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Dakos, V, Glaser SM, Hsieh CH, Sugihara G.  2017.  Elevated nonlinearity as an indicator of shifts in the dynamics of populations under stress. Journal of the Royal Society Interface. 14   10.1098/risf.2016.0845   AbstractWebsite

Populations occasionally experience abrupt changes, such as local extinctions, strong declines in abundance or transitions from stable dynamics to strongly irregular fluctuations. Although most of these changes have important ecological and at times economic implications, they remain notoriously difficult to detect in advance. Here, we study changes in the stability of populations under stress across a variety of transitions. Using a Ricker- type model, we simulate shifts from stable point equilibrium dynamics to cyclic and irregular boom- bust oscillations as well as abrupt shifts between alternative attractors. Our aim is to infer the loss of population stability before such shifts based on changes in nonlinearity of population dynamics. We measure nonlinearity by comparing forecast performance between linear and nonlinear models fitted on reconstructed attractors directly from observed time series. We compare nonlinearity to other suggested leading indicators of instability (variance and autocorrelation). We find that nonlinearity and variance increase in a similar way prior to the shifts. By contrast, autocorrelation is strongly affected by oscillations. Finally, we test these theoretical patterns in datasets of fisheries populations. Our results suggest that elevated nonlinearity could be used as an additional indicator to infer changes in the dynamics of populations under stress.

McGowan, JA, Deyle ER, Ye H, Carter ML, Perretti CT, Seger KD, de Verneil A, Sugihara G.  2017.  Predicting coastal algal blooms in Southern California. Ecology.   10.1002/ecy.1804   AbstractWebsite

The irregular appearance of planktonic algae blooms off the coast of southern California has been a source of wonder for over a century. Although large algal blooms can have significant negative impacts on ecosystems and human health, a predictive understanding of these events has eluded science, and many have come to regard them as ultimately random phenomena. However, the highly nonlinear nature of ecological dynamics can give the appearance of randomness and stress traditional methods—such as model fitting or analysis of variance—to the point of breaking. The intractability of this problem from a classical linear standpoint can thus give the impression that algal blooms are fundamentally unpredictable. Here, we use an exceptional time series study of coastal phytoplankton dynamics at La Jolla, CA, with an equation-free modeling approach, to show that these phenomena are not random, but can be understood as nonlinear population dynamics forced by external stochastic drivers (so-called “stochastic chaos”). The combination of this modeling approach with an extensive dataset allows us to not only describe historical behavior and clarify existing hypotheses about the mechanisms, but also make out-of-sample predictions of recent algal blooms at La Jolla that were not included in the model development. This article is protected by copyright. All rights reserved.

Deyle, ER, Maher MC, Hernandez RD, Basu S, Sugihara G.  2016.  Global environmental drivers of influenza. Proceedings of the National Academy of Sciences of the United States of America. 113:13081-13086.   10.1073/pnas.1607747113   AbstractWebsite

In temperate countries, influenza outbreaks are well correlated to seasonal changes in temperature and absolute humidity. However, tropical countries have much weaker annual climate cycles, and outbreaks show less seasonality and are more difficult to explain with environmental correlations. Here, we use convergent cross mapping, a robust test for causality that does not require correlation, to test alternative hypotheses about the global environmental drivers of influenza outbreaks from country-level epidemic time series. By moving beyond correlation, we show that despite the apparent differences in outbreak patterns between temperate and tropical countries, absolute humidity and, to a lesser extent, temperature drive influenza outbreaks globally. We also find a hypothesized U-shaped relationship between absolute humidity and influenza that is predicted by theory and experiment, but hitherto has not been documented at the population level. The balance between positive and negative effects of absolute humidity appears to be mediated by temperature, and the analysis reveals a key threshold around 75 degrees F. The results indicate a unified explanation for environmental drivers of influenza that applies globally.

