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Abstract

We demonstrate the potential of conditionally Gaussian state-space models in integrated population modeling, when certain model parameters may be functions of previous observations. The approach is applied to a heron census, and the data are best described by a model with three population-size thresholds which determine the population productivity. The model provides an explanation of how the population rebounds rapidly after major falls in size, which are characteristic of the data. By contrast, a simple logarithmic regression of productivity on population size was not significant. The results are of ecological interest, and suggest hypotheses for further investigation. Supplementary figures are available online.

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References

  • Abadi, F., Gimenez, O., Arlettaz, R., and Schaub, M. (2012), “Estimating the Strength of Density-Dependence in the Presence of Observation Errors Using Integrated Population Models”, submitted for publication.

  • Besbeas, P., and Morgan, B. J. T. (2012), “Kalman Filter Initialization for Integrated Population Modelling”, to appear in Applied Statistics.

  • Besbeas, P., Freeman, S. N., Morgan, B. J. T., and Catchpole, E. A. (2002), “Integrating Mark-Recapture-Recovery and Census Data to Estimate Animal Abundance and Demographic Parameters,” Biometrics, 58, 540–547.

    Article  MathSciNet  MATH  Google Scholar 

  • Besbeas, P., Lebreton, J.-D., and Morgan, B. J. T. (2003), “The Efficient Integration of Abundance and Demographic Data,” Applied Statistics, 52, 95–102.

    Article  MathSciNet  MATH  Google Scholar 

  • Besbeas, P., Freeman, S. N., and Morgan, B. J. T. (2005), “The Potential of Integrated Population Modelling,” Australian & New Zealand Journal of Statistics, 47, 35–48.

    Article  MathSciNet  MATH  Google Scholar 

  • Besbeas, P., Borysiewicz, R., and Morgan, B. J. T. (2009), “Completing the Ecological Jigsaw,” in Modelling Demographic Processes in Marked Populations. Environmental and Ecological Statistics Series, Vol. 3, eds. D. L. Thomson, E. G. Cooch, and M. J. Conroy, pp. 515–542.

    Google Scholar 

  • Breslow, N. (1974), “Covariance Analysis of Censored Survival Data,” Biometrics, 30, 89–99.

    Article  Google Scholar 

  • Brooks, S. P., King, R., and Morgan, B. J. T. (2004), “A Bayesian Approach to Combining Animal Abundance and Demographic Data,” Animal Biodiversity and Conservation, 27, 515–529.

    Google Scholar 

  • Buckland, S. T., Newman, K. B., Thomas, L., and Koesters, N. B. (2004), “State-Space Models for the Dynamics of Wild Animal Populations,” Ecological Modelling, 171, 157–175.

    Article  Google Scholar 

  • Crick, H. Q. P. (2004), “The Impact of Climate Change on Birds,” Ibis, 146 (Suppl. 1), 48–56.

    Article  Google Scholar 

  • Dennis, B., Ponciano, J. M., Lele, S. R., Taper, M. L., and Staples, D. F. (2006), “Estimating Density Dependence, Process Noise, and Observation Error,” Ecological Monographs, 76, 323–341.

    Article  Google Scholar 

  • de Valpine, P. (2002), “Review of Methods for Fitting Time-Series Models With Process and Observation Error and Likelihood Calculations for Nonlinear, Non-Gaussian State-Space Models,” Bulletin of Marine Science, 70, 455–471.

    Google Scholar 

  • de Valpine, P., and Hastings, A. (2002), “Fitting Population Models Incorporating Process Noise and Observation Error,” Ecological Monographs, 72, 57–76.

    Article  Google Scholar 

  • de Valpine, P., and Hilborn, R. (2005), “State-Space Likelihoods for Nonlinear Fisheries Time-Series,” Canadian Journal of Fisheries and Aquatic Sciences, 62, 1937–1952.

    Article  Google Scholar 

  • Ennola, K., Sarvala, J., and Devai, G. (1998), “Modelling Zooplankton Population Dynamics With the Extended Kalman Filtering Technique,” Ecological Modelling, 110, 135–149.

    Article  Google Scholar 

  • Freckleton, R. P., Watkinson, A. R., Green, R. E., and Sutherland, W. J. (2006), “Census Error and the Detection of Density Dependence,” Journal of Animal Ecology, 75, 837–851.

