Abstract
Time series of physical and biological properties of the ocean are a valuable resource for developing models for ecological forecasting and ecosystem-based management. Both the physics of the oceans and organisms living in it can exhibit nonlinear dynamics. We describe the development of a nonlinear model that predicts the abundance of the important zooplankton species Calanus finmarchicus from hydrographic data from the Gulf of Maine. The results of a neural network model, including model diagnostics and forecasts, are presented. The best neural network model based on generalized cross-validation includes variables of C. finmarchicus abundance, herring abundance, and the state of the Gulf of Maine waters, with meaningful time lags. Forecasts are constructed for the model fit to 1978–2003 bimonthly data and corresponding forecasts intervals are obtained by the stationary bootstrap.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Azarovitz, T. (1981), A Brief Historical Review of the Woods Hole Laboratory Trawl Survey Time Series. Canadian Special Publication of Fisheries and Aquatic Sciences.
Bailey, B., Doney, S., and Lima, I. (2004), “Quantifying the Effects of Dynamical Noise on the Predictability of a Simple Ecosystem Model,” Environmetrics, 15, 337–355.
Belgrano, A., Malmgren, B., and Lindahl, O. (2001), “Applications of Artificial Neural Networks (ANN) to Primary Production Time Series Data,” Journal of Plankton Research, 23, 651–658.
Conversi, A., Piontkovski, A., and Hameed, S. (2001), “Seasonal and Interannual Dynamics of Calanus finmarchicus in the Gulf of Maine (Northeastern U.S. Shelf) With Reference to the North Atlantic Oscillation,” Deep Sea Research II, 48, 519–520.
Darbyson, E., Swain, D., Chabot, D., and Castonguay, M. (2003), “Diel Variation in Feeding Rate and Prey Composition of Herring and Mackerel in the Southern Gulf of St. Lawrence,” Journal of Fish Biology, 63, 1235–1257.
Davis, C. (1987), “Zooplankton Life Cycles,” in Georges Bank, eds. R. Backus and D. Bourne, Cambridge: MIT Press, pp. 256–267.
Efron, B., and Tibshirani, R. (1993), An Introduction to the Bootstrap, New York: Chapman & Hall/CRC.
Ellner, S., Bailey, B., Bobashev, G., Gallant, A., Grenfell, B., and Nychka, D. (1998), “Noise and Nonlinearity in Measles Epidemics: Combining Mechanistic and Statistical Approaches to Population Modeling,” American Naturalist, 15, 425–440.
Ellner, S., Nychka, D., and Gallant, A. (1992), “LENNS, a Program to Estimate the Dominant Lyapunov Exponent of a Noisy Nonlinear System From Time Series Data,” 2235, Statistics Department, North Carolina State University, Raleigh, NC, 27695–8203: Institute of Statistics Mimeo Series.
Greene, C., and Pershing, A. (2003), “The Flip-Side of the North Atlantic Oscillation and Modal Shifts in Slope-Water Circulation Patterns,” Limnology & Oceanography, 48, 319–322.
— (2004), “Climate and the Conservation Biology of the North Atlantic Right Whale: The Right Whale at the Wrong Time?” Frontiers in Ecology and the Environment, 2, 29–34.
— (2007), “Climate-Driven Changes in Arctic Ocean Outflow Force Ecosystem Regime Shift in NW Atlantic,” Science, 315, 1084–1085.
Jossi, J., and Goulet, J. (1993), “Zooplankton Trends: U.S. North-East Shelf Ecosystem and Adjacent Regions Differ From North-East Atlantic and North Sea,” ICES Journal of Marine Science, 50, 303–313.
Kajitani, Y., Hipel, K., and McLleod, A. (2005), “Forecasting Nonlinear Time Series With Feed-Forward Neural Networks: A Case Study of Canadian Lynx Data,” Journal of Forecasting, 24, 105–117.