Ye, H, Sugihara G.  2016.  Information leverage in interconnected ecosystems: Overcoming the curse of dimensionality. Science. 353:922-925.   10.1126/science.aag0863   AbstractWebsite

In ecological analysis, complexity has been regarded as an obstacle to overcome. Here we present a straightforward approach for addressing complexity in dynamic interconnected systems. We show that complexity, in the form of multiple interacting components, can actually be an asset for studying natural systems from temporal data. The central idea is that multidimensional time series enable system dynamics to be reconstructed from multiple viewpoints, and these viewpoints can be combined into a single model. We show how our approach, multiview embedding (MVE), can improve forecasts for simulated ecosystems and a mesocosm experiment. By leveraging complexity, MVE is particularly effective for overcoming the limitations of short and noisy time series and should be highly relevant for many areas of science.

Rikkert, M, Dakos V, Buchman TG, de Boer R, Glass L, Cramer AOJ, Levin S, van Nes E, Sugihara G, Ferrari MD, Tolner EA, van de Leemput I, Lagro J, Melis R, Scheffer M.  2016.  Slowing down of recovery as generic risk marker for acute severity transitions in chronic diseases. Critical Care Medicine. 44:601-606.   10.1097/ccm.0000000000001564   AbstractWebsite

Objective: We propose a novel paradigm to predict acute attacks and exacerbations in chronic episodic disorders such as asthma, cardiac arrhythmias, migraine, epilepsy, and depression. A better generic understanding of acute transitions in chronic dynamic diseases is increasingly important in critical care medicine because of the higher prevalence and incidence of these chronic diseases in our aging societies. Data Sources: PubMed, Medline, and Web of Science. Study Selection: We selected studies from biology and medicine providing evidence of slowing down after a perturbation as a warning signal for critical transitions. Data Extraction: Recent work in ecology, climate, and systems biology has shown that slowing down of recovery upon perturbations can indicate loss of resilience across complex, nonlinear biologic systems that are approaching a tipping point. This observation is supported by the empiric studies in pathophysiology and controlled laboratory experiments with other living systems, which can flip from one state of clinical balance to a contrasting one. We discuss examples of such evidence in bodily functions such as blood pressure, heart rate, mood, and respiratory regulation when a tipping point for a transition is near. Conclusions: We hypothesize that in a range of chronic episodic diseases, indicators of critical slowing down, such as rising variance and temporal correlation, may be used to assess the risk of attacks, exacerbations, and even mortality. Identification of such early warning signals over a range of diseases will enhance the understanding of why, how, and when attacks and exacerbations will strike and may thus improve disease management in critical care medicine.

Deyle, ER, May RM, Munch SB, Sugihara G.  2016.  Tracking and forecasting ecosystem interactions in real time. Proceedings of the Royal Society B-Biological Sciences. 283   10.1098/rspb.2015.2258   AbstractWebsite

Evidence shows that species interactions are not constant but change as the ecosystem shifts to new states. Although controlled experiments and model investigations demonstrate how nonlinear interactions can arise in principle, empirical tools to track and predict them in nature are lacking. Here we present a practical method, using available time-series data, to measure and forecast changing interactions in real systems, and identify the underlying mechanisms. The method is illustrated with model data from a marine mesocosm experiment and limnologic field data from Sparkling Lake, WI, USA. From simple to complex, these examples demonstrate the feasibility of quantifying, predicting and understanding state-dependent, nonlinear interactions as they occur in situ and in real time-a requirement for managing resources in a nonlinear, non-equilibrium world.

Ye, H, Deyle ER, Gilarranz LJ, Sugihara G.  2015.  Distinguishing time-delayed causal interactions using convergent cross mapping. Scientific Reports. 5   10.1038/srep14750   AbstractWebsite

An important problem across many scientific fields is the identification of causal effects from observational data alone. Recent methods (convergent cross mapping, CCM) have made substantial progress on this problem by applying the idea of nonlinear attractor reconstruction to time series data. Here, we expand upon the technique of CCM by explicitly considering time lags. Applying this extended method to representative examples (model simulations, a laboratory predator-prey experiment, temperature and greenhouse gas reconstructions from the Vostok ice core, and long-term ecological time series collected in the Southern California Bight), we demonstrate the ability to identify different time-delayed interactions, distinguish between synchrony induced by strong unidirectional-forcing and true bidirectional causality, and resolve transitive causal chains.

