Modelling Killer Whale Feeding Behaviour Using a Spatially Adaptive Complex Region Spatial Smoother (CReSS) and Generalised Estimating Equations (GEEs)

  • Lindesay A. S. Scott-Hayward
  • Monique L. Mackenzie
  • Erin Ashe
  • Rob Williams


To develop appropriate spatial conservation planning for individual species, it is important to understand their habitat requirements and in particular to identify areas where critical life-history process such as breeding, weaning or feeding take place. The process of defining critical habitat often ignores behavioural aspects of animal distribution, which for highly migratory species like baleen whales whose feeding and breeding grounds are clearly demarcated and widely separated is not a problem. However, for other species like the endangered ‘Eastern North Pacific southern resident’ killer whale stock, critical life-history processes occur in the same waters. This killer whale stock lives in a topographically complex region (many islands) off the west coast of Canada/USA, which makes accurate mapping of densities or behaviours difficult using traditional generalised additive models. We present results on the spatial distribution of southern resident killer whale feeding grounds in 2006, using a binomial, complex region spatial smoothing model within a generalised estimating equation framework, which allows for both complex topography and correlated residuals. The model performs well and suggests a region to the south of San Juan Island as an area with a high probability of feeding, which could not have been as accurately established from a more traditional presence–absence model. We also calculate estimates of precision, which other studies did not include, enabling more informed management decisions for spatial conservation planning. A vignette containing the code along with an R workspace and function file is provided to allow the user to fit the models presented in this paper.

Supplementary materials accompanying this paper appear on-line.


Spatial modelling Habitat conservation Marine mammal Generalised additive model Residual correlation 



This fieldwork was permitted in the USA by ESA permit #781-1824-00 and in Canada by Marine Mammal 2006-07 and SARA-33 permits.

Supplementary material

13253_2015_209_MOESM1_ESM.html (1 mb)
Supplementary material 1 (html 1056 KB)


