Nonparametric forecasting outperforms parametric methods for a simulated multispecies system

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...

[1]  G Sugihara,et al.  Distinguishing error from chaos in ecological time series. , 1990, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[2]  David C. Smith,et al.  Lessons in modelling and management of marine ecosystems: the Atlantis experience , 2011 .

[3]  Steven V. Viscido,et al.  A statistical approach to quasi-extinction forecasting. , 2007, Ecology letters.

[4]  George Sugihara,et al.  Distinguishing random environmental fluctuations from ecological catastrophes for the North Pacific Ocean , 2005, Nature.

[5]  Julien Clinton Sprott,et al.  Extraction of dynamical equations from chaotic data , 1992 .

[6]  John H. Steele,et al.  Constructing end-to-end models using ECOPATH data , 2011 .

[7]  J. F. Gilliam,et al.  FUNCTIONAL RESPONSES WITH PREDATOR INTERFERENCE: VIABLE ALTERNATIVES TO THE HOLLING TYPE II MODEL , 2001 .

[8]  F. Takens Detecting strange attractors in turbulence , 1981 .

[9]  A. Mees,et al.  Dynamics from multivariate time series , 1998 .

[10]  D. H. Reed,et al.  The relationship between population size and temporal variability in population size , 2004 .

[11]  A. N. Sharkovskiĭ Dynamic systems and turbulence , 1989 .

[12]  George Sugihara,et al.  Nonlinear forecasting for the classification of natural time series , 1994, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[13]  M. B. Schaefer,et al.  Some Considerations of Population Dynamics and Economics in Relation to the Management of the Commercial Marine Fisheries , 1957 .

[14]  Leo Polansky,et al.  Likelihood ridges and multimodality in population growth rate models. , 2009, Ecology.

[15]  George Sugihara,et al.  Detecting and forecasting complex nonlinear dynamics in spatially structured catch-per-unit- effort time series for North Pacific albacore (Thunnus alalunga) , 2011 .

[16]  Dixon,et al.  Episodic fluctuations in larval supply , 1999, Science.

[17]  C. Walters,et al.  Are age-structured models appropriate for catch-effort data? , 1985 .

[18]  Catherine A Calder,et al.  Accounting for uncertainty in ecological analysis: the strengths and limitations of hierarchical statistical modeling. , 2009, Ecological applications : a publication of the Ecological Society of America.

[19]  James S. Clark,et al.  POPULATION TIME SERIES: PROCESS VARIABILITY, OBSERVATION ERRORS, MISSING VALUES, LAGS, AND HIDDEN STATES , 2004 .

[20]  Chih-hao Hsieh,et al.  Extending Nonlinear Analysis to Short Ecological Time Series , 2007, The American Naturalist.

[21]  L. Mark Berliner,et al.  Likelihood and Bayesian Prediction of Chaotic Systems , 1991 .

[22]  R. E. Grumbine What Is Ecosystem Management , 1994 .

[23]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .

[24]  George Sugihara,et al.  Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series , 1990, Nature.

[25]  P. Lehodey,et al.  A spatial population dynamics simulation model of tropical tunas using a habitat index based on environmental parameters , 1998 .

[26]  Y. Takeuchi Global Dynamical Properties of Lotka-Volterra Systems , 1996 .

[27]  Simon N. Wood,et al.  Super–sensitivity to structure in biological models , 1999, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[28]  Carl J. Walters,et al.  Ecopath with Ecosim: methods, capabilities and limitations , 2004 .

[29]  G. Sugihara,et al.  Generalized Theorems for Nonlinear State Space Reconstruction , 2011, PloS one.

[30]  G Sugihara,et al.  Residual delay maps unveil global patterns of atmospheric nonlinearity and produce improved local forecasts. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[31]  A. Hastings,et al.  Chaos in a Three-Species Food Chain , 1991 .

[32]  Martyn Plummer,et al.  JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling , 2003 .

[33]  W. Härdle,et al.  A Review of Nonparametric Time Series Analysis , 1997 .

[34]  Donald Ludwig,et al.  COMPARISON OF TWO MODELS AND TWO ESTIMATION METHODS FOR CATCH AND EFFORT DATA , 1988 .

[35]  A. Ives,et al.  Stability and variability in competitive communities. , 1999, Science.

[36]  Slocombe Ds,et al.  DEFINING GOALS AND CRITERIA FOR ECOSYSTEM-BASED MANAGEMENT , 1998 .

[37]  C. Geyer Markov Chain Monte Carlo Maximum Likelihood , 1991 .

[38]  T. Schreiber Interdisciplinary application of nonlinear time series methods , 1998, chao-dyn/9807001.

[39]  E. K. Pikitch,et al.  Ecosystem-Based Fishery Management , 2004, Science.

[40]  André E. Punt,et al.  Which ecological indicators can robustly detect effects of fishing , 2005 .

[41]  Jim M Cushing,et al.  Chaos and population control of insect outbreaks , 2001 .

[42]  Karen C. Abbott,et al.  Analysis of ecological time series with ARMA(p,q) models. , 2010, Ecology.