van Nes, EH, Scheffer M, Brovkin V, Lenton TM, Ye H, Deyle E, Sugihara G.  2015.  Causal feedbacks in climate change. Nature Climate Change. 5:445-448.   10.1038/nclimate2568   AbstractWebsite

The statistical association between temperature and greenhouse gases over glacial cycles is well documented(1), but causality behind this correlation remains difficult to extract directly from the data. A time lag of CO2 behind Antarctic temperature-originally thought to hint at a driving role for temperature(2,3)-is absent(4,5) at the last deglaciation, but recently confirmed at the last ice age inception(6) and the end of the earlier termination II (ref. 7). We show that such variable time lags are typical for complex nonlinear systems such as the climate, prohibiting straightforward use of correlation lags to infer causation. However, an insight from dynamical systems theory(8) now allows us to circumvent the classical challenges of unravelling causation from multivariate time series. We build on this insight to demonstrate directly from ice-core data that, over glacial-interglacial timescales, climate dynamics are largely driven by internal Earth system mechanisms, including a marked positive feedback effect from temperature variability on greenhouse-gas concentrations.

Clark, AT, Ye H, Isbell F, Deyle ER, Cowles J, Tilman GD, Sugihara G.  2015.  Spatial convergent cross mapping to detect causal relationships from short time series. Ecology. 96:1174-1181.   10.1890/   AbstractWebsite

Recent developments in complex systems analysis have led to new techniques for detecting causal relationships using relatively short time series, on the order of 30 sequential observations. Although many ecological observation series are even shorter, perhaps fewer than ten sequential observations, these shorter time series are often highly replicated in space (i.e., plot replication). Here, we combine the existing techniques of convergent cross mapping (CCM) and dewdrop regression to build a novel test of causal relations that leverages spatial replication, which we call multispatial CCM. Using examples from simulated and real-world ecological data, we test the ability of multispatial CCM to detect causal relationships between processes. We find that multispatial CCM successfully detects causal relationships with as few as five sequential observations, even in the presence of process noise and observation error. Our results suggest that this technique may constitute a useful test for causality in systems where experiments are difficult to perform and long time series are not available. This new technique is available in the multispatialCCM package for the R programming language.

Tsonis, AA, Deyle ER, May RM, Sugihara G, Swanson K, Verbeten JD, Wang GL.  2015.  Dynamical evidence for causality between galactic cosmic rays and interannual variation in global temperature. Proceedings of the National Academy of Sciences of the United States of America. 112:3253-3256.   10.1073/pnas.1420291112   AbstractWebsite

As early as 1959, it was hypothesized that an indirect link between solar activity and climate could be mediated by mechanisms controlling the flux of galactic cosmic rays (CR) [Ney ER (1959) Nature 183:451-452]. Although the connection between CR and climate remains controversial, a significant body of laboratory evidence has emerged at the European Organization for Nuclear Research [Duplissy J, et al. (2010) Atmos Chem Phys 10:1635-1647; Kirkby J, et al. (2011) Nature 476(7361):429-433] and elsewhere [Svensmark H, Pedersen JOP, Marsh ND, Enghoff MB, Uggerhoj Ul (2007) Proc R Soc A 463:385-396; Enghoff MB, Pedersen JOP, Uggerhoj Ul, Paling SM, Svensmark H (2011) Geophys Res Lett 38:L09805], demonstrating the theoretical mechanism of this link. In this article, we present an analysis based on convergent cross mapping, which uses observational time series data to directly examine the causal link between CR and year-to-year changes in global temperature. Despite a gross correlation, we find no measurable evidence of a causal effect linking CR to the overall 20th-century warming trend. However, on short interannual timescales, we find a significant, although modest, causal effect between CR and short-term, year-to-year variability in global temperature that is consistent with the presence of nonlinearities internal to the system. Thus, although CR do not contribute measurably to the 20th-century global warming trend, they do appear as a nontraditional forcing in the climate system on short interannual timescales.

