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Joint Modeling of Distances and Times in Point-Count Surveys

Author

Listed:
  • Adam Martin-Schwarze

    (University of Michigan)

  • Jarad Niemi

    (Iowa State University)

  • Philip Dixon

    (Iowa State University)

Abstract

Removal and distance modeling are two common methods to adjust counts for imperfect detection in point-count surveys. Several recent articles have formulated models to combine them into a distance-removal framework. We observe that these models fall into two groups building from different assumptions about the joint distribution of observed distances and first times to detection. One approach assumes the joint distribution results from a Poisson process (PP). The other assumes an independent joint (IJ) distribution with its joint density being the product of its marginal densities. We compose an IJ+PP model that more flexibly models the joint distribution and accommodates both existing approaches as special cases. The IJ+PP model matches the bias and coverage of the true model for data simulated from either PP or IJ models. In contrast, PP models underestimate abundance from IJ simulations, while IJ models overestimate abundance from PP simulations. We apply all three models to surveys of golden-crowned sparrows in Alaska. Only the IJ+PP model reasonably fits the joint distribution of observed distances and first times to detection. Model choice affects estimates of abundance and detection but has little impact on the magnitude of estimated covariate effects on availability and perceptibility. Supplementary materials accompanying this paper appear online.

Suggested Citation

  • Adam Martin-Schwarze & Jarad Niemi & Philip Dixon, 2021. "Joint Modeling of Distances and Times in Point-Count Surveys," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(2), pages 289-305, June.
    • Handle: RePEc:spr:jagbes:v:26:y:2021:i:2:d:10.1007_s13253-021-00437-3
    DOI: 10.1007/s13253-021-00437-3
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    References listed on IDEAS

    as
    1. D. L. Borchers & W. Zucchini & M. P. Heide-Jørgensen & A. Cañadas & R. Langrock, 2013. "Using Hidden Markov Models to Deal with Availability Bias on Line Transect Surveys," Biometrics, The International Biometric Society, vol. 69(3), pages 703-713, September.
    2. Richard J. Barker & Matthew R. Schofield & William A. Link & John R. Sauer, 2018. "On the reliability of N†mixture models for count data," Biometrics, The International Biometric Society, vol. 74(1), pages 369-377, March.
    3. Robert M. Dorazio & J. Andrew Royle, 2003. "Mixture Models for Estimating the Size of a Closed Population When Capture Rates Vary among Individuals," Biometrics, The International Biometric Society, vol. 59(2), pages 351-364, June.
    4. J. Andrew Royle, 2004. "N-Mixture Models for Estimating Population Size from Spatially Replicated Counts," Biometrics, The International Biometric Society, vol. 60(1), pages 108-115, March.
    5. Shirley Pledger, 2000. "Unified Maximum Likelihood Estimates for Closed Capture–Recapture Models Using Mixtures," Biometrics, The International Biometric Society, vol. 56(2), pages 434-442, June.
    6. David Louis Borchers & Martin James Cox, 2017. "Distance sampling detection functions: 2D or not 2D?," Biometrics, The International Biometric Society, vol. 73(2), pages 593-602, June.
    7. repec:bla:biomet:v:71:y:2015:i:4:p:1060-1069 is not listed on IDEAS
    8. Adam Martin-Schwarze & Jarad Niemi & Philip Dixon, 2017. "Assessing the Impacts of Time-to-Detection Distribution Assumptions on Detection Probability Estimation," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(4), pages 465-480, December.
    9. Duarte, Adam & Adams, Michael J. & Peterson, James T., 2018. "Fitting N-mixture models to count data with unmodeled heterogeneity: Bias, diagnostics, and alternative approaches," Ecological Modelling, Elsevier, vol. 374(C), pages 51-59.
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