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Completing the Ecological Jigsaw

  • Panagiotis Besbeas
  • Rachel S. Borysiewicz
  • Bryon J.T. Morgan
Chapter
Part of the Environmental and Ecological Statistics book series (ENES, volume 3)

Abstract

A challenge for integrated population methods is to examine the extent to which different surveys that measure different demographic features for a given species are compatible. Do the different pieces of the jigsaw fit together? One convenient way of proceeding is to generate a likelihood for census data using the Kalman filter, which is then suitably combined with other likelihoods that might arise from independent studies of mortality, fecundity, and so forth. The combined likelihood may then be used for inference. Typically the underlying model for the census data is a state-space model, and capture–recapture methods of various kinds are used to construct the additional likelihoods. In this paper we provide a brief review of the approach; we present a new way to start the Kalman filter, designed specifically for ecological processes; we investigate the effect of break-down of the independence assumption; we show how the Kalman filter may be used to incorporate density-dependence, and we consider the effect of introducing heterogeneity in the state-space model.

Key Words

Abundance data Diffuse initialization Exact initial Kalman filter Grey heron Grey seals Heterogeneity Initialisation of the Kalman filter Integrated analysis Joint likelihood Lack of independence Mark-recapture-recovery data Maximum likelihood Stable age distribution State-space model 

