Computing and Library Services - delivering an inspiring information environment

Fitting population dynamic models to time-series data by gradient matching

Ellner, Stephen P., Seifu, Yodit and Smith, Robert H. (2002) Fitting population dynamic models to time-series data by gradient matching. Ecology, 83 (8). pp. 2256-2270. ISSN 0012-9658

[img] PDF
Restricted to Registered users only

Download (575kB)


We describe and test a method for fitting noisy differential equation models to a time series of population counts, motivated by stage-structured models of insect and zooplankton populations. We consider semimechanistic models, in which the model structure is derived from knowledge of the life cycle, but the rate equations are estimated nonparametrically from the time-series data. The method involves smoothing the population time series x(t) in order to estimate the gradient dx/dt, and then fitting rate equations using penalized regression splines. Computer-intensive methods are used to estimate and remove the biases that result from the data being discrete time samples with sampling errors from a continuous time process. Semimechanistic modeling makes it possible to test assumptions about the mechanisms behind population fluctuations without the results being confounded by possibly arbitrary choices of parametric forms for process-rate equations. To illustrate this application, we analyze time-series data on laboratory populations of blowflies Lucilia cuprina and Lucilia sericata. The models assume that the populations are limited by competition among adults affecting their current birth and death rates. The results correspond to the actual experimental conditions. For L. cuprina (where the model's structure is appropriate) a good fit can be obtained, while for L. sericata (where the model is inappropriate), the fitted model does not reproduce some major features of the observed cycles. A documented set of R functions for all steps in the model-fitting process is provided as a supplement to this article.