Kane, J. (1984), “The Feeding-Habits of Co-Occurring Cod and Haddock Larvae From Georges Bank,” Marine Ecology Progress Series, 16, 9–20.
Kiorboe, T., and Munk, P. (1986), “Feeding and Growth of Larval Herring, Clupea harengus, in Relation to Density of Copepod Nauplii,” Environmental Biology of Fishes, 17, 133–139.
Kot, M., Schaffer, W., Truty, G., Graser, D., and Olsen, L. F. (1988), “Changing Criteria for Imposing Order,” Ecological Modelling, 43, 75–110.
Marshall, S., and Orr, A. (1955), The Biology of a Marine Copepod: Calanus finmarchicus (Gunnerus), Edinburgh: Oliver and Boyd.
Meise, C., and O’Reilly, J. (1996), “Spatial and Seasonal Patterns in Abundance and Age Composition of Calanus finmarchicus in the Gulf of Maine and on the Georges Bank,” Deep Sea Research II, 43, 1473–1501.
MERCINA (2001), “Oceanographic Responses to Climate in the Northwest Atlantic,” Oceanography, 14, 76–82.
Nychka, D., Ellner, S., and Bailey, B. (2001), NNREG: Neural Net Regression. R Package Version 1.1.
Nychka, D., Ellner, S., McCaffrey, D., and Gallant, A. (1992), “Finding Chaos in Noisy Systems,” Journal of the Royal Statistical Society, Series B, 54, 399–426.
Overholtz, W., Jacobson, L., Melvin, G., and Cieri, M. (2004), Stock Assessment of the Gulf of Maine—Georges Bank Herring Complex, 1959–2002. Northeast Fish. Sci. Ctr. Ref. Doc.
Pascual, M., and Ellner, S. (2000), “Linking Ecological Patterns to Environmental Forcing Via Nonlinear Time Series Models,” Ecology, 8, 2767–2780.
Pershing, A., Greene, C., Jossi, J., O’Brien, L., Brodziak, J., and Bailey, B. (2005), “Interdecadal Variability in the Gulf of Maine Zooplankton Community With Potential Impacts on Fish Recruitment,” ICES Journal of Marine Science, 62, 1511–1523.
Pershing, A., Record, N., Monger, B., Pendleton, D., and Woodard, L. (2009), “Model-Based Estimates of Calanus finmarchicus Abundance in the Gulf of Maine,” Marine Ecology – Progress Series, 378, 245–257.
Pettigrew, N., Xue, H., Irish, J., Perrie, W., Roesler, C., Thomas, A., and Townsend, D. (2008), “The Gulf of Maine Ocean Observing System: Generic Lessons Learned in the First Seven Years of Operation (2001–2008),” Marine Technology Society Journal, 42, 91–102.
Politis, D., and Romano, J. (1994), “The Stationary Bootstrap,” Journal of the American Statistical Association, 89 (428), 1303–1313.
R Development Core Team (2008), R: A Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing. ISBN 3-900051-07-0.
Ripley, B. (1996), Pattern Recognition and Neural Networks, Cambridge: Cambridge University Press.
Takens, F. (1981), Dynamical Systems and Turbulence. Lecture Notes in Mathematics, Vol. 898, Berlin: Springer.
Teraesvirta, T., Lin, C., and Granger, C. (1993), “Power of the Neural Network Linearity Test,” Journal of Time Series Analysis, 14, 209–220.
Tong, H. (1983), Threshold Models in Non-linear Time Series Analysis, New York: Springer.
Wahba, G. (1990), Spline Models for Observational Data, Philadelphia: SIAM.
Warner, A., and Hays, G. (1994), “Sampling by the Continuous Plankton Recorder Survey,” Progress in Oceanography, 34, 237–256.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bailey, B.A., Pershing, A.J. A Nonlinear Model for Predicting Interannual Changes in Calanus finmarchicus Abundance in the Gulf of Maine. JABES 18, 234–249 (2013). https://doi.org/10.1007/s13253-013-0133-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13253-013-0133-2