Abstract
We present a novel, non-parametric, frequentist approach for capture-recapture data based on a ratio estimator, which offers several advantages. First, as a non-parametric model, it does not require a known underlying distribution for parameters nor the associated assumptions, eliminating the need for post-hoc corrections or additional modeling to account for heterogeneity and other violated assumptions. Second, the model explicitly deals with dependence of trials by considering trials to be dependent; therefore, cluster sampling is handled naturally and additional adjustments are not necessary. Third, it accounts for ordering, utilizing the fact that a system with a small population will have a greater frequency of recaptures “early” in the survey work compared to an identical system with a larger population. We provide mathematical proof that our estimator attains asymptotic minimum variance under open systems. We apply the model to a data set of bottlenose dolphins (Tursiops truncatus) and compare results to those from classic closed models. We show that the model has an impressive rate of convergence and demonstrate that there’s an inverse relationship between population size and the proportion of the population that need to be sampled, while achieving the same degree of accuracy for abundance estimates. The model is flexible and can apply to ecological situations as well as other situations that lend themselves to capture recapture sampling.
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Acknowledgments
The authors would also like to thank reviewers Dr. Paul Wiegand, Dr. Nizam Uddin, Dr. Peter Kincaid (University of Central Florida) and Dr. Sat Gupta and Dr. Jan Rychtář (University of North Carolina at Greensboro) for providing invaluable insights and suggestions that led to a polished and improved manuscript. We are very grateful for their contributions. We are indebted to Dr. Mark Johnson (University of Central Florida) for providing the closed system problem. We are grateful to Dr. Jim Norris (Wake Forest University) for being a great sounding board in the formative stages of the paper. The authors are grateful to an anonymous scholar for very insightful modeling and statistical expertise.
Funding Computational resources were provided by the Advanced Research Computing Center at the University of Central Florida.
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Handling Editor: Bryan F. J. Manly.
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SUPPLEMENTARY MATERIALS Appendices A - E, referenced in Section 3, Appendix F, in Section 4, and appendix G in section 5, are available with this paper at the Biometrics website on Wiley Online Library. 389KB doc
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Rehman, Z., Toms, C.N. & Finch, C. Estimating abundance: a non parametric mark recapture approach for open and closed systems. Environ Ecol Stat 23, 623–638 (2016). https://doi.org/10.1007/s10651-016-0357-8
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DOI: https://doi.org/10.1007/s10651-016-0357-8