Early warning signs in social-ecological networks

Flagged observation analyses as a tool for scoping and communication in integrated ecosystem assessments

Working groups for integrated ecosystem assessments are often challenged with understanding and assessing recent change in ecosystems. As a basis for this, the groups typically have at their disposal many time series and will often need to prioritize which ones to follow up for closer analyses and assessment. In this article we provide a procedure termed Flagged Observation analysis that can be applied to all the available time series to help identifying time series that should be prioritized. The statistical procedure first applies a structural time series model including a stochastic trend model to the data to estimate the long-term trend. The model adopts a state space representation, and the trend component is estimated by a Kalman filter algorithm. The algorithm obtains one- or more-years-ahead prediction values using all past information from the data. Thus, depending on the number of years the investigator wants to consider as "the most recent", the expected trend for these years is estimated through the statistical procedure by using only information from the years prior to them. Forecast bands are estimated around the predicted trends for the recent years, and in the final step, an assessment is made on the extent to which observations from the most recent years fall outside these forecast bands. Those that do, may be identified as flagged observations. A procedure is also presented for assessing whether the combined information from all the most recent observations form a pattern that deviates from the predicted trend and thus represents an unexpected tendency that may be flagged. In addition to form the basis for identifying time series that should be prioritized in an integrated ecosystem assessment, flagged observations can provide the basis for communicating with managers and stakeholders about recent ecosystem change. Applications of the framework are illustrated with two worked examples.

Modelling coupled human-environment complexity for the future of the biosphere: strengths, gaps and promising directions

Humans and the environment form a single complex system where humans not only influence ecosystems but also react to them. Despite this, there are far fewer coupled human-environment system (CHES) mathematical models than models of uncoupled ecosystems. We argue that these coupled models are essential to understand the impacts of social interventions and their potential to avoid catastrophic environmental events and support sustainable trajectories on multi-decadal timescales. A brief history of CHES modelling is presented, followed by a review spanning recent CHES models of systems including forests and land use, coral reefs and fishing and climate change mitigation. The ability of CHES modelling to capture dynamic two-way feedback confers advantages, such as the ability to represent ecosystem dynamics more realistically at longer timescales, and allowing insights that cannot be generated using ecological models. We discuss examples of such key insights from recent research. However, this strength brings with it challenges of model complexity and tractability, and the need for appropriate data to parameterize and validate CHES models. Finally, we suggest opportunities for CHES models to improve human-environment sustainability in future research spanning topics such as natural disturbances, social structure, social media data, model discovery and early warning signals. This article is part of the theme issue 'Ecological complexity and the biosphere: the next 30 years'.

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.

Southern Ocean Food Web Modelling: Progress, Prognoses, and Future Priorities for Research and Policy Makers

Graphical summary of multiple aspects of Southern Ocean food web structure and function including alternative energy pathways through pelagic food webs, climate change and fisheries impacts and the importance of microbial networks and benthic systems.

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Tipping Cascades in a Multi-patch System with Noise and Spatial Coupling

Forecasting tipping points in spatially extended systems is a key area of interest to ecologists. A slowly declining spatially distributed population is an important example of an ecological system that could exhibit a cascade of tipping points. Here, we develop a spatial two-patch model with environmental stochasticity that is slowly forced through population collapse, in the presence of changing environmental conditions. We begin with a basic spatial model, then introduce a fast-slow version of the model using geometric singular perturbation theory, followed by the inclusion of stochasticity. Using the spectral density of the fluctuating subpopulation in each patch, we derive analytic expressions for candidate indicators of population extinction and evaluate their performance through a simulation study. We find that coupling and spatial heterogeneity decrease the magnitude of the proposed indicators in coupled populations relative to isolated populations. Moreover, the degree of coupling dictates the trends in summary statistics. We conclude that this theory may be applied to other contexts, including the control of invasive species.

Rethinking the design of resilience and adaptation indicators supporting coastal communities

As resilience and adaptation considerations become mainstreamed into public policy, there is an overarching desire to measure and quantify metrics and indicators that seek to evaluate the efficiency, effectiveness, and justness associated with outcomes of such processes. While much research has sought to develop specific indicators that may serve as proxies for these considerations, less research has focused on those normative aspects of indicator design that support a variety of goals associated with the accuracy, reproducibility, proxy value and multi-stakeholder translation of indicators, among various other goals and values. This perspective article sets forth a range of potential considerations that may be useful for those who seek to design and develop novel resilience and adaptation indicators ("RAIs"). These considerations are explored through a range of hypothetical examples that may be applicable to coastal communities that seek to address the practical challenges facing the design, execution, management and modification of RAIs.