    Article  Google Scholar 

  • Freeman, S. N., and Morgan, B. J. T. (1992), “A Modelling Strategy for Recovery Data From Birds Ringed as Nestlings,” Biometrics, 48, 217–236.

    Article  Google Scholar 

  • Gimenez, O., Barbraud, C., Crainiceanu, C., Jenouvrier, S., and Morgan, B. J. T. (2006), “Semiparametric Regression in Capture-Recapture Modelling,” Biometrics, 62, 691–698.

    Article  MathSciNet  MATH  Google Scholar 

  • Grenfell, B. T., Wilson, K., Finkenstädt, B. F., Coulson, T. N., Murray, S., Albon, S. D., Pemberton, J. M., Clutton-Brock, T. H., and Crawley, M. J. (1998), “Noise and Determinism in Synchronised Sheep Dynamics,” Nature, 394, 675–677.

    Article  Google Scholar 

  • Grosbois, V., Harris, M. P., Anker-Nilssen, T., McCleery, R. H., Shaw, D. N., Morgan, B. J. T., and Gimenez, O. (2009), “Survival at Multi-Population Scales Using Mark-Recapture Data,” Ecology, 90, 2922–2932.

    Article  Google Scholar 

  • Harvey, A. C. (1989), Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge: Cambridge University Press.

    Google Scholar 

  • Kitagawa, G. (1987), “Non-Gaussian State-Space Modeling of Nonstationary Time Series,” Journal of the American Statistical Association, 82, 1032–1063.

    Article  MathSciNet  MATH  Google Scholar 

  • Knape, J. (2008), “Estimability of Density Dependence in Models of Time Series Data,” Ecology, 89, 2994–3000.

    Article  Google Scholar 

  • Marchant, J. H., Freeman, S. N., Crick, H. P. Q., and Beaven, L. P. (2004), “The BTO Heronries Census of England and Wales 1928–2000: New Indices and a Comparison of Analytical Methods,” Ibis, 146, 323–334.

    Article  Google Scholar 

  • Meyer, R., and Millar, R. B. (1999), “BUGS in Bayesian Stock Assessments,” Canadian Journal of Fisheries and Aquatic Sciences, 56, 1078–1086.

    Google Scholar 

  • Millar, R. B., and Meyer, R. (2000), “Non-Linear State Space Modelling of Fisheries Biomass Dynamics by Using Metropolis–Hastings Within-Gibbs Sampling,” Applied Statistics, 49, 327–342.

    Article  MathSciNet  MATH  Google Scholar 

  • North, P. M., and Morgan, B. J. T. (1979), “Modelling Heron Survival Using Weather Data,” Biometrics, 35, 667–682.

    Article  MathSciNet  Google Scholar 

  • Schnute, J. (1994), “A General Framework for Developing Sequential Fisheries Models,” Canadian Journal of Fisheries and Aquatic Sciences, 51, 1676–1688.

    Article  Google Scholar 

  • Stenseth, N. C., Chan, K.-S., Tavecchia, G., Coulson, T., Mysterud, A., Clutton-Brock, T., and Grenfell, B. (2004), “Modelling Non-Additive and Nonlinear Signals From Climatic Noise in Ecological Time Series: Soay Sheep as an Example,” Proceedings of the Royal Society of London. Series B, 271, 1985–1993.

    Article  Google Scholar 

  • Tavecchia, G., Besbeas, P., Coulson, T., Morgan, B. J. T., and Clutton-Brock, T. H. (2009), “Estimating Population Size and Hidden Demographic Parameters With State-Space Modelling,” The American Naturalist, 173, 722–733.

    Article  Google Scholar 

  • Thomas, L., Buckland, S. T., Newman, K. B., and Harwood, J. (2004), “A Unified Framework for Modelling Wildlife Population Dynamics,” Australian & New Zealand Journal of Statistics, 47, 19–34.

    MathSciNet  Google Scholar 

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Correspondence to Byron J. T. Morgan.

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Besbeas, P., Morgan, B.J.T. A Threshold Model for Heron Productivity. JABES 17, 128–141 (2012). https://doi.org/10.1007/s13253-011-0080-8

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  • DOI: https://doi.org/10.1007/s13253-011-0080-8

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