Ye, H, Beamish RJ, Glaser SM, Grant SCH, Hsieh CH, Richards LJ, Schnute JT, Sugihara G.  2015.  Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling. Proceedings of the National Academy of Sciences of the United States of America. 112:E1569-E1576.   10.1073/pnas.1417063112   AbstractWebsite

It is well known that current equilibrium-based models fall short as predictive descriptions of natural ecosystems, and particularly of fisheries systems that exhibit nonlinear dynamics. For example, model parameters assumed to be fixed constants may actually vary in time, models may fit well to existing data but lack out-of-sample predictive skill, and key driving variables may be misidentified due to transient (mirage) correlations that are common in nonlinear systems. With these frailties, it is somewhat surprising that static equilibrium models continue to be widely used. Here, we examine empirical dynamic modeling (EDM) as an alternative to imposed model equations and that accommodates both nonequilibrium dynamics and nonlinearity. Using time series from nine stocks of sockeye salmon (Oncorhynchus nerka) from the Fraser River system in British Columbia, Canada, we perform, for the the first time to our knowledge, real-data comparison of contemporary fisheries models with equivalent EDM formulations that explicitly use spawning stock and environmental variables to forecast recruitment. We find that EDM models produce more accurate and precise forecasts, and unlike extensions of the classic Ricker spawner-recruit equation, they show significant improvements when environmental factors are included. Our analysis demonstrates the strategic utility of EDM for incorporating environmental influences into fisheries forecasts and, more generally, for providing insight into how environmental factors can operate in forecast models, thus paving the way for equation-free mechanistic forecasting to be applied in management contexts.

Liu, H, Fogarty MJ, Hare JA, Hsieh CH, Glaser SM, Ye H, Deyle E, Sugihara G.  2014.  Modeling dynamic interactions and coherence between marine zooplankton and fishes linked to environmental variability. Journal of Marine Systems. 131:120-129.   10.1016/j.jmarsys.2013.12.003   AbstractWebsite

The dynamics of marine fishes are closely related to lower trophic levels and the environment. Quantitatively understanding ecosystem dynamics linking environmental variability and prey resources to exploited fishes is crucial for ecosystem-based management of marine living resources. However, standard statistical models typically grounded in the concept of linear system may fail to capture the complexity of ecological processes. We have attempted to model ecosystem dynamics using a flexible, nonparametric class of nonlinear forecasting models. We analyzed annual time series of four environmental indices, 22 marine copepod taxa, and four ecologically and commercially important fish species during 1977 to 2009 on Georges Bank, a highly productive and intensively studied area of the northeast U.S. continental shelf ecosystem. We examined the underlying dynamic features of environmental indices and copepods, quantified the dynamic interactions and coherence with fishes, and explored the potential control mechanisms of ecosystem dynamics from a nonlinear perspective. We found: (I) the dynamics of marine copepods and environmental indices exhibiting clear nonlinearity; (2) little evidence of complex dynamics across taxonomic levels of copepods; (3) strong dynamic interactions and coherence between copepods and fishes; and (4) the bottom-up forcing of fishes and top-down control of copepods coexisting as target trophic levels vary. These findings highlight the nonlinear interactions among ecosystem components and the importance of marine zooplankton to fish populations which point to two forcing mechanisms likely interactively regulating the ecosystem dynamics on Georges Bank under a changing environment. (C) 2013 Elsevier B.V. All rights reserved.

Glaser, SM, Ye H, Sugihara G.  2014.  A nonlinear, low data requirement model for producing spatially explicit fishery forecasts. Fisheries Oceanography. 23:45-53.   10.1111/fog.12042   AbstractWebsite

Spatial variability can confound accurate estimates of catch per unit effort (CPUE), especially in highly migratory species. The incorporation of spatial structure into fishery stock assessment models should ultimately improve forecasts of stock biomass. Here, we describe a nonlinear time series model for producing spatially explicit forecasts of CPUE that does not require ancillary environmental or demographic data, or specification of a model functional form. We demonstrate this method using spatially resolved (1 degrees x1 degrees cells) CPUE time series of North Pacific albacore in the California Current System. The spatial model is highly significant (P<0.00001) and outperforms two spatial null models. We then create a spatial forecast map for years beyond the range of data. Such approaches can guide spatial management of resources and provide a complement to more data-intensive, highly parameterized population dynamics and ecosystem models currently in use.