Evaluating the performance of multivariate indicators of resilience loss

Various complex systems, such as the climate, ecosystems, and physical and mental health can show large shifts in response to small changes in their environment. These 'tipping points' are notoriously hard to predict based on trends. However, in the past 20 years several indicators pointing to a loss of resilience have been developed. These indicators use fluctuations in time series to detect critical slowing down preceding a tipping point. Most of the existing indicators are based on models of one-dimensional systems. However, complex systems generally consist of multiple interacting entities. Moreover, because of technological developments and wearables, multivariate time series are becoming increasingly available in different fields of science. In order to apply the framework of resilience indicators to multivariate time series, various extensions have been proposed. Not all multivariate indicators have been tested for the same types of systems and therefore a systematic comparison between the methods is lacking. Here, we evaluate the performance of the different multivariate indicators of resilience loss in different scenarios. We show that there is not one method outperforming the others. Instead, which method is best to use depends on the type of scenario the system is subject to. We propose a set of guidelines to help future users choose which multivariate indicator of resilience is best to use for their particular system.

Dimensionality reduction of complex dynamical systems

One of the outstanding problems in complexity science and engineering is the study of high-dimensional networked systems and of their susceptibility to transitions to undesired states as a result of changes in external drivers or in the structural properties. Because of the incredibly large number of parameters controlling the state of such complex systems and the heterogeneity of its components, the study of their dynamics is extremely difficult. Here we propose an analytical framework for collapsing complex N-dimensional networked systems into an S+1-dimensional manifold as a function of S effective control parameters with S << N. We test our approach on a variety of real-world complex problems showing how this new framework can approximate the system's response to changes and correctly identify the regions in the parameter space corresponding to the system's transitions. Our work offers an analytical method to evaluate optimal strategies in the design or management of networked systems.

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We analytically collapse N-dimensional networked dynamics in low-dimensional manifolds

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We test this approach on a variety of real-world complex problems

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We accurately predict the system's response to changes in parameter values

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We identify regions in parameter space corresponding to system's critical transitions

Social-Ecological Connectivity to Understand Ecosystem Service Provision across Networks in Urban Landscapes

Landscape connectivity is a critical component of dynamic processes that link the structure and function of networks at the landscape scale. In the Anthropocene, connectivity across a landscape-scale network is influenced not only by biophysical land use features, but also by characteristics and patterns of the social landscape. This is particularly apparent in urban landscapes, which are highly dynamic in land use and often in social composition. Thus, landscape connectivity, especially in cities, must be thought of in a social-ecological framework. This is relevant when considering ecosystem services—the benefits that people derive from ecological processes and properties. As relevant actors move through a connected landscape-scale network, particular services may “flow” better across space and time. For this special issue on dynamic landscape connectivity, we discuss the concept of social-ecological networks using urban landscapes as a focal system to highlight the importance of social-ecological connectivity to understand dynamic urban landscapes, particularly in regards to the provision of urban ecosystem services.

Foreseeing the future of mutualistic communities beyond collapse

Changing conditions may lead to sudden shifts in the state of ecosystems when critical thresholds are passed. Some well-studied drivers of such transitions lead to predictable outcomes such as a turbid lake or a degraded landscape. Many ecosystems are, however, complex systems of many interacting species. While detecting upcoming transitions in such systems is challenging, predicting what comes after a critical transition is terra incognita altogether. The problem is that complex ecosystems may shift to many different, alternative states. Whether an impending transition has minor, positive or catastrophic effects is thus unclear. Some systems may, however, behave more predictably than others. The dynamics of mutualistic communities can be expected to be relatively simple, because delayed negative feedbacks leading to oscillatory or other complex dynamics are weak. Here, we address the question of whether this relative simplicity allows us to foresee a community's future state. As a case study, we use a model of a bipartite mutualistic network and show that a network's post-transition state is indicated by the way in which a system recovers from minor disturbances. Similar results obtained with a unipartite model of facilitation suggest that our results are of relevance to a wide range of mutualistic systems.

