Abstract
We consider the problem of analyzing long-term experiments with panels of nonlinear time-series data in the framework of generalized additive models. Our approach is developed for testing and estimating the (partial) common dynamic structure across treatment groups. We illustrate our approach with a detailed analysis of an ecotoxicological experiment on the effect of sublethal doses of a toxic substance (cadmium) on the long-run dynamic structure of the greenbottle blowfly (Lucilia sericata). The general model for the blowfly experiment is a generalized additive model which is derived from a stage-structured ecological model. We discuss the relationship between the components of the generalized additive model and those of the underlying stage-structured model. In particular, our proposed approach casts new insights on the effect of toxic diet on the population dynamic structure of the blowfly.
Similar content being viewed by others
References
Atkinson, A. C. (1985), Plots, Transformations and Regression, New York: Oxford University Press.
Bowman, A. W., and Azzalini, A. (1997), Applied Smoothing Techniques for Data Analysis, Oxford: Oxford University Press.
Box, G. E. P., and Tiao, G. C. (1975), “Intervention Analysis with Applications to Economic and Environmental Problems,” Journal of the American Statistical Association, 70, 70–79.
Breiman, L., and Friedman, J. H., (1985), “Estimating Optimal Transformations for Multiple Regression and Correlation,” Journal of the American Statistical Association, 80, 580–619.
Brillinger, D. R. (1981), Time Series: Data Analysis and Theory, New York: Holt, Rinehart & Winston.
Chan, K.-S., Kristoffersen, A. B., and Stenseth, N. C. (2003), “Bürmann Expansion and Test for Additivity,” Biometrika, 90, 209–222.
Chan, K. S., and Tong, H (2001), Chaos: A Statistical Perspective, New York: Springer Verlag.
Chan, K. S., Tong, H., and Stenseth, N. Chr.(2004), “Testing for Common Structures in a Panel of Threshold Models,” Biometrics, 60, 225–232.
Chen, R., Liu, J. S., and Tsay, R. S. (1995), “Additivity Tests for Nonlinear Autoregression,” Biometrika, 82, 369–83.
Daniels, S. (1994), “Effects of Cadmium Toxicity on Population Dynamics of the Blowfly Lucilia sericata,” PhD thesis, University of Reading.
de Boor, C. (1978), A Practical Guide to Splines, New York: Springer-Verlag.
Hastie, T. J., and Tibshirani, R. J. (1990), Generalized Additive Models, London: Chapman and Hall.
Hinde, J., and Demétrio, G. B. (1998), “Overdispersion: Models and Estimation,” Computational Statistics & Data Analysis, 27, 151–170.
Kristoffersen, A. B., Lingjærde, O. C., Stenseth, N. C., and Shimada, M. (2001), “Nonparametric Modelling of Nonlinear Density Dependence: a Three-Species Host-Parasitoid System,” Journal of Animal Ecology, 70, 808–819; Erratum: 70, 1098.
Lingjærde, O. C., Stenseth, N. C., Kristoffersen, A. B., Smith, R.H., Moe, S. J., Read, J. M., Daniels, S., and Simkiss, K. (2001), “Exploring Non-linearities in the Stage-Specific Density-Dependent Structure of Experimental Blowfly Populations Using Non-parametric Additive Modelling,” Ecology, 82, 2645–2658.
MathSoft (1999), S-Plus 5 for Unix: Guide to Statistics, Seattle, WA: MathSoft, Inc.
May, R. M. (1976), “Simple Mathematical Models With Very Complicated Dynamics,” Nature, 261, 459–467.
— (1986), “When 2 and 2 Do Not Make 4. Nonlinear Phenomena in Ecology,” Proceedings of Royal Society of London, B, 228, 241–266.
Moe, J. S., Stenseth, N. C., and Smith, R. E. (2002), “Density-Dependence in Blowfly Populations: Experimental Evaluation of Non-parametric Time-Series Modelling,” Oikos, 98, 523–533.
Pierce, D. A., and Schafer, D. W. (1986), “Residuals in Generalized Linear Models,” Journal of the American Statistical Association, 81, 977–986.
Royama, T. (1996), Analytical Population Dynamics, New York: Chapman and Hall.
Smith, R. H., Daniels, S., Simkiss, K., Bell, E. D., Ellner, S. P., and Forrest, B. (2000), “Blowflies as a Case Study in Non-linear Population Dynamics,” in Chaos in Real Data: The Analysis of Non-linear Dynamics in Short Ecological Time Series, eds. J. N. Perry, R. H. Smith, I. P. Woiwod, and D. Morse, Netherlands: Kluwer.
Stenseth, N. C., Chan, K.-S., Tong, H., Boonstra, R., Boutin, R., Krebs, C. J., Post, E., O’Donoghue, M., Yoccoz, N. G., Forchhammer, M. C., and Hurrell, J. W. (1999), “Common Dynamic Structure of Canada Lynx Populations Within Three Climatic Regions,” Science, 285, 1071–1073.
Tong, H. (1990), Non-linear Time Series: A Dynamical System Approach, Oxford: Oxford University Press.
Venables, W. N., and Ripley, B. D. (1999), Modern Applied Statistics with S-PLUS (3rd ed.), New York: Springer-Verlag.
Weisberg, S. (1985), Applied Linear Regression (2nd ed.), New York: Wiley.
Xia, Y., Tong, H., Li, W. K., and Zhu, L.-X. (2002), “An Adaptive Estimation of Dimension Reduction Space” (with discussion), Journal of the Royal Statistical Society, Series B, 63, 363–410.
Yao, Q., Tong, H., Finkenstäd, B., and Stenseth, N. C. (2000), “Common Structure in Panels of Short Ecological Time Series,” Proceedings of Royal Society of London, B, 267, 2459–2467.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chan, G., Chan, KS., Stenseth, N.C. et al. Analyzing nonlinear population dynamics data. JABES 9, 200–215 (2004). https://doi.org/10.1198/1085711043587
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1198/1085711043587