National Research Council (Ed.).  2014.  Evaluating the Effectiveness of Fish Stock Rebuilding Plans in the United States. :154., Washington, DC: The National Academies Press AbstractWebsite

In the United States (U.S.), the Fishery Conservation and Management Act of 1976, now known as the Magnuson-Stevens Fishery Conservation and Management Act (MSFCMA), was the first major legislation to regulate federal fisheries in the U.S. Fishery Conservation Zone (later designated as the U.S. exclusive economic zone). The re-authorization of the MSFCMA passed by Congress in 2006 included additional mandates for conserving and rebuilding fish stocks and strengthening the role of scientific advice in fisheries management. Approximately 20% of the fisheries that have been assessed are considered overfished according to the September 2012 stock status Report to Congress prepared by the U.S. National Oceanic and Atmospheric Administration (NOAA). Overfished refers to a stock that is below the minimum stock size threshold, commonly set to half the stock size at which maximum sustainable yield (MSY) is achieved. Under the provisions of the MSFCMA, rebuilding plans for overfished stocks should take no more than 10 years, except when certain provisions apply. Rebuilding mandates have led to substantial reductions in catch and effort for many fisheries, raising concerns about the consequent social and economic impacts to the fishing communities and industry. Evaluating the Effectiveness of Fish Stock Rebuilding Plans in the United States reviews the technical specifications that underlie current federally-implemented rebuilding plans, and the outcomes of those plans. According to this report, fisheries management has evolved substantially since 1977 when the U.S. extended its jurisdiction to 8 200 miles, in the direction of being more prescriptive and precautionary in terms of preventing overfishing and rebuilding overfished fisheries. However, the trade-offs between precaution and yield have not been fully evaluated. Evaluating the Effectiveness of Fish Stock Rebuilding Plans in the United States discusses the methods and criteria used to set target fishing mortality and biomass levels for rebuilding overfished stocks, and to determine the probability that a particular stock will rebuild by a certain date. This report will be of interest to the fishing industry, ecology professionals, and members of Congress as they debate the renewal of the Magnuson-Stevens Fishery Conservation and Management Act.

Glaser, SM, Fogarty MJ, Liu H, Altman I, Hsieh C-H, Kaufman L, MacCall AD, Rosenberg AA, Ye H, Sugihara G.  2013.  Complex dynamics may limit prediction in marine fisheries. Fish and Fisheries.   10.1111/faf.12037   AbstractWebsite

Complex nonlinear dynamics in marine fisheries create challenges for prediction and management, yet the extent to which they occur in fisheries is not well known. Using nonlinear forecasting models, we analysed over 200 time series of survey abundance and landings from two distinct ecosystems for patterns of dynamic complexity (dimensionality and nonlinear dynamics) and predictability. Differences in system dimensionality and nonlinear dynamics were associated with time series that reflected human intervention via fishing effort, implying the coupling between human and natural systems generated dynamics distinct from those detected in the natural resource subsystem alone. Estimated dimensionality was highest for landings and higher in abundance indices of unfished species than fished species. Fished species were more likely to display nonlinear dynamics than unfished species, and landings were significantly less predictable than abundance indices. Results were robust to variation in life history characteristics. Dynamics were predictable over a 1-year time horizon in seventy percent of time series, but predictability declined exponentially over a 5-year horizon. The ability to make predictions in fisheries systems is therefore extremely limited. To our knowledge, this is the first cross-system comparative study, and the first at the scale of individual species, to analyse empirically the dynamic complexity observed in fisheries data and to quantify predictability broadly. We outline one application of short-term forecasts to a precautionary approach to fisheries management that could improve how uncertainty and forecast error are incorporated into assessment through catch limit buffers.