Item Type: Article
Additional Information: © Ecological Society of America
Uncontrolled Keywords: blowflies, gradient matching, Lucilia cuprina, Lucilia sericata, model fitting, partially specified models, population dynamics, semimechanistic models, semiparametric models, stage structured models
Subjects: G Geography. Anthropology. Recreation > G Geography (General)
Q Science > QR Microbiology
Schools: School of Applied Sciences
References: Briggs, C. J., W. W. Murdoch, and R. M. Nisbet. 1999. Recent developments in theory for biological control of insect pests by parasitoids. Pages 22-42 in B. A. Hawkins and H. V. Cornell, editors. Theoretical approaches to biological control. Cambridge University Press, Cambridge, UK. Carroll, R. J., J. D. Maca, and D. Ruppert. 1999. Nonparametric estimation in the presence of measurement errors. Biometrika 86:541-554. Carroll, R. J., D. Ruppert, and L. W. Stefanski. 1995. Measurement error in nonlinear models. Chapman and Hall, New York, New York, USA. Caswell, H. 2000. Matrix population models. Second edition. Sinauer, Sunderland, Massachusetts, USA. Cook, J. R., and L. A. Stefanski. 1994. Simulation-extrapolation estimation in parametric measurement error models. Journal of the American Statistical Association 89:13 14- 1328. Daniels, S. 1994. Effects of cadmium toxicity on population dynamics of the blowfly Llicilia sericata. Dissertation. University of Reading, Reading, UK. Dennis, B., and M. Taper. 1994. Density dependence in time series observations of natural populations: estimation and testing. Ecological Monographs 64:205-224. de Valpine, P., and A. Hastings. 2002. Fitting population models incorporating process noise and observation error. Ecological Monographs 72:57-76. Eilers, P. H. C., and B. D. Marx. 1996. Flexible smoothing with B-splines and penalties (with discussion). Statistical Sciences 11:89-121. Ellner, S. P., B. A. Bailey, G. V. Bobashev, A. R. Gallant, B. T. Grenfell, and D. W. Nychka. 1998. Noise and nonlinearity in measles epidemics: combining mechanistic and statistical approaches to population modeling. American Naturalist 151:425-440. Ellner, S. P., B. E. Kendall, S. N. Wood, E. McCauley, C. J. Briggs. 1997. Inferring mechanism from time-series data: delay-differential equations. Physica D 100: 182-194. Fan, J., and I. Gijbels. 1996. Local polynomial modeling and its applications. Chapman and Hall, New York, New York, USA. Forrest, B. 1996. Toxins and blowfly population dynamics. Dissertation. University of Leicester, Leicester, UK. GouriCroux, C., and A. Montfort. 1996. Simulation-based econometric inference. Oxford University Press, Oxford, UK. Gurney, W. S. C., S. P. Blythe, and R. M. Nisbet. 1980. Nicholson's blowflies revisited. Nature 287: 17-2 1. Gurney, W. S. C., and R. M. Nisbet. 1985. Fluctuation periodicity, generation separation, and the expression of larval competition. Theoretical Population Biology 28:150- 180. Gurney, W. S. C.. and R. M. Nisbet. 1998. Ecological dynamics. Oxford University Press, Oxford, UK. Haefner, J. W. 1996. Modeling biological systems: principles and applications. Chapman and Hall, New York, New York. USA. Hastings, A. M. 1997. Population biology: concepts and models. Springer-Verlag, New York, New York, USA. Hilborn, R., and M. Mangel. 1997. The ecological detective: confronting models with data. Princeton University Press, Princeton, New Jersey, USA. Hudson, P. J., A. P. Dobson, and D. Newborn. 1998. Prevention of population cycles by parasite removal. Science 282:2256-2258. Ihaka, R., and R. Gentleman. 1996. R: a language for data analysis and graphics. Journal of Computational and Graphical Statistics 5:299-314. Ives, A. R., S. R. Carpenter, andB. Dennis. 1999. Community interaction webs and zooplankton responses to planktivory manipulations. Ecology 80: 1405-1 421. Kendall, B. E., C. J. Briggs, W. W. Murdoch, P. Turchin, S. P. Ellner, E. McCauley, R. Nisbet, and S. N. Wood. 1999. Why do populations cycle? A synthesis of statistical and mechanistic modeling approaches. Ecology 80: 1789-1 805. Korpimaki, E., and K. Norrdahl. 1998. Experimental reduction of predators reverses the crash phase of small-rodent cycles. Ecology 79:2448-2455. Laska, M. S., and J. T. Wootton. 1998. Theoretical concepts and empirical approaches to measuring interaction strength. Ecology 79:461-476. Lingjzrde, 0 . C., N. C. Stenseth, A. B. Kristoffersen, R. H. Smith, S. J. Moe, J. M. Read, S. Daniels, and K. Simkiss. 2001. Exploring non-linearities in the stage-specific density- dependent structure of experimental blowfly populations using non-parametric additive modeling. Ecology 82: 2645-2658. McCauley, E., R. M. Nisbet, A. M. DeRoos, W. W. Murdoch, and W. S. C. Gurney. 1996. Structured population models of herbivorous zooplankton. Ecological Monographs 66: 479-501. Murdoch, W. W. 1994. Population regulation in theory and practice. Ecology 75:271-287. Murdoch, W. W., and C. J. Briggs. 