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

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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.

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References

  • Catchpole EA, Morgan BJT (1997) Detecting parameter redundancy. Biometrika 84:187–196

    Article  Google Scholar 

  • Catchpole EA, Morgan BJT, Freeman SN (1998) Estimation in parameter redundant models. Biometrika 85:462–468

    Article  Google Scholar 

  • Catchpole EA, Kgosi PM, Morgan BJT (2001) On the near singularity of models for animal recovery data. Biometrics 57:720–726

    Article  CAS  Google Scholar 

  • 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 845–865

  • 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 50:375–387

    Article  CAS  Google Scholar 

  • 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:https://doi.org/10.1007/s13253-010-0026-6

  • Cole DJ, Morgan BJT (2010b) Detecting parameter redundancy in covariate models. Biometrika. doi:https://doi.org/10.1093/biomet/asq041

  • Cole DJ, Morgan BJT, Titterington DM (2010) Determining the parametric structure of non-linear models. Math Biosci (in press)

  • Corless RM, Jeffrey DJ (1997) The turing factorization of a rectangular matrix. Sigsam Bull 31:20–28

    Article  Google Scholar 

  • Cormack RM (1964) Estimates of survival from the sightings of marked animals. Biometrika 51:429–438

    Article  Google Scholar 

  • Gimenez O, Choquet R, Lebreton J (2003) Parameter redundancy in multistate capture–recapture models. Biom J 45:704–722

    Article  Google Scholar 

  • Gimenez O, Viallefont A, Choquet R, Catchpole EA, Morgan BJT (2004) Methods for investigating parameter redundancy. Anim Biodivers Conserv 27:561–572

    Google Scholar 

  • 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 797–826

  • 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 12:177–194

    Article  Google Scholar 

  • Jolly GM (1965) Explicit estimates from capture–recapture data with both death and immigration. Biometrika 52:225–247

    Article  CAS  Google Scholar 

  • Mackenzie DI, Nichols JD, Seamans ME, and Gutierrez RJ (2009) Modeling species occurrence dynamics with multiple states and imperfect detection. Ecology 90:823–835

    Article  Google Scholar 

  • 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 349–363

  • Rouan L, Choquet R, Pradel R (2009) A general framework for modeling memory in capture–recapture data. J Agric Biol Environ Stat 14:338–355

    Article  Google Scholar 

  • Seber GAF (1965) A note on the multiple recapture census. Biometrika 52:249–259

    Article  CAS  Google Scholar 

  • Viallefont A, Lebreton JD, Reboulet AM, Gory G (1998) Parameter identifiability and model selection in capture–recapture models: a numerical approach. Biom J 40:1–13

    Article  Google Scholar 

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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.

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Correspondence to Diana J. Cole.

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Communicated by M. Schaub.

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Cole, D.J. Determining parameter redundancy of multi-state mark–recapture models for sea birds. J Ornithol 152 (Suppl 2), 305–315 (2012). https://doi.org/10.1007/s10336-010-0574-0

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  • DOI: https://doi.org/10.1007/s10336-010-0574-0

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