Perretti, CT, Sugihara G, Munch SB.  2013.  Nonparametric forecasting outperforms parametric methods for a simulated multispecies system. Ecology. 94:794-800.   10.1890/12-0904.1   AbstractWebsite

Ecosystem dynamics are often complex, nonlinear, and characterized by critical thresholds or phase shifts. To implement sustainable management plans, resource managers need to accurately forecast species abundance. Moreover, an ecosystem-based approach to management requires forecasting the dynamics of all relevant species and the ability to anticipate indirect effects of management decisions. It is therefore crucial to determine which forecasting methods are most robust to observational and structural uncertainty. Here we describe a nonparametric method for multispecies forecasting and evaluate its performance relative to a suite of parametric models. We found that, in the presence of noise, it is often possible to obtain more accurate forecasts from the nonparametric method than from the model that was used to generate the data. The inclusion of data from additional species yielded a large improvement for the nonparametric model, a smaller improvement for the control model, and only a slight improvement for the alternative parametric models. These results suggest that flexible nonparametric modeling should be considered for ecosystem management.

Deyle, ER, Fogarty M, Hsieh CH, Kaufman L, MacCall AD, Munch SB, Perretti CT, Ye H, Sugihara G.  2013.  Predicting climate effects on Pacific sardine. Proceedings of the National Academy of Sciences of the United States of America. 110:6430-6435.   10.1073/pnas.1215506110   AbstractWebsite

For many marine species and habitats, climate change and overfishing present a double threat. To manage marine resources effectively, it is necessary to adapt management to changes in the physical environment. Simple relationships between environmental conditions and fish abundance have long been used in both fisheries and fishery management. In many cases, however, physical, biological, and human variables feed back on each other. For these systems, associations between variables can change as the system evolves in time. This can obscure relationships between population dynamics and environmental variability, undermining our ability to forecast changes in populations tied to physical processes. Here we present a methodology for identifying physical forcing variables based on nonlinear forecasting and show how the method provides a predictive understanding of the influence of physical forcing on Pacific sardine.

Perretti, CT, Munch SB, Sugihara G.  2013.  Model-free forecasting outperforms the correct mechanistic model for simulated and experimental data. Proceedings of the National Academy of Sciences of the United States of America. 110:5253-5257.   10.1073/pnas.1216076110   AbstractWebsite

Accurate predictions of species abundance remain one of the most vexing challenges in ecology. This observation is perhaps unsurprising, because population dynamics are often strongly forced and highly nonlinear. Recently, however, numerous statistical techniques have been proposed for fitting highly parameterized mechanistic models to complex time series, potentially providing the machinery necessary for generating useful predictions. Alternatively, there is a wide variety of comparatively simple model-free forecasting methods that could be used to predict abundance. Here wepose a rather conservative challenge and ask whether a correctly specified mechanistic model, fit with commonly used statistical techniques, can provide better forecasts than simple model-free methods for ecological systems with noisy nonlinear dynamics. Using four different control models and seven experimental time series of flour beetles, we found that Markov chain Monte Carlo procedures for fitting mechanistic models often converged on best-fit parameterizations far different from the known parameters. As a result, the correctly specified models provided inaccurate forecasts and incorrect inferences. In contrast, a model-free method based on state-space reconstruction gave the most accurate short-term forecasts, even while using only a single time series from the multivariate system. Considering the recent push for ecosystem-based management and the increasing call for ecological predictions, our results suggest that a flexible model-free approach may be the most promising way forward.

