory Fish Select for Coordinated Collective Motion in Virtual Prey

Evolving Group Formation Grouping behavior in prey species has long been thought to constitute an adaptation against predation; however, it has been difficult to characterize the mechanisms by which predator selection shapes prey movement and grouping behavior. Using an approach that combines the selection imposed by a live predator, the bluegill sunfish, with manipulation of computer-generated “prey,” Ioannou et al. (p. 1212, published online 16 August; see the Perspective by Romey) show that “prey” that behave as a group are more likely to survive that those that move in other ways. Computer-generated prey evolve coordinated group behaviors when attacked by bluegill sunfish. Movement in animal groups is highly varied and ranges from seemingly disordered motion in swarms to coordinated aligned motion in flocks and schools. These social interactions are often thought to reduce risk from predators, despite a lack of direct evidence. We investigated risk-related selection for collective motion by allowing real predators (bluegill sunfish) to hunt mobile virtual prey. By fusing simulated and real animal behavior, we isolated predator effects while controlling for confounding factors. Prey with a tendency to be attracted toward, and to align direction of travel with, near neighbors tended to form mobile coordinated groups and were rarely attacked. These results demonstrate that collective motion could evolve as a response to predation, without prey being able to detect and respond to predators.

Spatial variance and spatial skewness: leading indicators of regime shifts in spatial ecological systems

Ecosystems can undergo large-scale changes in their states, known as catastrophic regime shifts, leading to substantial losses to services they provide to humans. These shifts occur rapidly and are difficult to predict. Several early warning signals of such transitions have recently been developed using simple models. These studies typically ignore spatial interactions, and the signal provided by these indicators may be ambiguous. We employ a simple model of collapse of vegetation in one and two spatial dimensions and show, using analytic and numerical studies, that increases in spatial variance and changes in spatial skewness occur as one approaches the threshold of vegetation collapse. We identify a novel feature, an increasing spatial variance in conjunction with a peaking of spatial skewness, as an unambiguous indicator of an impending regime shift. Once a signal has been detected, we show that a quick management action reducing the grazing activity is needed to prevent the collapse of vegetated state. Our results show that the difficulties in obtaining the accurate estimates of indicators arising due to lack of long temporal data can be alleviated when high-resolution spatially extended data are available. These results are shown to hold true independent of various details of model or different spatial dispersal kernels such as Gaussian or heavily fat tailed. This study suggests that spatial data and monitoring multiple indicators of regime shifts can play a key role in making reliable predictions on ecosystem stability and resilience.

Early warning signals of ecological transitions: methods for spatial patterns.

A number of ecosystems can exhibit abrupt shifts between alternative stable states. Because of their important ecological and economic consequences, recent research has focused on devising early warning signals for anticipating such abrupt ecological transitions. In particular, theoretical studies show that changes in spatial characteristics of the system could provide early warnings of approaching transitions. However, the empirical validation of these indicators lag behind their theoretical developments. Here, we summarize a range of currently available spatial early warning signals, suggest potential null models to interpret their trends, and apply them to three simulated spatial data sets of systems undergoing an abrupt transition. In addition to providing a step-by-step methodology for applying these signals to spatial data sets, we propose a statistical toolbox that may be used to help detect approaching transitions in a wide range of spatial data. We hope that our methodology together with the computer codes will stimulate the application and testing of spatial early warning signals on real spatial data.

Leadership, collective motion and the evolution of migratory strategies

Migration is a hallmark life history strategy of a diverse range of organisms, and also ubiquitous in ontogenic processes including normal embryonic development as well as tumor progression. In such scenarios, individual organisms/cells typically respond to long range (and often noisy) environmental cues. In addition, individuals may interact socially with one another leading to emergent group-level navigational abilities. Although much progress has been made in understanding the mechanisms of taxis, there is a lack of theoretical and quantitative understanding of how individuals trade-off information obtained through their own migratory ability and that via social interactions. Here, we discuss results and insights from a recent computational model developed to investigate the evolution of leadership and collective motion in migratory populations. It is shown that, for a broad range of parameter values, only a small proportion of the population gather directional information while the majority employ social cues alone. More generally, ecological conditions for the evolution of resident, solitary and collective migratory strategies are obtained. We discuss how consideration of both proximate and ultimate factors within the same framework may provide insights into preserving migratory patterns that are in grave danger due to anthropogenic pressures.

