Estimation of detection probability in aerial surveys of antarctic pack-ice seals

  • Colin Southwell
  • David Borchers
  • Charles G. M. Paxton
  • Louise Burt
  • William de la Mare
Article

Abstract

We use line transect detection functions together with generalized linear and additive models to estimate detection probability when detection on the line (“g(0)”) may not be certain. The methods provide a flexible way of modeling detection probability for independent observer surveys, and for investigating the effects of explanatory variables. Analysis of data from an aerial survey of pack-ice seals produced g(0) estimates substantially below 1 for some observers (it varied from 0.80 to 0.98), demonstrated a fairly complex dependence of detection probability on covariates, and showed negative correlation between observers’ search width and their g(0). In addition to illustrating the utility of generalized additive models for capturing the effect of covariates on detection probability, the analysis suggests that detection functions may be sufficiently variable that use of g(0) correction factors obtained from other surveys would be inadvisable. We recommend that estimation of g(0) be considered for all aerial surveys; if g(0) is found to be very close to 1, estimation from subsequent surveys under the assumption that it is 1 may be reasonable, but without any estimation of g(0), the assumption that it is 1 is a matter of faith.

Key words

Generalized additive model Generalized linear model Heterogeneity Line transect Mark-recapture 

References

  1. Borchers, D. L. (1996), “Line Transect Abundance Estimation with Uncertain Detection on the Trackline,” unpublished Ph.D. dissertation, University of Cape Town.Google Scholar
  2. Borchers, D. L., Buckland, S. T., Goedhart, P. W., Clarke, E. D., and Hedley S. L. (1998a), “Horvitz-Thompson Estimators for Double-Platform Line Transect Surveys,” Biometrics, 54, 1221–1237.MATHCrossRefGoogle Scholar
  3. Borchers, D. L., Zucchini, W., and Fewster, R. M. (1998b), “Mark-Recapture Models for Line Transect Surveys,” Biometrics, 54, 1207–1220.MATHCrossRefGoogle Scholar
  4. Borchers, D. L., Laake, J. L., Southwell, C., and Paxton, C. G. M. (2006), “Accommodating Unmodelled Heterogeneity in Double-Observer Distance Sampling Surveys,” Biometrics, 62, 372–378.CrossRefMathSciNetGoogle Scholar
  5. Buckland, S. T., Anderson, D. R., Burnham, K. P., Laake, J. L., Borchers, D. L., and Thomas, L. (2001), Introduction to Distance Sampling: Estimating Abundance of Biological Populations, Oxford: Oxford University Press.MATHGoogle Scholar
  6. Buckland, S. T., Breiwick, J. M., Cattanach, K. L., and Laake, J. L. (1993), “Estimated Population Size of the Californian Gray Whale,” Marine Mammal Science, 9, 235–249.CrossRefGoogle Scholar
  7. Burnham, K. P., Buckland, S. T., Laake, J. L., Borchers, D. L., Marques, T. A., Bishop, J. R. B., and Thomas, L. (2004), “Further Topics in Distance Sampling,” in Advanced Distance Sampling, eds. S. T. Buckland, D. R. Anderson, K. P. Burnham, J. L. Laake, D. L. Borchers, and L. Thomas, Oxford: Oxford University Press.Google Scholar
  8. Butterworth, D. S., and Borchers, D. L. (1988), “Estimates of g(0) for Minke Schools from the Results of the Independent Observer Experiment on the 1985/86 and 1986/87 IWC/IDCR Antarctic Assessment Cruises,” Report to the International Whaling Commission, 38, 301–313.Google Scholar
  9. Chen, S. X. (1999), “Estimation in Independent Observer Line Transect Surveys for Clustered Populations,” Biometrics, 55, 754–759.MATHCrossRefGoogle Scholar
