Two-Stage Bayesian Study Design for Species Occupancy Estimation

  • Gurutzeta Guillera-ArroitaEmail author
  • Martin S. Ridout
  • Byron J. T. Morgan


A problem of interest for ecology and conservation is that of determining the best allocation of survey effort in studies aimed at estimating the proportion of sites occupied by a species. Many species are difficult to detect and often remain undetected during surveys at sites where they are present. Hence, for the estimator of species occupancy to be unbiased, detectability needs to be taken into account. In such studies there is a trade-off between sampling more sites and expending more survey effort within each site. This design problem has not been addressed to date with an explicit consideration of the uncertainty in assumed parameter values. In this article we apply sequential and Bayesian design techniques and show how a simple two-stage design can significantly improve the efficiency of the study. We further investigate the optimal allocation of survey effort between the two study stages, given a prior distribution for the parameter values. We address this problem using asymptotic approximations and then explore how the results change when the sample size is small, considering second-order approximations and highlighting the value of simulations as a tool for study design. Given the efficiency gain, we recommend following the sequential design approach for species occupancy estimation. This article has supplementary material online.

Key Words

Binary data Imperfect detection Multistage Optimal design Pilot study Second-order approximation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Supplementary material

13253_2014_171_MOESM1_ESM.pdf (575 kb)
Supplementary material: small-sample considerations (PDF 575 kB)


  1. Abdelbasit, K. M., and Plackett, R. L. (1983), “Experimental Design for Binary Data,” Journal of the American Statistical Association, 78, 90–98. CrossRefzbMATHMathSciNetGoogle Scholar
  2. Atkinson, A. C., and Donev, A. N. (1992), Optimum Experimental Designs, Oxford: Clarendon Press. zbMATHGoogle Scholar
  3. Bailey, L. L., Hines, J. E., Nichols, J. D., and MacKenzie, D. I. (2007), “Sampling Design Trade-Offs in Occupancy Studies with Imperfect Detection: Examples and Software,” Ecological Applications, 17, 281–290. CrossRefGoogle Scholar
  4. Chaloner, K., and Verdinelli, I. (1995), “Bayesian Experimental Design: A Review,” Statistical Science, 10, 273–304. CrossRefzbMATHMathSciNetGoogle Scholar
  5. Field, S. A., O’Connor, P. J., Tyre, A. J., and Possingham, H. P. (2007), “Making Monitoring Meaningful,” Austral Ecology, 32, 485–491. CrossRefGoogle Scholar
  6. Guillera-Arroita, G., and Lahoz-Monfort, J. J. (2012), “Designing Studies to Detect Differences in Species Occupancy: Power Analysis Under Imperfect Detection,” Methods in Ecology and Evolution, 3, 860–869. CrossRefGoogle Scholar
  7. Guillera-Arroita, G., Morgan, B. J. T., Ridout, M. S., and Linkie, M. (2011), “Species Occupancy Modeling for Detection Data Collected Along a Transect,” Journal of Agricultural, Biological, and Environmental Statistics, 16, 301–317. CrossRefMathSciNetGoogle Scholar
  8. Guillera-Arroita, G., Ridout, M. S., and Morgan, B. J. T. (2010), “Design of Occupancy Studies with Imperfect Detection,” Methods in Ecology and Evolution, 1, 131–139. CrossRefGoogle Scholar
  9. Kalish, L. A. (1990), “Efficient Design for Estimation of Median Lethal Dose and Quantal Dose-Response Curves,” Biometrics, 46, 737–748. CrossRefMathSciNetGoogle Scholar
  10. Kéry, M. (2002), “Inferring the Absence of a Species: A Case Study of Snakes,” The Journal of Wildlife Management, 66, 330–338. CrossRefGoogle Scholar
  11. Kéry, M., and Schmidt, B. R. (2008), “Imperfect Detection and Its Consequences for Monitoring for Conservation,” Community Ecology, 9, 207–216. CrossRefGoogle Scholar
  12. Legg, C. J., and Nagy, L. (2006), “Why Most Conservation Monitoring Is, but Need Not Be, a Waste of Time,” Journal of Environmental Management, 78, 194–199. CrossRefGoogle Scholar
  13. MacKenzie, D. I., and Royle, J. A. (2005), “Designing Occupancy Studies: General Advice and Allocating Survey Effort,” Journal of Applied Ecology, 42, 1105–1114. CrossRefGoogle Scholar
  14. MacKenzie, D. I., Nichols, J. D., Lachman, G. B., Droege, S., Royle, J. A., and Langtimm, C. A. (2002), “Estimating Site Occupancy Rates When Detection Probabilities Are Less than One,” Ecology, 83, 2248–2255. CrossRefGoogle Scholar
  15. MacKenzie, D. I., Nichols, J. D., Royle, J. A., Pollock, K. H., Bailey, L. L., and Hines, J. E. (2006), Occupancy Estimation and Modeling: Inferring Patterns and Dynamics of Species Occurrence, New York: Academic Press. Google Scholar
  16. Ridout, M. S. (1995), “Three-Stage Designs for Seed Testing Experiments,” Journal of the Royal Statistical Society. Series C. Applied Statistics, 44, 153–162. zbMATHGoogle Scholar
  17. Shenton, L. R., and Bowman, K. O. (1977), Maximum Likelihood Estimation in Small Samples, London: Griffin. zbMATHGoogle Scholar
  18. Tyre, A. J., et al. (2003), “Improving Precision and Reducing Bias in Biological Surveys: Estimating False-Negative Error Rates,” Ecological Applications, 13, 1790–1801. CrossRefGoogle Scholar
  19. Yoccoz, N. G., Nichols, J. D., and Boulinier, T. (2001), “Monitoring of Biological Diversity in Space and Time,” Trends in Ecology & Evolution, 16, 446–453. CrossRefGoogle Scholar
  20. Zacks, S. (1996), “Adaptive Designs for Parametric Models,” in Handbook of Statistics, Vol. 13, Amsterdam: Elsevier, pp. 151–180. Google Scholar

Copyright information

© International Biometric Society 2014

Authors and Affiliations

  • Gurutzeta Guillera-Arroita
    • 1
    • 2
    Email author
  • Martin S. Ridout
    • 1
  • Byron J. T. Morgan
    • 1
  1. 1.School of Mathematics, Statistics and Actuarial ScienceUniversity of KentCanterburyUK
  2. 2.School of BotanyUniversity of MelbourneParkvilleAustralia

Personalised recommendations