Lack of critical slowing down suggests that financial meltdowns are not critical transitions, yet rising variability could signal systemic risk

Complex systems inspired analysis suggests a hypothesis that financial meltdowns are abrupt critical transitions that occur when the system reaches a tipping point. Theoretical and empirical studies on climatic and ecological dynamical systems have shown that approach to tipping points is preceded by a generic phenomenon called critical slowing down, i.e. an increasingly slow response of the system to perturbations. Therefore, it has been suggested that critical slowing down may be used as an early warning signal of imminent critical transitions. Whether financial markets exhibit critical slowing down prior to meltdowns remains unclear. Here, our analysis reveals that three major US (Dow Jones Index, S&P 500 and NASDAQ) and two European markets (DAX and FTSE) did not exhibit critical slowing down prior to major financial crashes over the last century. However, all markets showed strong trends of rising variability, quantified by time series variance and spectral function at low frequencies, prior to crashes. These results suggest that financial crashes are not critical transitions that occur in the vicinity of a tipping point. Using a simple model, we argue that financial crashes are likely to be stochastic transitions which can occur even when the system is far away from the tipping point. Specifically, we show that a gradually increasing strength of stochastic perturbations may have caused to abrupt transitions in the financial markets. Broadly, our results highlight the importance of stochastically driven abrupt transitions in real world scenarios. Our study offers rising variability as a precursor of financial meltdowns albeit with a limitation that they may signal false alarms.

Robustness of early warning signals of regime shifts in time-delayed ecological models

Various ecological and other complex dynamical systems may exhibit abrupt regime shifts or critical transitions, wherein they reorganize from one stable state to another over relatively short time scales. Because of potential losses to ecosystem services, forecasting such unexpected shifts would be valuable. Using mathematical models of regime shifts, ecologists have proposed various early warning signals of imminent shifts. However, their generality and applicability to real ecosystems remain unclear because these mathematical models are considered too simplistic. Here, we investigate the robustness of recently proposed early warning signals of regime shifts in two well-studied ecological models, but with the inclusion of time-delayed processes. We find that the average variance may either increase or decrease prior to a regime shift and, thus, may not be a robust leading indicator in time-delayed ecological systems. In contrast, changing average skewness, increasing autocorrelation at short time lags, and reddening power spectra of time series of the ecological state variable all show trends consistent with those of models with no time delays. Our results provide insights into the robustness of early warning signals of regime shifts in a broader class of ecological systems.

Rising Variability, Not Slowing Down, as a Leading Indicator of a Stochastically Driven Abrupt Transition in a Dryland Ecosystem

Complex systems can undergo abrupt state transitions near critical points. Theory and controlled experimental studies suggest that the approach to critical points can be anticipated by critical slowing down (CSD), that is, a characteristic slowdown in the dynamics. The validity of this indicator in field ecosystems, where stochasticity is important in driving transitions, remains unclear. We analyze long-term data from a dryland ecosystem in the Shapotou region of China and show that the ecosystem underwent an abrupt transition from a nearly bare to a moderate grass cover state. Prior to the transition, the system showed no (or weak) signatures of CSD but exhibited expected increasing trends in the variability of the grass cover, quantified by variance and skewness. These surprising results are consistent with the theoretical expectation of stochastically driven abrupt transitions that occur away from critical points; indeed, a driver of vegetation—annual rainfall—showed rising variance prior to the transition. Our study suggests that rising variability can potentially serve as a leading indicator of stochastically driven transitions in real-world ecosystems.

On the Systemic Fragility of Finance‐Led Growth

The paper sets up a model of economic crisis by investigating the role played by movement in asset price as a driver of the dynamic interaction between the real and the financial sectors. Such movement influences income determination in the real economy in the short period through aggregate demand leading to the emergence of two macroeconomic regimes. A short period flow model, underpinned by the stock flow consistent accounting framework, is developed to formalize the dynamics of interaction between real and financial sectors mediated by movement in asset price, generates bistability, abrupt crashes, and systemic fragility in the macroeconomic regimes.