Finding the direction of lowest resilience in multivariate complex systems

The dynamics of complex systems, such as ecosystems, financial markets and the human brain, emerge from the interactions of numerous components. We often lack the knowledge to build reliable models for the behaviour of such network systems. This makes it difficult to predict potential instabilities. We show that one could use the natural fluctuations in multivariate time series to reveal network regions with particularly slow dynamics. The multidimensional slowness points to the direction of minimal resilience, in the sense that simultaneous perturbations on this set of nodes will take longest to recover. We compare an autocorrelation-based method with a variance-based method for different time-series lengths, data resolution and different noise regimes. We show that the autocorrelation-based method is less robust for short time series or time series with a low resolution but more robust for varying noise levels. This novel approach may help to identify unstable regions of multivariate systems or to distinguish safe from unsafe perturbations.

Indicators of transitions in biological systems

In the face of global biodiversity declines, predicting the fate of biological systems is a key goal in ecology. One popular approach is the search for early warning signals (EWSs) based on alternative stable states theory. In this review, we cover the theory behind nonlinearity in dynamic systems and techniques to detect the loss of resilience that can indicate state transitions. We describe the research done on generic abundance-based signals of instability that are derived from the phenomenon of critical slowing down, which represent the genesis of EWSs research. We highlight some of the issues facing the detection of such signals in biological systems - which are inherently complex and show low signal-to-noise ratios. We then document research on alternative signals of instability, including measuring shifts in spatial autocorrelation and trait dynamics, and discuss potential future directions for EWSs research based on detailed demographic and phenotypic data. We set EWSs research in the greater field of predictive ecology and weigh up the costs and benefits of simplicity vs. complexity in predictive models, and how the available data should steer the development of future methods. Finally, we identify some key unanswered questions that, if solved, could improve the applicability of these methods.

Unifying relationships between complexity and stability in mutualistic ecological communities

Conserving ecosystem function and associated services requires deep understanding of the underlying basis of system stability. While the study of ecological dynamics is a mature and diverse field, the lack of a general model that predicts a broad range of theoretical and empirical observations has allowed unresolved contradictions to persist. Here we provide a general model of mutualistic ecological interactions between two groups and show for the first time how the conditions for bi-stability, the nature of critical transitions, and identifiable leading indicators in time-series can be derived from the basic parameters describing the underlying ecological interactions. Strong mutualism and nonlinearity in handling-time are found to be necessary conditions for the occurrence of critical transitions. We use the model to resolve open questions concerning the effects of heterogeneity in inter-species interactions on both resilience and abundance, and discuss these in terms of potential trade-offs in real systems. This framework provides a basis for rich investigations of ecological system dynamics, and may be generalizable across many ecological contexts.

Resilience in the global food system

Ensuring food security requires food production and distribution systems function throughout disruptions. Understanding the factors that contribute to the global food system's ability to respond and adapt to such disruptions (i.e. resilience) is critical for understanding the long-term sustainability of human populations. Variable impacts of production shocks on food supply between countries indicate a need for national-scale resilience indicators that can provide global comparisons. However, methods for tracking changes in resilience have had limited application to food systems. We developed an indicator-based analysis of food systems resilience for the years 1992-2011. Our approach is based on three dimensions of resilience: socio-economic access to food in terms of income of the poorest quintile relative to food prices, biophysical capacity to intensify or extensify food production, and the magnitude and diversity of current domestic food production. The socio-economic indicator has large variability, but with low values concentrated in Africa and Asia. The biophysical capacity indicator is highest in Africa and Eastern Europe, in part because of high potential for extensification of cropland and for yield gap closure in cultivated areas. However, the biophysical capacity indicator has declined globally in recent years. The production diversity indicator has increased slightly, with a relatively even geographic distribution. Few countries had exclusively high or low values for all indicators. Collectively, these results are the basis for global comparisons of resilience between nations, and provide necessary context for developing generalizations about the resilience in the global food system.

Multifractality and Network Analysis of Phase Transition

Many models and real complex systems possess critical thresholds at which the systems shift dramatically from one sate to another. The discovery of early-warnings in the vicinity of critical points are of great importance to estimate how far the systems are away from the critical states. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the multifractal and geometrical properties of the magnetization time series of the two-dimensional Ising model. Multifractality of the time series near the critical point has been uncovered from the generalized Hurst exponents and singularity spectrum. Both long-term correlation and broad probability density function are identified to be the sources of multifractality. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties. Evolution of the topological quantities of the visibility graph, along with the variation of multifractality, serve as new early-warnings of phase transition. Those methods and results may provide new insights about the analysis of phase transition problems and can be used as early-warnings for a variety of complex systems.