  1. Agresti, A. (2002), Categorical Data Analysis, 2\(^{nd}\) edn John Wiley & Sons Inc.Google Scholar
  2. Araújo, M., and Guisan, A. (2006) , “Five (or so) challenges for species distribution modelling,” Journal of Biogeography, 33, 1677–1688.Google Scholar
  3. Ashe, E., Noren, D., and Williams, R. (2010), “Animal behaviour and marine protected areas: incorporating behavioural data into the selection of marine protected areas for an endangered killer whale population,” Animal Conservation, 13(2), 196–203.Google Scholar
  4. Belotti, E., Kreisinger, J., Romportl, D., Heurich, M., and Bufka, L. (2014), “Eurasian lynx hunting red deer: is there an influence of a winter enclosure system?,” European Journal of Wildlife Research, 60(3), 441–457.Google Scholar
  5. Brown, H., and Prescott, R. (2006), Applied mixed models in medicine, John Wiley & Sons Inc.Google Scholar
  6. Buckland, S. T., Burnham, K. P., and Augustin, N. H. ( 1997), “Model Selection: An Integral Part of Inference,” Biometrics, 53, 603–618.Google Scholar
  7. Burnham, K. P., and Anderson, D. R. ( 2004), “Multimodel Inference: Understanding AIC and BIC in model selection,” Sociological methods & research, 33(2), 261–304.Google Scholar
  8. Burnham, K. P., and Anderson, D. R. ( 2010), Model Selection and Multimodel Inference: A practical information-theoretic approach, 2\(^{nd}\) edn Springer.Google Scholar
  9. Camphuysen, K. C., Shamoun-Baranes, J., Bouten, W., and Garthe, S. (2012), “Identifying ecologically important marine areas for seabirds using behavioural information in combination with distribution patterns,” Biological Conservation, 156, 22–29.Google Scholar
  10. Cramer, J. (2003), Logit models: from economics and other fields, Cambridge University Press.Google Scholar
  11. Floyd, R. W. (1962), “Algorithm 97: Shortest path,” Communications of the ACM, 5, 345.Google Scholar
  12. Gerrodette, T., and Eguchi, T. (2011), “Precautionary design of a marine protected area based on a habitat model,” Endangered Species Research, 15(2), 159–166.Google Scholar
  13. Goetz, K. T., Montgomery, R. A., Hoef, J. M., Hobbs, R. C., and Johnson, D. S. (2012), “Identifying essential summer habitat of the endangered beluga whale Delphinapterus leucas in Cook Inlet, Alaska,” Endangered Species Research, 16(2), 135–147.Google Scholar
  14. Halekoh, U., Hojsgaard, S., and Yan, J. ( 2006), “The R package geepack for Generalized Estimating Equations,” Journal of Statistical Software, 15(2).Google Scholar
  15. Halpern, B. S., Walbridge, S., Selkoe, K. A., Kappel, C. V., Micheli, F., D’Agrosa, C., Bruno, J. F., Casey, K. S., Ebert, C., Fox, H. E. et al. (2008), “A global map of human impact on marine ecosystems,” Science, 319(5865), 948–952.Google Scholar
  16. Hansen, M. . H., and Kooperberg, C. ( 2002), “Spline Adaptation in Extended Linear Models, Statistical Science,” 17, 2–51.Google Scholar
  17. Hardin, J., and Hilbe, J. (2002), Generalized Estimating Equations, Chapman & Hall/CRC.Google Scholar
  18. Hastie, T. J., and Tibshirani, R. J. ( 1990), Generalized Additive Models, Chapman & Hall.Google Scholar
  19. Hauser, D., Logsdon, M., Holmes, E., VanBlaricom, G., and Osborne, R. (2007), “Summer distribution patterns of southern resident killer whales Orcinus orca: core areas and spatial segregation of social groups,” Marine Ecology Progress Series, 351, 301–310.Google Scholar
  20. Hawkins, B. (2012), “Eight (and a half) deadly sins of spatial analysis,” Journal of Biogeography, 39, 1–9.Google Scholar
  21. Hedley, S. L., and Buckland, S. T. ( 2004), “Spatial models for line transect sampling,” Journal of Agricultural, Biological, and Environmental Statistics, 9(2), 181–199.Google Scholar
  22. Heithaus, M., Dill, L., Marshall, G., and Buhleier, B. (2002), “Habitat use and foraging behavior of tiger sharks (Galeocerdo cuvier) in a seagrass ecosystem,” Marine Biology, 140(2), 237–248.Google Scholar
  23. Hosmer, D., and Lemeshow, S. (1989), “Logistic regression for matched case-control studies,” Applied logistic regression, 2, 223–259.Google Scholar
  24. Jang, D., and Oh, H.-S. (2011), “Enhancement of spatially adaptive smoothing splines via parameterization of smoothing parameters,” Computational Statistics and Data Analysis, 55, 1029–1040.Google Scholar
  25. John, P. W. M., Johnson, M. E., Moore, L. M., and Ylvisaker, D. (1995), “Minimax distance designs in two-level factorial experiments,” Journal of Statistical Planning and Inference, 44, 249–263.Google Scholar
  26. Jonsen, I. D., Myers, R. A., and James, M. C. ( 2007), “Identifying leatherback turtle foraging behaviour from satellite telemetry using a switching state-space model,” Marine Ecology Progress Series, 337, 255–264.Google Scholar
