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Munch SB, Rogers TL, Symons CC, Anderson D, Pennekamp F. Constraining nonlinear time series modeling with the metabolic theory of ecology. Proc Natl Acad Sci U S A 2023; 120:e2211758120. [PMID: 36930600 PMCID: PMC10041132 DOI: 10.1073/pnas.2211758120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2022] [Accepted: 02/08/2023] [Indexed: 03/18/2023] Open
Abstract
Forecasting the response of ecological systems to environmental change is a critical challenge for sustainable management. The metabolic theory of ecology (MTE) posits scaling of biological rates with temperature, but it has had limited application to population dynamic forecasting. Here we use the temperature dependence of the MTE to constrain empirical dynamic modeling (EDM), an equation-free nonlinear machine learning approach for forecasting. By rescaling time with temperature and modeling dynamics on a "metabolic time step," our method (MTE-EDM) improved forecast accuracy in 18 of 19 empirical ectotherm time series (by 19% on average), with the largest gains in more seasonal environments. MTE-EDM assumes that temperature affects only the rate, rather than the form, of population dynamics, and that interacting species have approximately similar temperature dependence. A review of laboratory studies suggests these assumptions are reasonable, at least approximately, though not for all ecological systems. Our approach highlights how to combine modern data-driven forecasting techniques with ecological theory and mechanistic understanding to predict the response of complex ecosystems to temperature variability and trends.
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Affiliation(s)
- Stephan B. Munch
- Southwest Fisheries Science Center, National Marine Fisheries Service, National Oceanic and Atmospheric Administration, Santa Cruz, CA95060
- Department of Applied Mathematics, University of California, Santa Cruz, CA95060
| | - Tanya L. Rogers
- Southwest Fisheries Science Center, National Marine Fisheries Service, National Oceanic and Atmospheric Administration, Santa Cruz, CA95060
| | - Celia C. Symons
- Department of Ecology and Evolutionary Biology, University of California, Irvine, CA92697
| | - David Anderson
- Department of Zoology, University of British Columbia, Vancouver, BCV6T 1Z4, Canada
| | - Frank Pennekamp
- Department of Evolutionary Biology and Environmental Studies, University of Zurich, Zurich8057, Switzerland
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Munch SB, Rogers TL, Sugihara G. Recent developments in empirical dynamic modelling. Methods Ecol Evol 2023. [DOI: 10.1111/2041-210x.13983] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/06/2023]
Affiliation(s)
- Stephan B. Munch
- Southwest Fisheries Science Center, National Marine Fisheries Service National Oceanic and Atmospheric Administration Santa Cruz California USA
- Department of Applied Mathematics University of California Santa Cruz California USA
| | - Tanya L. Rogers
- Southwest Fisheries Science Center, National Marine Fisheries Service National Oceanic and Atmospheric Administration Santa Cruz California USA
| | - George Sugihara
- Scripps Institution of Oceanography University of California San Diego La Jolla California USA
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Munch SB, Rogers TL, Johnson BJ, Bhat U, Tsai CH. Rethinking the Prevalence and Relevance of Chaos in Ecology. ANNUAL REVIEW OF ECOLOGY, EVOLUTION, AND SYSTEMATICS 2022. [DOI: 10.1146/annurev-ecolsys-111320-052920] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
Chaos was proposed in the 1970s as an alternative explanation for apparently noisy fluctuations in population size. Although readily demonstrated in models, the search for chaos in nature proved challenging and led many to conclude that chaos is either rare or nigh impossible to detect. However, in the intervening half-century, it has become clear that ecosystems are replete with the enabling conditions for chaos. Chaos has been repeatedly demonstrated under laboratory conditions and has been found in field data using updated detection methods. Together, these developments indicate that the apparent rarity of chaos was an artifact of data limitations and overreliance on low-dimensional population models. We invite readers to reevaluate the relevance of chaos in ecology, and we suggest that chaos is not as rare or undetectable as previously believed.