National Research Council (Ed.).  2013.  Abrupt Impacts of Climate Change: Anticipating Surprises. , Washington, DC: The National Academies Press AbstractWebsite

Climate is changing, forced out of the range of the past million years by levels of carbon dioxide and other greenhouse gases not seen in the Earth's atmosphere for a very, very long time. Lacking action by the world's nations, it is clear that the planet will be warmer, sea level will rise, and patterns of rainfall will change. But the future is also partly uncertain -- there is considerable uncertainty about how we will arrive at that different climate. Will the changes be gradual, allowing natural systems and societal infrastructure to adjust in a timely fashion? Or will some of the changes be more abrupt, crossing some threshold or "tipping point" to change so fast that the time between when a problem is recognized and when action is required shrinks to the point where orderly adaptation is not possible? Abrupt Impacts of Climate Change is an updated look at the issue of abrupt climate change and its potential impacts. This study differs from previous treatments of abrupt changes by focusing on abrupt climate changes and also abrupt climate impacts that have the potential to severely affect the physical climate system, natural systems, or human systems, often affecting multiple interconnected areas of concern. The primary timescale of concern is years to decades. A key characteristic of these changes is that they can come faster than expected, planned, or budgeted for, forcing more reactive, rather than proactive, modes of behavior. Abrupt Impacts of Climate Change summarizes the state of our knowledge about potential abrupt changes and abrupt climate impacts and categorizes changes that are already occurring, have a high probability of occurrence, or are unlikely to occur. Because of the substantial risks to society and nature posed by abrupt changes, this report recommends the development of an Abrupt Change Early Warning System that would allow for the prediction and possible mitigation of such changes before their societal impacts are severe. Identifying key vulnerabilities can help guide efforts to increase resiliency and avoid large damages from abrupt change in the climate system, or in abrupt impacts of gradual changes in the climate system, and facilitate more informed decisions on the proper balance between mitigation and adaptation. Although there is still much to learn about abrupt climate change and abrupt climate impacts, to willfully ignore the threat of abrupt change could lead to more costs, loss of life, suffering, and environmental degradation. Abrupt Impacts of Climate Change makes the case that the time is here to be serious about the threat of tipping points so as to better anticipate and prepare ourselves for the inevitable surprises.

Liu, H, Fogarty MJ, Glaser SM, Altman I, Hsieh CH, Kaufman L, Rosenberg AA, Sugihara G.  2012.  Nonlinear dynamic features and co-predictability of the Georges Bank fish community. Marine Ecology Progress Series. 464:195-207.   10.3354/meps09868   AbstractWebsite

We examined evidence for nonlinear dynamics in fishery-independent survey data for an assemblage of 26 fish species on Georges Bank spanning the period 1963 to 2008. We used nonlinear time series analysis to determine (1) the presence of nonlinear dynamics in fish populations on Georges Bank, (2) the minimum number of dimensions required to effectively describe system dynamics, (3) the strength of patterns of co-predictability among all possible pairs of fish species, and (4) identification of groups of species characterized by similar dynamics. Here, nonlinear behavior refers to non-equilibrium dynamics, including chaos. The population trajectories of all 26 species exhibited strong density-dependent feedback as indicated by a Partial Rate Correlation Function analysis. Significant evidence of complex dynamical behavior was found for approximately 1 in 5 species. Low dimensionality for many of the individual series was identified, suggesting that for a given level of predictability, this system can be represented by a relatively small number of critically important ecological variables. Further, we found high levels of co-predictability among pairwise combinations of individual species. We identified 4 major species groups sharing similar dynamic features on the basis of patterns of co-predictability, and explored potential mechanisms for interpreting the groupings in terms of trophic interactions and life history characteristics.

Sugihara, G, May R, Ye H, Hsieh CH, Deyle E, Fogarty M, Munch S.  2012.  Detecting causality in complex ecosystems. Science. 338:496-500.   10.1126/science.1227079   Abstract

Identifying causal networks is important for effective policy and management recommendations on climate, epidemiology, financial regulation, and much else. We introduce a method, based on nonlinear state space reconstruction, that can distinguish causality from correlation. It extends to nonseparable weakly connected dynamic systems (cases not covered by the current Granger causality paradigm). The approach is illustrated both by simple models (where, in contrast to the real world, we know the underlying equations/relations and so can check the validity of our method) and by application to real ecological systems, including the controversial sardine-anchovy-temperature problem.

