Advertisement

Journal of Ornithology

, Volume 152, Supplement 2, pp 305–315 | Cite as

Determining parameter redundancy of multi-state mark–recapture models for sea birds

  • Diana J. Cole
EURING Proceedings

Abstract

Multi-state mark–recapture models are structurally complex models, and in particular the complexity increases when there are unobservable states. Until recently, determining whether or not such models were parameter redundant was only possible numerically. In this paper, we show how it now possible to examine parameter redundancy of such models symbolically. The advantage of this approach is that you can determine exactly how many parameters can be estimated in a model for any number of years of marking and recovery, as well as which combinations of parameters can be estimated. Here, we illustrate how the new methodology works for multi-state models. We further develop rules for determining the parameter redundancy status of a whole family of multi-state mark–recapture models.

Keywords

Derivative matrix Ecology Exhaustive summaries Identifiability Maple 

Notes

Acknowledgments

Thanks to Byron Morgan, the session chair and two referees for their comments on this paper, and to Christine Hunter for her description of multi-state mark–recapture models for seabird populations.

Supplementary material

10336_2010_574_MOESM1_ESM.pdf (149 kb)
Supplementary material 1 (PDF 149 kb)

References

  1. Catchpole EA, Morgan BJT (1997) Detecting parameter redundancy. Biometrika 84:187–196CrossRefGoogle Scholar
  2. Catchpole EA, Morgan BJT, Freeman SN (1998) Estimation in parameter redundant models. Biometrika 85:462–468CrossRefGoogle Scholar
  3. Catchpole EA, Kgosi PM, Morgan BJT (2001) On the near singularity of models for animal recovery data. Biometrics 57:720–726PubMedCrossRefGoogle Scholar
  4. Choquet R, Rouan L, Pradel R (2009) Program E-SURGE: a software application for fitting Multievent models. In: Thomson DL, Cooch EG, Conroy MJ (eds) Environmental and ecological statistics series, vol 3. Springer, Berlin, pp 845–865Google Scholar
  5. Clobert J, Lebreton JD, Allaine D, Gaillard JM (1994) The estimation of age-specific breeding probabilities from recaptures or resightings in vertebrate populations: II. Longitudinal models. Biometrics 50:375–387PubMedCrossRefGoogle Scholar
  6. Cole DJ, Morgan BJT (2010a) A note on determining parameter redundancy in age-dependent tag return models for estimating fishing mortality, natural mortality and selectivity. J Agric Biol Environ Stat. doi: 10.1007/s13253-010-0026-6
  7. Cole DJ, Morgan BJT (2010b) Detecting parameter redundancy in covariate models. Biometrika. doi: 10.1093/biomet/asq041
  8. Cole DJ, Morgan BJT, Titterington DM (2010) Determining the parametric structure of non-linear models. Math Biosci (in press)Google Scholar
  9. Corless RM, Jeffrey DJ (1997) The turing factorization of a rectangular matrix. Sigsam Bull 31:20–28CrossRefGoogle Scholar
  10. Cormack RM (1964) Estimates of survival from the sightings of marked animals. Biometrika 51:429–438Google Scholar
  11. Gimenez O, Choquet R, Lebreton J (2003) Parameter redundancy in multistate capture–recapture models. Biom J 45:704–722CrossRefGoogle Scholar
  12. Gimenez O, Viallefont A, Choquet R, Catchpole EA, Morgan BJT (2004) Methods for investigating parameter redundancy. Anim Biodivers Conserv 27:561–572Google Scholar
  13. Hunter CM, Caswell H (2009) Rank and redundancy of multi-state mark-recapture models for seabird populations with unobservable states. In: Thomson DL, Cooch EG, Conroy MJ (eds) Environmental and ecological statistics series: vol 3. Springer, Berlin, pp 797–826Google Scholar
  14. Jiang H, Pollock KH, Brownie C, Hightower JE, Hoenig JM and Hearn WS (2007) Age-dependent tag return models for estimating fishing mortality, natural mortality and selectivity. J Agric Biol Environ Stat 12:177–194CrossRefGoogle Scholar
  15. Jolly GM (1965) Explicit estimates from capture–recapture data with both death and immigration. Biometrika 52:225–247PubMedGoogle Scholar
  16. Mackenzie DI, Nichols JD, Seamans ME, and Gutierrez RJ (2009) Modeling species occurrence dynamics with multiple states and imperfect detection. Ecology 90:823–835PubMedCrossRefGoogle Scholar
  17. Pledger S, Efford M, Pollock K, Collazo J, Lyons J (2009) Stopover duration analysis with departure probability dependent on unknown time since arrival. In: Thomson DL, Cooch EG and Conroy MJ (eds) Ecological and environmental statistics series, vol 3. Springer, Berlin, pp 349–363Google Scholar
  18. Rouan L, Choquet R, Pradel R (2009) A general framework for modeling memory in capture–recapture data. J Agric Biol Environ Stat 14:338–355CrossRefGoogle Scholar
  19. Seber GAF (1965) A note on the multiple recapture census. Biometrika 52:249–259PubMedGoogle Scholar
  20. Viallefont A, Lebreton JD, Reboulet AM, Gory G (1998) Parameter identifiability and model selection in capture–recapture models: a numerical approach. Biom J 40:1–13CrossRefGoogle Scholar

Copyright information

© Dt. Ornithologen-Gesellschaft e.V. 2010

Authors and Affiliations

  1. 1.School of Mathematics, Statistics and Actuarial ScienceUniversity of KentCanterburyUK

Personalised recommendations