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Affiliation(s)
- Stephan B. Munch
- Department of Applied Mathematics, University of California, Santa Cruz, California, USA
- Southwest Fisheries Science Center, National Marine Fisheries Service, National Oceanic and Atmospheric Administration, Santa Cruz, California, USA
| | - Tanya L. Rogers
- Southwest Fisheries Science Center, National Marine Fisheries Service, National Oceanic and Atmospheric Administration, Santa Cruz, California, USA
| | - Bethany J. Johnson
- Department of Applied Mathematics, University of California, Santa Cruz, California, USA
| | - Uttam Bhat
- Institute of Marine Sciences, University of California, Santa Cruz, California, USA
| | - Cheng-Han Tsai
- Department of Applied Mathematics, University of California, Santa Cruz, California, USA
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Johnson B, Gomez M, Munch SB. Leveraging spatial information to forecast nonlinear ecological dynamics. Methods Ecol Evol 2020. [DOI: 10.1111/2041-210x.13511] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Bethany Johnson
- Department of Applied Mathematics University of California Santa Cruz CA USA
| | - Marcella Gomez
- Department of Applied Mathematics University of California Santa Cruz CA USA
| | - Stephan B. Munch
- Southwest Fisheries Science Center Fisheries Ecology Division National Oceanic and Atmospheric Administration Santa Cruz CA USA
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Frossard V, Rimet F, Perga ME. Causal networks reveal the dominance of bottom-up interactions in large, deep lakes. Ecol Modell 2018. [DOI: 10.1016/j.ecolmodel.2017.11.021] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Tajima S, Mita T, Bakkum DJ, Takahashi H, Toyoizumi T. Locally embedded presages of global network bursts. Proc Natl Acad Sci U S A 2017; 114:9517-9522. [PMID: 28827362 PMCID: PMC5594667 DOI: 10.1073/pnas.1705981114] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Spontaneous, synchronous bursting of neural population is a widely observed phenomenon in nervous networks, which is considered important for functions and dysfunctions of the brain. However, how the global synchrony across a large number of neurons emerges from an initially nonbursting network state is not fully understood. In this study, we develop a state-space reconstruction method combined with high-resolution recordings of cultured neurons. This method extracts deterministic signatures of upcoming global bursts in "local" dynamics of individual neurons during nonbursting periods. We find that local information within a single-cell time series can compare with or even outperform the global mean-field activity for predicting future global bursts. Moreover, the intercell variability in the burst predictability is found to reflect the network structure realized in the nonbursting periods. These findings suggest that deterministic local dynamics can predict seemingly stochastic global events in self-organized networks, implying the potential applications of the present methodology to detecting locally concentrated early warnings of spontaneous seizure occurrence in the brain.
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Affiliation(s)
- Satohiro Tajima
- Department of Basic Neuroscience, University of Geneva, Centre Médical Universitaire, Genève 1211, Switzerland;
- Precursory Research for Embryonic Science and Technology (PRESTO), Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012, Japan
- RIKEN Brain Science Institute, Wako, Saitama 351-0198, Japan
| | - Takeshi Mita
- Graduate School of Information Science and Technology, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Douglas J Bakkum
- Department of Biosystems Science and Engineering, ETH Zurich, Basel 4058, Switzerland
| | - Hirokazu Takahashi
- Graduate School of Information Science and Technology, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
- Research Center for Advanced Science and Technology, The University of Tokyo, Meguro-ku, Tokyo 153-8904, Japan
| | - Taro Toyoizumi
- RIKEN Brain Science Institute, Wako, Saitama 351-0198, Japan
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Perretti CT, Sugihara G, Munch SB. Nonparametric forecasting outperforms parametric methods for a simulated multispecies system. Ecology 2013. [DOI: 10.1890/12-0904.1] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Why fishing magnifies fluctuations in fish abundance. Nature 2008; 452:835-9. [PMID: 18421346 DOI: 10.1038/nature06851] [Citation(s) in RCA: 223] [Impact Index Per Article: 13.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2007] [Accepted: 02/22/2008] [Indexed: 11/08/2022]
Abstract
It is now clear that fished populations can fluctuate more than unharvested stocks. However, it is not clear why. Here we distinguish among three major competing mechanisms for this phenomenon, by using the 50-year California Cooperative Oceanic Fisheries Investigations (CalCOFI) larval fish record. First, variable fishing pressure directly increases variability in exploited populations. Second, commercial fishing can decrease the average body size and age of a stock, causing the truncated population to track environmental fluctuations directly. Third, age-truncated or juvenescent populations have increasingly unstable population dynamics because of changing demographic parameters such as intrinsic growth rates. We find no evidence for the first hypothesis, limited evidence for the second and strong evidence for the third. Therefore, in California Current fisheries, increased temporal variability in the population does not arise from variable exploitation, nor does it reflect direct environmental tracking. More fundamentally, it arises from increased instability in dynamics. This finding has implications for resource management as an empirical example of how selective harvesting can alter the basic dynamics of exploited populations, and lead to unstable booms and busts that can precede systematic declines in stock levels.
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Affiliation(s)
- Vishwesha Guttal
- Department of Physics, The Ohio State University, 191 W Woodruff Ave, Columbus, OH 43210-1117, USA.