Sugihara, G, Beddington J, Hsieh CH, Deyle E, Fogarty M, Glaser SM, Hewitt R, Hollowed A, May RM, Munch SB, Perretti C, Rosenberg AA, Sandin S, Ye H.  2011.  Are exploited fish populations stable? Proceedings of the National Academy of Sciences of the United States of America. 108:E1224-E1225.   10.1073/pnas.1112033108   AbstractWebsite
Glaser, SM, Ye H, Maunder M, MacCall A, Fogarty M, Sugihara G.  2011.  Detecting and forecasting complex nonlinear dynamics in spatially structured catch-per-unit-effort time series for North Pacific albacore (Thunnus alalunga). Canadian Journal of Fisheries and Aquatic Sciences. 68:400-412.   10.1139/f10-160   AbstractWebsite

The presence of complex, nonlinear dynamics in fish populations, and uncertainty in the structure (functional form) of those dynamics, pose challenges to the accuracy of forecasts produced by traditional stock assessment models. We describe two nonlinear forecasting models that test for the hallmarks of complex behavior, avoid problems of structural uncertainty, and produce good forecasts of catch-per-unit-effort (CPUE) time series in both standardized and nominal (unprocessed) form. We analyze a spatially extensive, 40-year-long data set of annual CPUE time series of North Pacific albacore (Thunnus alalunga) from 1 degrees x 1 degrees cells from the eastern North Pacific Ocean. The use of spatially structured data in compositing techniques improves out-of-sample forecasts of CPUE and overcomes difficulties commonly encountered when using short, incomplete time series. These CPUE series display low-dimensional, nonlinear structure and significant predictability. Such characteristics have important implications for industry efficiency in terms of future planning and can inform formal stock assessments used for the management of fisheries.

Deyle, ER, Sugihara G.  2011.  Generalized theorems for nonlinear state space reconstruction. Plos One. 6   10.1371/journal.pone.0018295   AbstractWebsite

Takens' theorem (1981) shows how lagged variables of a single time series can be used as proxy variables to reconstruct an attractor for an underlying dynamic process. State space reconstruction (SSR) from single time series has been a powerful approach for the analysis of the complex, non-linear systems that appear ubiquitous in the natural and human world. The main shortcoming of these methods is the phenomenological nature of attractor reconstructions. Moreover, applied studies show that these single time series reconstructions can often be improved ad hoc by including multiple dynamically coupled time series in the reconstructions, to provide a more mechanistic model. Here we provide three analytical proofs that add to the growing literature to generalize Takens' work and that demonstrate how multiple time series can be used in attractor reconstructions. These expanded results (Takens' theorem is a special case) apply to a wide variety of natural systems having parallel time series observations for variables believed to be related to the same dynamic manifold. The potential information leverage provided by multiple embeddings created from different combinations of variables (and their lags) can pave the way for new applied techniques to exploit the time-limited, but parallel observations of natural systems, such as coupled ecological systems, geophysical systems, and financial systems. This paper aims to justify and help open this potential growth area for SSR applications in the natural sciences.

Tsonis, AA, Swanson KL, Sugihara G, Tsonis PA.  2010.  Climate change and the demise of Minoan civilization. Climate of the Past. 6:525-530.   10.5194/cp-6-525-2010   AbstractWebsite

Climate change has been implicated in the success and downfall of several ancient civilizations. Here we present a synthesis of historical, climatic, and geological evidence that supports the hypothesis that climate change may have been responsible for the slow demise of Minoan civilization. Using proxy ENSO and precipitation reconstruction data in the period 1650-1980 we present empirical and quantitative evidence that El Nino causes drier conditions in the area of Crete. This result is supported by modern data analysis as well as by model simulations. Though not very strong, the ENSO-Mediterranean drying signal appears to be robust, and its overall effect was accentuated by a series of unusually strong and long-lasting El Nino events during the time of the Minoan decline. Indeed, a change in the dynamics of the El Nino/Southern Oscillation (ENSO) system occurred around 3000 BC, which culminated in a series of strong and frequent El Nino events starting at about 1450 BC and lasting for several centuries. This stressful climatic trend, associated with the gradual demise of the Minoans, is argued to be an important force acting in the downfall of this classic and long-lived civilization.