1996. Theory for biological control: recent developments. Ecology 77:2001-2013. Nicholson, A. J. 1954. An outline of the dynamics of animal populations. Australian Journal of Zoology 2:9-65. Nicholson. A. J. 1957. The self-adjustment of populations to change. Cold Spring Harbor Symposia on Quantitative Biology 22: 153-173. Nychka, D. W., S. Ellner, A. R. Gallant, and D. McCaffrey. 1992. Finding chaos in noisy systems (with discussion). Journal of the Royal Statistical Society Series B 54:399- 426. Ohman, M. D., and S. N. Wood. 1996. Mortality estimates for planktonic copepods: Psrudocalanus newmani in a temperate fjord. Limnology and Oceanography 41: 126-1 35. Oksendal, B. 1998. Stochastic differential equations: an introduction with applications. Fifth edition. Springer-Verlag, New York, New York, USA. Olsen, L. F., and W. M. Schaffer. 1990. Chaos versus noisy periodicity: alternative hypotheses for childhood epidemics. Science 249:499-504. Perry, J. N. 2000. Overciew. Pages 173-190 in J. N. Perry, R. H. Smith, I. P. Woiwod, and D. Morse. editors. Chaos in real data: the analysis of non-linear dynamics from short ecological time series. Kluwer Academic, Dordrecht, The Netherlands. Pfister, C. 1995. Estimating competition coefficients from census data: a test with field manipulations of tidepool fishes. American Naturalist 146:27 1-29 1. Readshaw. J. L., and W. R. Cuff. 1980. A model of Nicholson's blowfly cycles and its relevance to predation theory. Journal of Animal Ecology 49:1005-1010. Readshaw, J. L., and A. C. M. van Gerwen. 1983. Agespecific survival, fecundity and fertility of the adult blowfly, Lucilia cupri~la, in relation to crowding, protein food, and population cycles. Journal of Animal Ecclogy 52:879- 887. Ruppert, D., and R. J. Carroll. 1997. Penalized regression splines. Technical Report TR1249. Department of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York, USA. Ruppert, D., and R. J. Carroll. 2000. Spatially adaptive penalties for spline fitting. Australian and New Zealand Journal of Statistics 42:205-223. Smith. R. H., S. Daniels. K. Simkiss. E. D. Bell, S. P. Ellner, and B. Forrest. 2000. Blowflies as a case study in nonlinear population dynamics. Pages 137-172 in J. N. Perry, R. H. Smith. I. P. Woiwod, and D. Morse, editors. Chaos in real data: the analysis of non-linear dynamics from short ecological time series. Kluwer Academic, Dordrecht, The Netherlands. Stefanski, L. A., and J. R. Cook. 1995. Simulation-extrapolation: the measurement error jackknife. Journal of the American Statistical Association 90:1247-1 256. Stokes, T. K., W. S. C. Gurney, R. M. Nisbet. and S. P. Blythe. 1988. Parameter evolution in a laboratory insect population. Theoretical Population Biology 34:248-265. Tidd, C. W., L. F. Olsen, and W. M. Schaffer. 1993. The case for chaos in childhood epidemics. 11. Predicting historical epidemics from mathematical models. Proceedings of the Royal Society of London B 254:257-273. Tuljapurkar, S., and H. Caswell, editors. 1997. Structuredpopulation models in marine, terrestrial, and freshwater systems. Chapman and Hall, New York, New York, USA. Turchin. P., and S. P. Ellner. 2000tr. Modelling time-series data. Pages 33-48 in J. N. Perry, R. H. Smith, I. P. Woiwod, and D. Morse, editors. Chaos in real data: the analysis of non-linear dynamics from short ecological time series. Kluwer Academic, Dordrecht, The Netherlands. Turchin, P., and S. P Ellner. 2000b. Living on the edge of Caswell, editors. 1997. Structured-population models in chaos: population dynamics of Fennoscandian voles. Ecol- marine, terrestrial, and freshwater systems. Chapman and ogy 81:3099-3116. Hall, New York, New York, USA. Wahba, G. 1990. Spline models for observational data. So- Wood, S. N. 1999. Semi-parametric population models. Pages ciety for Industrial and Applied Mathematics, Philadelphia, 41-50 in Challenges in applied population biology. Aspects Pennsylvania, USA. of applied biology. Volume 53. Association of Applied Bi- Wood, S. N. 1994. Obtaining birth and mortality patterns ologists, Warwick, UK. Wood, S. N. 2001. Partially specified ecological models. Ecofrom structured population trajectories. Ecological Mono- logical Monographs 71: 1-25. graphs 64:23-44. Wood, S. N., and M. B. Thomas. 1999. Super sensitivity to Wood, S. N. 1997. Inverse problems and structured-popu- structure in biological models. Proceedings of the Royal lation dynamics. Pages 555-586 in S. Tuljapurkar and H. Society of London B 266:565-570.
Depositing User: Sara Taylor
Date Deposited: 08 Jun 2007
Last Modified: 28 Aug 2021 23:35


Downloads per month over past year

Repository Staff Only: item control page

View Item View Item

University of Huddersfield, Queensgate, Huddersfield, HD1 3DH Copyright and Disclaimer All rights reserved ©