Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling.
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.
Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093; hye@ucsd.edu gsugihara@ucsd.edu.
Hao
H
Ye
Pacific Biological Station, Fisheries and Oceans Canada, Nanaimo, BC V9T 6N7, Canada;
Richard J
RJ
Beamish
Joseph S. Korbel School of International Studies, University of Denver, Denver, CO 80210;
Sarah M
SM
Glaser
Fisheries and Oceans Canada, Delta, BC V3M 6A2, Canada; and.
Sue C H
SC
Grant
Institute of Oceanography and Institute of Ecology and Evolutionary Biology, National Taiwan University, Taipei, Taiwan 10617.
Chih-Hao
CH
Hsieh
Pacific Biological Station, Fisheries and Oceans Canada, Nanaimo, BC V9T 6N7, Canada;
Laura J
LJ
Richards
Pacific Biological Station, Fisheries and Oceans Canada, Nanaimo, BC V9T 6N7, Canada;
Jon T
JT
Schnute
Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093; hye@ucsd.edu gsugihara@ucsd.edu.
George
G
Sugihara
D000818:Animals; D001955:British Columbia; D017753:Ecosystem; D004784:Environmental Monitoring; D005260:Female; D005398:Fisheries; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D009792:Oceans and Seas; D011157:Population Dynamics; D045483:Rivers; D012474:Salmon; D013045:Species Specificity
ecosystem forecasting; empirical dynamic modeling; fisheries ecology; nonlinear dynamics; physical–biological interactions