Zigzag survey designs in line transect sampling

Article

Abstract

Zigzag survey lines are frequently used in shipboard and aerial line transect surveys of animal populations. Analysis proceeds assuming that coverage probability through the survey region is uniform. We show that the two types of zigzag design that are in wide use do not generally have this property, and explore the degree of bias in abundance estimates that can be anticipated. We construct a zigzag design for convex survey regions that has even coverage probability with respect to distance along a design axis. We also provide Horvitz-Thompson estimators that allow coverage probability to vary by location through the survey region.

Key Words

Automated design algorithms Coverage probability Sighting surveys Survey design Systematic designs Zigzag designs 

References

  1. Barlow, J. (1994), “Abundance of Large Whales in California Coastal Waters: A Comparison of Ships Surveys in 1979/80 and in 1991,” Report of the International Whaling Commission, 44, 399–406.Google Scholar
  2. Borchers, D. L., Buckland, S. T., Goedhart, P. W., Clarke, E. D., and Hedley, S. L. (1998), “Horvitz-Thompson Estimators for Double-platform Line Transect Surveys,” Biometrics, 54, 1221–1237.MATHCrossRefGoogle Scholar
  3. Borchers, D. L., and Haw, M. D. (unpublished), “Estimation of Minke Whale Abundance from the 1987/8 IWC/IDCR Antarctic Assessment Cruise in Area III,” Paper SC/41/SHMi4; available from the International Whaling Commission.Google Scholar
  4. Branch, T. A., and Butterworth, D. L. (2001), “Estimates of Abundance South of 60° S for Cetacean Species Sighted Frequently on the 1978/79 to 1997/98 IWC/IDCR-SOWER Sighting Surveys,” Journal of Cetacean Research and Management, 3, 251–270.Google Scholar
  5. Buckland, S. T., Cattanach, K. L., and Gunnlaugsson, Th. (1992), “Fin Whale Abundance in the North Atlantic, Estimated from Icelandic and Faroese NASS-87 and NASS-89 Data,” Report of the International Whaling Commission, 42, 645–651.Google Scholar
  6. Buckland, S. T., Anderson, D. R., Burnham, K. P., Laake, J. L., Borchers, D. L., and Thomas, L. (2001), An Introduction to Distance Sampling, Oxford: Oxford University Press.Google Scholar
  7. Chen, S. X., and Cowling, A. (2001), “Measurement Errors in Line Transect Surveys where Detectability Varies with Distance and Size,” Biometrics, 57, 732–742.CrossRefMathSciNetGoogle Scholar
  8. Clarke, E. D., Spear, L. B., McCracken, M. L., Marques, F. F. C., Borchers, D. L., Buckland, S. T., and Ainley, D. G. (2003), “Application of Generalized Additive Models to Estimate Size of Seabird Populations and Temporal Trend from Survey Data Collected at Sea,” Journal of Applied Ecology, 40, 278–292.Google Scholar
  9. Cooke, J. G. (1985), “Estimation of Abundance from Surveys,” unpublished manuscript.Google Scholar
  10. Foote, K. G., and Stefansson, G. (1993), “Definition of the Problem of Estimating Fish Abundance Over an Area from Acoustic Line Transect Measurements of Density,” ICES Journal of Marine Science, 50, 369–381.CrossRefGoogle Scholar
  11. Hammond, P. S., Berggren, P., Benke, H., Borchers, D. L., Collet, A., Heide-Jørgensen, M. P., Heimlich, S., Hiby, A. R., Leopold, M. F., and Øien, N. (2002), “Abundance of Harbour Porpoise and Other Cetaceans in the North Sea and Adjacent Waters,” Journal of Applied Ecology, 39, 361–376.CrossRefGoogle Scholar
  12. Hedley, S. L., and Buckland, S. T. (2004), “Spatial Models for Line Transect Sampling,” Journal of Agricultural, Biological, and Environmental Statistics, 9, 181–199.CrossRefGoogle Scholar
  13. Horvitz, D. G., and Thompson, D. J. (1952), “A Generalization of Sampling without Replacement from a Finite Universe,” Journal of the American Statistical Association, 47, 663–685.MATHCrossRefMathSciNetGoogle Scholar
  14. Huggins, R. M. (1989), “On the Statistical Analysis of Capture Experiments,” Biometrika, 76, 133–140.MATHCrossRefMathSciNetGoogle Scholar
  15. Marques, F. F. C., and Buckland, S. T. (2003), “Incorporating Covariates into Standard Line Transect Analyses,” Biometrics, 59, 924–935.MATHCrossRefMathSciNetGoogle Scholar
  16. O’Connell, V. M., and Carlile, D. W. (1993), “Habitat-specific Density of Adult Yelloweye Rockfish Sebastes Ruberrimus in the Eastern Gulf of Alaska,” Fishery Bulletin, 91, 304–309.Google Scholar
  17. Pojar, T.M., Bowden, D. C., and Gill, R. B. (1995), “Aerial Counting Experiments to Estimate Pronghorn Density and Herd Structure,” Journal of Wildlife Management, 59, 117–128.CrossRefGoogle Scholar
  18. Pople, A. R., Cairns, S. C., Clancy, T. F., Grigg, G. C., Beard, L. A., and Southwell, C. J. (1998), “An Assessment of the Accuracy of Kangaroo Surveys Using Fixed-Wing Aircraft,” Wildlife Research, 25, 315–326.CrossRefGoogle Scholar
  19. Strindberg, S. (2001), “Optimized Automated Survey Design in Wildlife Population Assessment,” PhD thesis, University of St. Andrews.Google Scholar
  20. Trenkel, V. M., Buckland, S. T., McLean, C., and Elston, D. A. (1997), “Evaluation of Aerial Line Transect Methodology for Estimating Red Deer (Cervus elaphus) Abundance in Scotland,” Journal of Environmental Management, 50, 39–50.CrossRefGoogle Scholar
  21. van Hensbergen, H. J., Berry, M. P. S., and Juritz, J. (1996), “Helicopter-based Line-transect Estimates of Some Southern African Game Populations,” South African Journal of Wildlife Research, 26, 81–87.Google Scholar
  22. White, G. C., Bartmann, R. M., Carpenter, L. H., and Garrott, R. A. (1989), “Evaluation of Aerial Line Transects for Estimating Mule Deer Densities,” Journal of Wildlife Management, 53, 625–635.CrossRefGoogle Scholar
  23. Wiig, Ø., and Derocher, A. E. (1999), “Application of Aerial Survey Methods to Polar Bears in the Barents Sea,” 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 Press, pp. 27–36.Google Scholar

Copyright information

© International Biometric Society 2004

Authors and Affiliations

  1. 1.Living Landscapes Program, International Conservation ProgramsWildlife Conservation SocietyBronx
  2. 2.Centre for Research into Ecological and Environmental ModellingThe ObservatorySt. AndrewsScotland

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