References

  1. Baillie SR, Green RE (1987) The importance of variation in recovery rates when estimating survival rates from ringing recoveries. Acta Ornithol. 23:41–60.Google Scholar
  2. Barker RJ, Kavalieris L (2001) Efficiency gain from auxiliary data requiring additional nuisance parameters. Biometrics 57:563–566.CrossRefzbMATHMathSciNetGoogle Scholar
  3. Barry SC, Brooks SP, Catchpole EA, Morgan BJT (2003) The analysis of ring-recovery data using random effects. Biometrics 59:54–65.CrossRefzbMATHMathSciNetGoogle Scholar
  4. Besbeas P, Freeman SN, Morgan BJT (2005) The potential of integrated population modelling. Aust. N. Z. J. Stat. 47:35–48.CrossRefzbMATHMathSciNetGoogle Scholar
  5. Besbeas P, Freeman SN, Morgan BJT, Catchpole EA (2002) Integrating mark-recapture-recovery and census data to estimate animal abundance and demographic parameters. Biometrics 58:540–547.CrossRefzbMATHMathSciNetGoogle Scholar
  6. Besbeas P, Lebreton J-D, Morgan BJT (2003) The efficient integration of abundance and demographic data. Appl. Stat. 52:95–102.zbMATHMathSciNetGoogle Scholar
  7. Besbeas P, Morgan BJT (2006) Kalman filter initialization for modelling population dynamics. Submitted for publication.Google Scholar
  8. Brooks SP, King R, Morgan BJT (2004) A Bayesian approach to combining animal abundance and demographic data. Anim, Biodivers. Conserv. 27:515–529.Google Scholar
  9. Burnham KP, Rexstad EA (1993) Modeling heterogeneity in survival rates of banded waterfowl. Biometrics 49:1194–1208.CrossRefzbMATHGoogle Scholar
  10. Caswell H (2001) Matrix population models: construction, analysis, and interpretation. 2nd edition. Sinauer Association, Sunderland, MA.Google Scholar
  11. Chen G (Ed.) (1993) Approximate Kalman filtering. World Scientific Publishers, Singapore.Google Scholar
  12. Clark JS, Ferraz G, Oguge N, Hays H, Di Costanzo J (2005) Hierarchical Bayes for structured, variable populations: from recapture data to life-history prediction. Ecology 86:2232–2244.CrossRefGoogle Scholar
  13. Crowder MJ (1978) Beta-binomial ANOVA for proportions. Appl. Stat. 27:34–37.CrossRefGoogle Scholar
  14. de Jong P (1991) The diffuse Kalman filter. Ann. Statist. 19:1073–1083.CrossRefzbMATHMathSciNetGoogle Scholar
  15. Dennis B, Ponciano JM, Lele SR, Taper ML, Staples DF (2006) Estimating density dependence, process noise, and observation error. Ecol. Monogr. 76:323–341.CrossRefGoogle Scholar
  16. 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. Bull. Mar. Sci. 70:455–471.Google Scholar
  17. de Valpine P (2003) Better inferences from population-dynamics experiments using Monte Carlo state-space likelihood methods. Ecology 84:3064–3077.CrossRefGoogle Scholar
  18. de Valpine P (2004) Monte Carlo state-space likelihoods by weighted posterior kernel density estimation. J. Am. Stat. Assoc. 99:523–534.CrossRefzbMATHGoogle Scholar
  19. de Valpine P, Hastings A (2003) Fitting population models incorporating process noise and observation error. Ecol. Monogr. 72:57–76.CrossRefGoogle Scholar
  20. de Valpine P, Hilborn R (2005) State-space likelihoods for nonlinear fisheries time-series. Can. J. Fish. Aquat. Sci. 62:1937–1952.CrossRefGoogle Scholar
  21. Durbin J, Koopman SJ (2001) Time series analysis by state space methods. Oxford University Press, Oxford.zbMATHGoogle Scholar
  22. Freeman SN, Morgan BJT (1992) A modelling strategy for recovery data from birds ringed as nestlings. Biometrics 48:217–236.CrossRefGoogle Scholar
  23. Gauthier G, Besbeas P, Lebreton J-D, Morgan BJT (2007) Population growth in Greater Snow Geese: a modelling approach integrating demographic and population survey information. Ecology 88(6):1420–1429.Google Scholar
  24. Gomez V, Maravall A (1993) Initializing the Kalman filter with incompletely specified initial conditions. pp 39–63 In Approximate Kalman filtering. Chen G. (Ed.). World Scientific Publishers, Singapore.CrossRefGoogle Scholar
  25. Hall AJ, McConnell BJ, Barker RJ (2001) Factors affecting first-year survival in grey seals and their implications for life history strategy. J. Anim. Ecol. 70:138–149.CrossRefGoogle Scholar
  26. Harvey AC (1989) Forecasting, structural time series models and the Kalman filter. Cambridge University Press, Cambridge.Google Scholar
  27. Harvey AC, Phillips GDA (1979) Maximum-likelihood estimation of regression models with autoregressive-moving average disturbances. Biometrika 66:49–58.zbMATHMathSciNetGoogle Scholar
  28. Koopman SJ, Durbin J (2003) Filtering and smoothing of state vector for diffuse state-space models. J. Time Ser. Anal. 24:85–98.CrossRefzbMATHMathSciNetGoogle Scholar
  29. Meinhold RJ, Singpurwalla ND (1983) Understanding the Kalman filter. Am Statist. 37:123–127.Google Scholar
  30. Meyer R, Millar RB (1999) BUGS in Bayesian stock assessments. Can. J. Fish Aquat. Sci. 56:1078–1086.CrossRefGoogle Scholar
  31. Millar RB, Meyer R (2000a) Bayesian state-space modeling of age-structured data: fitting a model is just the beginning. Can J. Fish. Aquat. Sci. 57:43–50.CrossRefGoogle Scholar
  32. Millar RB, Meyer R (2000b) Non-linear state space modelling of fisheries biomass dynamics by using Metropolis-Hastings within-Gibb sampling. Appl. Stat. 49:327–342.zbMATHMathSciNetGoogle Scholar
  33. Morgan BJT, Freeman SN (1989) A model with first-year variation for ring-recovery data. Biometrics 45:1087–1102.CrossRefzbMATHGoogle Scholar
  34. North PM, Morgan BJT (1979) Modelling heron survival using weather data. Biometrics 35: 667–682.CrossRefMathSciNetGoogle Scholar
  35. Pollock KH, Raveling DG (1982) Assumptions of modern band-recovery models, with emphasis on heterogeneous survival rates. J. Wild. Man. 46:88–98.CrossRefGoogle Scholar
  36. Sullivan PJ (1992) A Kalman filter approach to catch-at-length analysis. Biometrics 48:237–258.CrossRefzbMATHGoogle Scholar
  37. Tavecchia G, Besbeas P, Coulson T, Morgan BJT, Clutton-Brock TH (2007) Estimating population size and hidden demographic parameters with state-space modelling. Submitted for publication.Google Scholar
  38. Webster R, Heuvelink GBM, (2006) The Kalman filter for the pedologist’s tool kit. Eur. J. Soil Sci. 57:758–773.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Panagiotis Besbeas
    • 1
  • Rachel S. Borysiewicz
  • Bryon J.T. Morgan
  1. 1.Institute of Mathematics, Statistics and Actuarial ScienceUniversity of KentCanterburyEngland

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