  10. — (2000), “A nimal Abundance Estimation in Independent Observer Line Transect Surveys,” Environmental and Ecological Statistics, 7, 285–299.CrossRefGoogle Scholar
  11. Chen, S. X., and Lloyd, C. J. (2000), “A Nonparametric Approach to the Analysis of Two-Stage Mark-Recapture Experiments,” Biometrika, 87, 633–649.MATHCrossRefMathSciNetGoogle Scholar
  12. Drummer, T. D., and McDonald, L. L. (1987), “Size Bias in Line Transect Sampling,” Biometrics, 43, 13–21.MATHCrossRefGoogle Scholar
  13. Evans-Mack, D., Raphael, M. G., and Laake, J. L. (2002), “Probability of Detecting Marbled Murrelets at Sea: Effects of Single Versus Paired Observers,” Journal of Wildlife Management, 66, 865–873.CrossRefGoogle Scholar
  14. Hastie, T. J., and Tibshirani, R. J. (1990), Generalized Additive Models, London: Chapman and Hall.MATHGoogle Scholar
  15. Hiby, L., and Lovell, P. (1998), “Using Aircraft in Tandem Formation to Estimate Abundance of Harbour Porpoise,” Biometrics, 54, 1280–1289.MATHCrossRefGoogle Scholar
  16. Johnson, B. K., Lindzey, F. G., and Guenzel, R. J. (1991), “Use of Aerial Line Transect Surveys to Estimate Pronghorn Populations in Wyoming,” Wildlife Society Bulletin, 19, 315–321.Google Scholar
  17. Laake, J. (1999), “Distance Sampling with Independent Observers: Reducing Bias from Heterogeneity by Weakening the Conditional Independence Assumption,” in Marine Mammal Survey and Assessment Methods, eds. G. W. Garner, S. C. Amstrup, J. L. Laake, B. F. J. Manly, L. L. McDonald, and D. G. Robertson, Rotterdam: Balkema.Google Scholar
  18. Manly, B. F. J., McDonald, L. L., and Garner, G. W. (1996), “Maximum Likelihood Estimation for the Double-Count Method with Independent Observers,” Journal of Agricultural, Biological, and Environmental Statistics, 1, 170–189.CrossRefMathSciNetGoogle Scholar
  19. Marques, F. F. C., and Buckland, S. T. (2003), “Incorporating Covariates into Standard Line Transect Analyses,” Biometrics, 59, 924–935.MATHCrossRefMathSciNetGoogle Scholar
  20. Polacheck, T., and Smith, T. D. (1989), “A Proposed Methodology for Field Testing Line Transect Theory for Shipboard Surveys of Cetaceans,” Report to the International Whaling Commission, 39, 341–345.Google Scholar
  21. Quang, P. X., and Becker, E. F. (1997), “Combining Line Transect and Double Count Sampling Techniques for Aerial Surveys,” Journal of Agricultural, Biological, and Environmental Statistics, 2, 230–242.CrossRefMathSciNetGoogle Scholar
  22. R Development Core Team (2006), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, http://www.R-project.org.Google Scholar
  23. Ruppert, D., Wand, M.P., and Carroll, R. J. (2003), Semiparametric Regression, Cambridge: Cambridge University Press.MATHGoogle Scholar
  24. S-plus (1988–1999), Mathsoft Inc.Google Scholar
  25. Southwell, C., de la Mare, W., Underwood, M., Quartararo, F., and Cope, K. (2002), “An Automated System to Log and Process Distance Sight-Resight Aerial Survey Data,” Wildlife Society Bulletin, 30, 394–404.Google Scholar

Copyright information

© International Biometric Society 2007

Authors and Affiliations

  • Colin Southwell
    • 1
  • David Borchers
    • 2
  • Charles G. M. Paxton
    • 2
  • Louise Burt
    • 2
  • William de la Mare
    • 3
  1. 1.Australian Government Antarctic DivisionChannel HighwayKingstonAustralia
  2. 2.School of Mathematics and StatisticsUniversity of St. Andrews, The ObservatorySt. AndrewsScotland
  3. 3.School of Resource and Environmental ManagementSimon Fraser UniversityBurnabyCanada

Personalised recommendations