Spatial models for line transect sampling

  • Sharon L. HedleyEmail author
  • Stephen T. Buckland


This article develops methods for fitting spatial models to line transect data. These allow animal density to be related to topographical, environmental, habitat, and other spatial variables, helping wildlife managers to identify the factors that affect abundance. They also enable estimation of abundance for any subarea of interest within the surveyed region, and potentially yield estimates of abundance from sightings surveys for which the survey design could not be randomized, such as surveys conducted from platforms of opportunity. The methods are illustrated through analyses of data from a shipboard sightings survey of minke whales in the Antarctic.

Key Words

Distance sampling Generalized additive model Generalized linear model Population size estimation Sightings survey Spatial distribution 


  1. Augustin, N. H., Mugglestone, M. A., and Buckland, S. T. (1998), “The Role of Simulation inModelling Spatially Correlated Data,” Environmetrics, 9, 175–196.CrossRefGoogle Scholar
  2. Branch, T. A., and Butterworth, D. S. (2001), “Southern Hemisphere Minke Whales: Standardised Abundance Estimates from the 1978/79 to 1997/98 IDCR-SOWER Surveys,” Journal of Cetacean Research and Management, 3, 143–174.Google Scholar
  3. Buckland, S. T. (1984), “Monte Carlo Confidence Intervals,” Biometrics, 40, 811–817.zbMATHCrossRefGoogle Scholar
  4. Buckland, S.T., Anderson, D. R., Burnham, K. P., Laake, J. L., Borchers, D. L., and Thomas, L. (2001), Introduction to Distance Sampling, Oxford: Oxford University Press.zbMATHGoogle Scholar
  5. Buckland, S. T., Burnham, K. P., and Augustin, N. H. (1997), “Model Selection: An Integral Part of Inference,” Biometrics, 53, 603–618.zbMATHCrossRefGoogle Scholar
  6. Christensen, O. F., and Waagepetersen, R. (2002), “Bayesian Prediction of Spatial Count Data Using Generalized Linear Mixed Models,” Biometrics, 58, 280–286.CrossRefMathSciNetGoogle Scholar
  7. Cressie, N. A. C. (1991), Statistics for Spatial Data, New York: Wiley.zbMATHGoogle Scholar
  8. Diggle, P. J., Tawn, J. A., and Moyeed, R. A. (1998), “Model-Based Geostatistics,” Applied Statistics, 47, 299–350.zbMATHMathSciNetGoogle Scholar
  9. Ferguson, J. W. H., and Bester, M. N. (2002), “The Treatment of Spatial Autocorrelation in Biological Surveys: The Case of Line Transect Surveys,” Antarctic Science, 14, 115–122.CrossRefGoogle Scholar
  10. Gotway, C. A., and Stroup, W. W. (1997), “A Generalized Linear Model Approach to Spatial Data Analysis and Prediction,” Journal of Agricultural, Biological, and Environmental Statistics, 2, 157–178.CrossRefMathSciNetGoogle Scholar
  11. Hastie, T. J., and Tibshirani, R. J. (1990), Monographs on Statistics and Applied Probability. 43. Generalized Additive Models, London: Chapman and Hall.Google Scholar
  12. Högmander, H. (1991), “A Random Field Approach to Transect Counts of Wildlife Populations,” Biometrical Journal, 33, 1013–1023.zbMATHCrossRefGoogle Scholar
  13. —(1995), Methods of Spatial Statistics in Monitoring Wildlife Populations, Jyväskylä: University of Jyväskylä.Google Scholar
  14. 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.zbMATHCrossRefMathSciNetGoogle Scholar
  15. Jefferson, T. A., Leatherwood, S., and Webber,M. A. (1993), FAO Species Identification Guide. Marine Mammals of the World, Rome: FAO.Google Scholar
  16. Lin, X. H., and Zhang, D. W. (1999), “Inference in Generalized Additive Mixed Models by Using Smoothing Splines,” Journal of the Royal Statistical Society, Series B, 61, 381–400.zbMATHCrossRefMathSciNetGoogle Scholar
  17. Marques, F. F. C. (2001), “Estimating Wildlife Distribution and Abundance from Line Transect Surveys Conducted from Platforms of Opportunity,” unpublished Ph.D. thesis, University of St. Andrews, Scotland.Google Scholar
  18. Seber, G. A. F. (1982), The Estimation of Animal Abundance and Related Parameters (2nd ed.), London: Edward Arnold.Google Scholar
  19. Stoyan, D. (1982), “A Remark on the Line Transect Method,” Biometrical Journal, 24, 191–195.zbMATHCrossRefMathSciNetGoogle Scholar
  20. Thomas, L., Laake, J. L., Strindberg, S., Marques, F. F. C., Buckland, S. T., Borchers, D. L., Anderson, D. R., Burnham, K. P., Hedley, S. L., Pollard, J. H., and Bishop, J. R. B. (2003), Distance 4.1, Research Unit for Wildlife Population Assessment, University of St. Andrews, U.K.; available from Scholar
  21. Wood, S. N. (2000), “Modelling and Smoothing Parameter Estimation with Multiple Quadratic Penalties,” Journal of the Royal Statistical Society, Series B, 62, 413–428.CrossRefGoogle Scholar
  22. Zhang, H. (2002), “On Estimation and Prediction for Spatial Generalized Linear Mixed Models,” Biometrics, 58, 129–136.CrossRefMathSciNetGoogle Scholar

Copyright information

© International Biometric Society 2004

Authors and Affiliations

  1. 1.Research Unit for Wildlife Population AssessmentUniversity of St. AndrewsScotland
  2. 2.Centre for Reseach into Ecological and Environmental ModellingUniversity of St. AndrewsScotland

Personalised recommendations