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.

A Data Driven Network Approach to Rank Countries Production Diversity and Food Specialization

The easy access to large data sets has allowed for leveraging methodology in network physics and complexity science to disentangle patterns and processes directly from the data, leading to key insights in the behavior of systems. Here we use country specific food production data to study binary and weighted topological properties of the bipartite country-food production matrix. This country-food production matrix can be: 1) transformed into overlap matrices which embed information regarding shared production of products among countries, and or shared countries for individual products, 2) identify subsets of countries which produce similar commodities or subsets of commodities shared by a given country allowing for visualization of correlations in large networks, and 3) used to rank country fitness (the ability to produce a diverse array of products weighted on the type of food commodities) and food specialization (quantified on the number of countries producing a specific food product weighted on their fitness). Our results show that, on average, countries with high fitness produce both low and high specializion food commodities, whereas nations with low fitness tend to produce a small basket of diverse food products, typically comprised of low specializion food commodities.

Detecting the Collapse of Cooperation in Evolving Networks

The sustainability of biological, social, economic and ecological communities is often determined by the outcome of social conflicts between cooperative and selfish individuals (cheaters). Cheaters avoid the cost of contributing to the community and can occasionally spread in the population leading to the complete collapse of cooperation. Although such collapse often unfolds unexpectedly, it is unclear whether one can detect the risk of cheater’s invasions and loss of cooperation in an evolving community. Here, we combine dynamical networks and evolutionary game theory to study the abrupt loss of cooperation with tools for studying critical transitions. We estimate the risk of cooperation collapse following the introduction of a single cheater under gradually changing conditions. We observe an increase in the average time it takes for cheaters to be eliminated from the community as the risk of collapse increases. We argue that such slow system response resembles slowing down in recovery rates prior to a critical transition. In addition, we show how changes in community structure reflect the risk of cooperation collapse. We find that these changes strongly depend on the mechanism that governs how cheaters evolve in the community. Our results highlight novel directions for detecting abrupt transitions in evolving networks.

Resilience and reactivity of global food security

The escalating food demand by a growing and increasingly affluent global population is placing unprecedented pressure on the limited land and water resources of the planet, underpinning concerns over global food security and its sensitivity to shocks arising from environmental fluctuations, trade policies, and market volatility. Here, we use country-specific demographic records along with food production and trade data for the past 25 y to evaluate the stability and reactivity of the relationship between population dynamics and food availability. We develop a framework for the assessment of the resilience and the reactivity of the coupled population-food system and suggest that over the past two decades both its sensitivity to external perturbations and susceptibility to instability have increased.

Cross-depth analysis of marine bacterial networks suggests downward propagation of temporal changes

Interactions among microbes and stratification across depths are both believed to be important drivers of microbial communities, though little is known about how microbial associations differ between and across depths. We have monitored the free-living microbial community at the San Pedro Ocean Time-series station, monthly, for a decade, at five different depths: 5 m, the deep chlorophyll maximum layer, 150 m, 500 m and 890 m (just above the sea floor). Here, we introduce microbial association networks that combine data from multiple ocean depths to investigate both within- and between-depth relationships, sometimes time-lagged, among microbes and environmental parameters. The euphotic zone, deep chlorophyll maximum and 890 m depth each contain two negatively correlated 'modules' (groups of many inter-correlated bacteria and environmental conditions) suggesting regular transitions between two contrasting environmental states. Two-thirds of pairwise correlations of bacterial taxa between depths lagged such that changes in the abundance of deeper organisms followed changes in shallower organisms. Taken in conjunction with previous observations of seasonality at 890 m, these trends suggest that planktonic microbial communities throughout the water column are linked to environmental conditions and/or microbial communities in overlying waters. Poorly understood groups including Marine Group A, Nitrospina and AEGEAN-169 clades contained taxa that showed diverse association patterns, suggesting these groups contain multiple ecological species, each shaped by different factors, which we have started to delineate. These observations build upon previous work at this location, lending further credence to the hypothesis that sinking particles and vertically migrating animals transport materials that significantly shape the time-varying patterns of microbial community composition.