1. Detecting Parameter Redundancy in Ecological State-Space Models Diana Cole and Rachel McCrea National Centre for Statistical Ecology, University of Kent

2. Lapwing Example

3. Symbolic Method for Detecting Parameter Redundancy

4. Parameter Redundancy in State-Space Models

5. Lapwing Example State-Space Model

6. Integrated Models

7. Lapwing Example State-Space Model Combined with Ring-Recovery Data

8. Extended Symbolic Method

9. Multi-Site Model McCrea et al (2010) consider a multi-site state-space model for great cormorants (Phalacrocorax carbo). Census data consisted of annual nest counts at 2 different sites (simplification of 3 sites). State-space model, where  1,k survival prob. of immature animals,  2,k survival prob. of breeders, ρ k productivity,  k prob. becoming a breeder and  kj transition prob. (site k). new born immature breeders 1 2 1 2 1 2

10. Multi-Site Model

11. Discussion Parameter redundancy of state-space models can be investigate by expanding the expectation of the observation process. It is not always necessary to combine state-space models with other types of data, even when not all states are observed. It is often possible to estimate more than expected. It is possible to investigate parameter redundancy in integrated models by combining exhaustive summaries for each data set. The reparameterisation theorem and extension theorem have been combined to create a simpler method to investigate parameter redundancy in integrated models.

12. References 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. Catchpole, E. A. and Morgan, B. J. T. (1997) Detecting parameter redundancy. Biometrika, 84, 187-196. Catchpole, E. A., Morgan, B. J. T and Freeman, S. N. (1998) Estimation in parameter redundant models. Biometrika, 85, 462-468. Cole, D. J., Morgan, B. J. T. and Titterington, D. M. (2010) Determining the parametric structure of models. Mathematical Biosciences, 228, 16-30. Cole, D. J. and McCrea, R. S. (2012) Parameter Redundancy in Discrete State-Space and Integrated Models. Cole, D.J., Morgan, B.J.T., Catchpole, E.A. and Hubbard, B. A. (2012) Parameter Redundancy in Mark-Recovery Models. Biometrical Journal, 54, 507-523. McCrea, R. S., Morgan, B. J. T., Gimenez, O, Besbeas, P., Lebreton, J. D., Bregnballe, T. (2010) Multi-Site Integrated Population Modelling. JABES, 15, 539-561.