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Faster Asymptotic Solutions for N-Mixtures on Large Populations

Author

Listed:
  • M. R. P. Parker

    (Simon Fraser University)

  • J. Cao

    (Simon Fraser University)

  • L. L. E. Cowen

    (University of Victoria)

  • L. T. Elliott

    (Simon Fraser University)

Abstract

We derive an asymptotic likelihood function for open-population N-mixture models and show that it has favorable computational complexity and accuracy when compared to the traditional likelihood function for large population sizes. We validate our asymptotic model with simulation studies and apply our model to estimate the population size of Ancient Murrelet chicks, comparing against results obtained using the traditional N-mixture likelihood and an alternative asymptotic model based on the multivariate normal distribution. For the Ancient Murrelet case study, our asymptotic model computes twice as fast as the traditional models, eleven times faster when parallel processing is used, and provides higher-precision estimates than the asymptotic multivariate normal model. We provide an open-source implementation of our methods in the quickNmix R package.Supplementary material to this paper is provided online.

Suggested Citation

  • M. R. P. Parker & J. Cao & L. L. E. Cowen & L. T. Elliott, 2025. "Faster Asymptotic Solutions for N-Mixtures on Large Populations," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 30(3), pages 730-745, September.
    • Handle: RePEc:spr:jagbes:v:30:y:2025:i:3:d:10.1007_s13253-024-00618-w
    DOI: 10.1007/s13253-024-00618-w
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    References listed on IDEAS

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    1. Matthew R. P. Parker & Laura L. E. Cowen & Jiguo Cao & Lloyd T. Elliott, 2023. "Computational Efficiency and Precision for Replicated-Count and Batch-Marked Hidden Population Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(1), pages 43-58, March.
    2. Emily B. Dennis & Byron J.T. Morgan & Martin S. Ridout, 2015. "Computational aspects of N-mixture models," Biometrics, The International Biometric Society, vol. 71(1), pages 237-246, March.
    3. Ben Brintz & Claudio Fuentes & Lisa Madsen, 2018. "An asymptotic approximation to the N‐mixture model for the estimation of disease prevalence," Biometrics, The International Biometric Society, vol. 74(4), pages 1512-1518, December.
    4. 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.
    5. Zhao, Qing & Royle, J. Andrew, 2019. "Dynamic N-mixture models with temporal variability in detection probability," Ecological Modelling, Elsevier, vol. 393(C), pages 20-24.
    6. 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.
    7. D. Dail & L. Madsen, 2011. "Models for Estimating Abundance from Repeated Counts of an Open Metapopulation," Biometrics, The International Biometric Society, vol. 67(2), pages 577-587, June.
    8. 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.
    9. Fiske, Ian & Chandler, Richard, 2011. "unmarked: An R Package for Fitting Hierarchical Models of Wildlife Occurrence and Abundance," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 43(i10).
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