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Global Patterns of Nonlinearity in Real and GCM-Simulated Atmospheric Data. ACTA ACUST UNITED AC 2008. [DOI: 10.1007/978-3-540-78938-3_2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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Hsieh C, Anderson C, Sugihara G. Extending Nonlinear Analysis to Short Ecological Time Series. Am Nat 2008; 171:71-80. [DOI: 10.1086/524202] [Citation(s) in RCA: 73] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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Abstract
Brains are usually described as input/output systems: they transform sensory input into motor output. However, the motor output of brains (behavior) is notoriously variable, even under identical sensory conditions. The question of whether this behavioral variability merely reflects residual deviations due to extrinsic random noise in such otherwise deterministic systems or an intrinsic, adaptive indeterminacy trait is central for the basic understanding of brain function. Instead of random noise, we find a fractal order (resembling Lévy flights) in the temporal structure of spontaneous flight maneuvers in tethered Drosophila fruit flies. Lévy-like probabilistic behavior patterns are evolutionarily conserved, suggesting a general neural mechanism underlying spontaneous behavior. Drosophila can produce these patterns endogenously, without any external cues. The fly's behavior is controlled by brain circuits which operate as a nonlinear system with unstable dynamics far from equilibrium. These findings suggest that both general models of brain function and autonomous agents ought to include biologically relevant nonlinear, endogenous behavior-initiating mechanisms if they strive to realistically simulate biological brains or out-compete other agents.
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Affiliation(s)
- Alexander Maye
- Universitätsklinikum Hamburg-Eppendorf, Zentrum für Experimentelle Medizin, Institut für Neurophysiologie und Pathophysiologie, Hamburg, Germany
| | - Chih-hao Hsieh
- Scripps Institution of Oceanography, University of California San Diego, La Jolla, California, United States of America
| | - George Sugihara
- Scripps Institution of Oceanography, University of California San Diego, La Jolla, California, United States of America
| | - Björn Brembs
- Freie Universität Berlin, Institut für Biologie–Neurobiologie, Berlin, Germany
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Abstract
Determining the relative contributions of intrinsic and extrinsic processes to the regulation of biological populations has been a recurrent ecological issue. Recent discussions concerning ecosystem "regime shifts" again raise the question of whether population fluctuations are mainly controlled by external forcing. Results of nonlinear time series analyses indicate that pelagic populations typically do not passively track stochastic environmental variables. Rather, population dynamics are better described as nonlinear amplification of physical forcing by biological interactions. However, we illustrate that in some cases populations do show linear tracking of the physical environment. To explain why population dynamics can sometimes be linear, we propose the linear tracking window hypothesis: populations are most likely to track the stochastic environmental forcing when their generation time matches the characteristic time scale of the environmental signal. While our observations follow this hypothesis well, our results indicate that the linear tracking window is a necessary but not a sufficient condition.
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Affiliation(s)
- Chih-Hao Hsieh
- Scripps Institution of Oceanography, University of California-San Diego, La Jolla, California 92093-0218, USA.
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Hsieh CH, Glaser SM, Lucas AJ, Sugihara G. Distinguishing random environmental fluctuations from ecological catastrophes for the North Pacific Ocean. Nature 2005; 435:336-40. [PMID: 15902256 DOI: 10.1038/nature03553] [Citation(s) in RCA: 253] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2004] [Accepted: 03/14/2005] [Indexed: 11/08/2022]
Abstract
The prospect of rapid dynamic changes in the environment is a pressing concern that has profound management and public policy implications. Worries over sudden climate change and irreversible changes in ecosystems are rooted in the potential that nonlinear systems have for complex and 'pathological' behaviours. Nonlinear behaviours have been shown in model systems and in some natural systems, but their occurrence in large-scale marine environments remains controversial. Here we show that time series observations of key physical variables for the North Pacific Ocean that seem to show these behaviours are not deterministically nonlinear, and are best described as linear stochastic. In contrast, we find that time series for biological variables having similar properties exhibit a low-dimensional nonlinear signature. To our knowledge, this is the first direct test for nonlinearity in large-scale physical and biological data for the marine environment. These results address a continuing debate over the origin of rapid shifts in certain key marine observations as coming from essentially stochastic processes or from dominant nonlinear mechanisms. Our measurements suggest that large-scale marine ecosystems are dynamically nonlinear, and as such have the capacity for dramatic change in response to stochastic fluctuations in basin-scale physical states.
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Affiliation(s)
- Chih-hao Hsieh
- Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California 92093-0202, USA
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