Publications

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2018
Munch, SB, Giron-Nava A, Sugihara G.  2018.  Nonlinear dynamics and noise in fisheries recruitment: A global meta-analysis. Fish and Fisheries. 19:964-973.   10.1111/faf.12304   AbstractWebsite

The relative importance of environmental and intrinsic controls on recruitment in fishes has been studied for over a century. Despite this, we are not much closer to predicting recruitment. Rather, recent analyses suggest that recruitment is virtually independent of stock size and, instead, seems to occur in distinct environmental regimes. This issue of whether or not recruitment and subsequent production are coupled to stock size is highly relevant to management. Here, we apply empirical dynamical modelling (EDM) to a global database of 185 fish populations to address the questions of whether or not variation in recruitment is (a) predictable and (b) coupled to stock size. We find that a substantial fraction of recruitment variation is predictable using only the observed history of fluctuations (similar to 40% on average). In addition, although recruitment is often coupled to stock size (107 of 185 stocks), stock size alone explains very little of the variation in recruitment; In similar to 90% of the stocks analysed, EDM forecasts have substantially lower prediction error than models based solely on stock size. We find that predictability varies across taxa and improves with the number of generations that have been sampled. In the light of these results, we suggest that EDM will be of greatest use in managing relatively short-lived species.

2016
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.

2015
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.

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.

2014
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.

2011
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.

2005
Hsieh, CH, Reiss C, Watson W, Allen MJ, Hunter JR, Lea RN, Rosenblatt RH, Smith PE, Sugihara G.  2005.  A comparison of long-term trends and variability in populations of larvae of exploited and unexploited fishes in the Southern California region: A community approach. Progress in Oceanography. 67:160-185.   10.1016/j.pocean.2005.05.002   AbstractWebsite

We have constructed an "expert-knowledge classification system" to categorize 309 fish taxa in the California Cooperative Oceanic Fisheries Investigations ichthyoplankton database into primary (coastal, coastal-oceanic, and oceanic) assemblages based on their principal ecological domains and subsequently, secondary assemblages according to the habitat affinities of adults. We examined effects of fishing, climate, adult habitat, and age-at-maturation on long-term variation of fish populations. We tested the hypothesis that populations of unexploited taxa, track climatic trends more closely than those of exploited taxa insofar as climatic signals may be confounded by fishing effects. Most oceanic taxa (23/34) showed a significant relationship with environmental variables and followed the trend of the Pacific Decadal Oscillation. Very few coastal (3/10) and coastal-oceanic (3/23) taxa exhibited a significant relationship with environmental signals; however, several fluctuated coherently, and age-at-maturation is an important factor. The lack of close correlation between fish populations and environmental signals in the coastal and coastal-oceanic assemblages indicates that these species might show nonlinear biological responses to external forcing rather than a simple linear tracking of environmental variables. We did not find a systematic pattern indicating that fishing influenced population fluctuation of exploited species. Constrained comparisons of exploited to unexploited species living in the same habitat and reaching maturity at the same age revealed evidence of overexploitation for some species but not for all. Our results suggest that considering life history and ecological characteristics of fish species and applying a community approach are important in understanding fishing effects on fish populations in the context of a changing environment. (c) 2005 Elsevier Ltd. All rights reserved.