Abstract
Misidentification of animals is a common problem for many capture-recapture experiments. Considerably misleading inference may be obtained when traditional models are used for capture-recapture data with misidentification. In this paper, we investigate the so-called band-read error model for modeling misidentification, assuming that it is possible to identify one marked individual as another on each capture occasion. Currently, fitting this model relies primarily on a Bayesian Markov chain Monte Carlo approach, while maximum likelihood is difficult because there is not a computationally efficient likelihood function available. The Bayesian method is exact but requires considerable computation time. We propose an approximate model for modeling misidentification and then develop a fast maximum-likelihood approach for the approximate model using likelihood constructed by the saddlepoint approximation method. We demonstrate the promising performance of our proposed method by simulation and by comparisons with the Bayesian inference under the original model. We apply the method to analyze capture-recapture data from a population of Northern Dusky Salamanders (Desmognathus fuscus) collected in North Carolina, USA.
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Data Availibility
The salamanders data and the R code used in the manuscript are available on the first author’s GitHub (https://github.com/wzhang721).
References
Bailey LL (2004) Evaluating elastomer marking and photo identification methods for terrestrial salamanders: marking effects and observer bias. Herpetological Review 35:38–41
Bailey LL, Simons TR, Pollock KH (2004) Estimating detection probability parameters for Plethodon salamanders using the robust capture-recapture design. Journal of Wildlife Management 68:1–13
Barndorff-Nielsen OE, Cox DR (1989) Asymptotic techniques for use in statistics. Chapman and Hall, London
Bonner SJ, Schofield MR, Noren P, Price SJ (2016) Extending the latent multinomial model with complex error processes and dynamic Markov bases. The Annals of Applied Statistics 10:246–263
Butler RW (2007) Saddlepoint approximations with applications. Cambridge University Press, Cambridge
Cormack RM (1964) Estimates of survival from the sighting of marked animals. Biometrika 51:429–438
Curtis JMR (2006) Visible implant elastomer color determination, tag visibility, and tag loss: potential sources of error for mark-recapture studies. North American Journal of Fisheries Management 26:327–337
Daniels HE (1954) Saddlepoint approximations in statistics. The Annals of Mathematical Statistics 25:631–650
Davison AC, Hinkley DV (1997) Bootstrap methods and their application. Cambridge University Press, Cambridge
Goodman J (2020) Asymptotic accuracy of the saddlepoint approximation for maximum likelihood estimation. arXiv preprint arXiv:200511028
Grant EHC (2008) Visual implant elastomer mark retention through metamorphosis in amphibian larvae. Journal of Wildlife Management 72:1247–1252
Heemeyer JL, Homyack JA, Haas CA (2007) Retention and readability of visible implant elastomer marks in Eastern Red-backed Salamanders (Plethodon cinereus). Herpetological Review 38:425–428
Jolly GM (1965) Explicit estimates from capture-recapture data with both death and immigration-stochastic model. Biometrika 52:225–247
Kristensen K, Nielsen A, Berg CW, Skaug HJ, Bell BM (2016) TMB: Automatic differentiation and Laplace approximation. Journal of Statistical Software 70:1–21
Link WA, Yoshizaki J, Bailey LL, Pollock KH (2010) Uncovering a latent multinomial: Analysis of mark-recapture data with misidentification. Biometrics 66:178–185
Lugannani R, Rice S (1980) Saddlepoint approximation for the distribution of the sum of independent random variables. Advances in Applied Probability 12:475–490
Marold MR (2001) Evaluating visual implant elastomer polymer for marking small, stream-dwelling salamanders. Herpetological Review 32:91–92
Morrison TA, Yoshizaki J, Nichols JD, Bolger DT (2011) Estimating survival in photographic capture-recapture studies: Overcoming misidentification error. Methods in Ecology and Evolution 2:454–463
Otis DL, Burnham KP, White GC, Anderson DR (1978) Statistical inference from capture data on closed animal populations. Wildlife Monographs 62:3–135
Price SJ, Browne RA, Dorcas ME (2012) Resistance and resilience of a stream salamander to supraseasonal drought. Herpetologica 68:312–323
Schofield MR, Bonner SJ (2015) Connecting the latent multinomial. Biometrics 71:1070–1080
Seber GAF (1965) A note on the multiple-recapture census. Biometrika 52:249–259
Vale RTR, Fewster RM, Carroll EL, Patenaude NJ (2014) Maximum likelihood estimation for model \({M}_{t, \alpha }\) for capture-recapture data with misidentification. Biometrics 70:962–971
White GC, Burnham KP (1999) Program MARK: survival estimation from populations of marked animals. Bird Study 46:S120–S139
Wright JA, Barker RJ, Schofield MR, Frantz AC, Byrom AE, Gleeson DM (2009) Incorporating genotype uncertainty into mark-recapture-type models for estimating abundance using DNA samples. Biometrics 65:833–840
Yoshizaki J (2007) Use of natural tags in closed population capture-recapture studies: Modeling misidentification. PhD thesis, North Carolina State University
Zhang W, Bravington MV, Fewster RM (2019) Fast likelihood-based inference for latent count models using the saddlepoint approximation. Biometrics 75:723–733
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WZ and SJB conceived the ideas and designed methodology; SJP collected the data; WZ, SJP and SJB analyzed the data; WZ led the writing of the manuscript. All authors contributed critically to the drafts and gave final approval for publication.
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The authors declare that they have no conflict of interest.
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Communicated by Pierre Dutilleul.
This work was funded by the Natural Sciences and Engineering Research Council of Canada (Grant Number 43024-2016)
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Zhang, W., Price, S.J. & Bonner, S.J. Maximum likelihood inference for the band-read error model for capture-recapture data with misidentification. Environ Ecol Stat 28, 405–422 (2021). https://doi.org/10.1007/s10651-021-00492-6
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DOI: https://doi.org/10.1007/s10651-021-00492-6