  27. Kaschner, K., Quick, N. J., Jewell, R., Williams, R., and Harris, C. M. (2012), “Global coverage of cetacean line-transect surveys: status quo, data gaps and future challenges,” PloS one, 7(9).Google Scholar
  28. Krivobokova, T., Crainiceanu, C. M., and Kauermann, G. (2008), “Fast Adaptive Penalized Splines,” Journal of Computational and Graphical Statistics, 17(1), 1–20.Google Scholar
  29. Lascelles, B. G., Langham, G. M., Ronconi, R. A., and Reid, J. B. (2012), “From hotspots to site protection: Identifying Marine Protected Areas for seabirds around the globe,” Biological Conservation, 156, 5–14.Google Scholar
  30. Liu, C., Berry, P., Dawson, T., and Pearson, R. ( 2005), “Selecting thresholds of occurrence in the prediction of species distributions,” Ecography, 28, 385–393.Google Scholar
  31. Ludwig, D., Hilborn, R., and Walters, C. ( 1993), “Uncertainty, resource exploitation, and conservation: lessons from history,” Science, 260(5104), 17–36.Google Scholar
  32. Lusseau, D., Bain, D., Williams, R., and Smith, J. ( 2009), “Vessel traffic distupts the foraging behaviour of southern resident killer whales Orcinus orca,” Endangered Species Research, 6, 211–221.Google Scholar
  33. Lusseau, D., Williams, R., Wilson, B., Grellier, K., Barton, T. R., Hammond, P. S., and Thompson, P. M. (2004), “Parallel influence of climate on the behaviour of Pacific killer whales and Atlantic bottlenose dolphins,” Ecology Letters, 7(11), 1068–1076.Google Scholar
  34. Mann, J. (1999), “Behavioural Sampling Methods for Cetaceans: A Review and Critique,” Marine Mammal Science, 15(1), 102–122.Google Scholar
  35. NMFS (2008), “Recovery plan for Southern Resident Killer Wales (Orcinus orca).,” in Federal Register, Vol. 251, Seattle, WA, USA, National Marine Fisheries Service, Northwest Region.: National Marine Fisheries Service, pp. 20870–20890.Google Scholar
  36. Noss, R. F., Quigley, H. B., Hornocker, M. G., Merrill, T., and Paquet, P. C. (1996), “Conservation biology and carnivore conservation in the Rocky Mountains,” Conservation Biology, 10(4), 949–963.Google Scholar
  37. O’Leary, B., Brown, R., Johnson, D., Von Nordheim, H., Ardron, J., Packeiser, T., and Roberts, C. (2012), “The first network of marine protected areas (MPAs) in the high seas: the process, the challenges and where next,” Marine Policy, 36(3), 598–605.Google Scholar
  38. Pan, W. (2001a), “Akaikes’s Information Criterion in Generalized Estimating Equations,” Biometrics, 57(1), 120–125.Google Scholar
  39. Pan, W. (2001b), “Model Selection in Estimating Equations,” Biometrics, 57, 529–534.Google Scholar
  40. Panigada, S., Zanardelli, M., MacKenzie, M., Donovan, C., Melin, F., and Hammond, P. (2008), “Modelling habitat preferences for fin whales and striped dolphins in the Pelagos Sanctuary (Western Mediterranean Sea) with physiographic and remote sensing variables,” Remote Sensing of Environment, 112(8), 3400–3412.Google Scholar
  41. Pearce, J., and Ferrier, S. (2000), “Evaluating the predictive performance of habitat models developed using logistic regression,” Ecological Modelling, 133, 225–245.Google Scholar
  42. Priotta, E., Matthiopoulos, J., Mackenzie, M., Scott-Hayward, L. A. S., and Rendell, L. (2011), “Modelling sperm whale habitat preference: a novel approach combining transect and follow data,” Marine Ecology Progress Series, 436, 257–272.Google Scholar
  43. R Core Team (2013), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria.Google Scholar
  44. Ramsay, T. O. (2002), “Spline smoothing over difficult regions,” Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64(1), 307–319.Google Scholar
  45. Redfern, J., Ferguson, M., Becker, E., Hyrenbach, K., Good, C. P., Barlow, J., Kaschner, K., Baumgartner, M. F., Forney, K., Ballance, L. et al. (2006), “Techniques for cetacean-habitat modeling,” Marine Ecology Progress Series, 310, 271–295.Google Scholar
  46. Richards, S. A. (2008), “Dealing with overdispersed count data in applied ecology,” Journal of Applied Ecology, 45(1), 218–227.Google Scholar
  47. Scott-Hayward, L. A. S., Mackenzie, M. L., Donovan, C. R., Walker, C. G., and Ashe, E. (2014), “Complex Region Spatial Smoother (CReSS),” Journal of Computational and Graphical Statistics, 23(2), 340–360.Google Scholar
  48. Tepsich, P., Rosso, M., Halpin, P. N., and Moulins, A. (2014), “Habitat preferences of two deep-diving cetacean species in the northern Ligurian Sea,” Marine Ecology Progress Series, 508, 247–260.Google Scholar
  49. Vaz, S., Martin, C. S., Eastwood, P. D., Ernande, B., Carpentier, A., Meaden, G. J., and Coppin, F. (2008), “Modelling species distributions using regression quantiles,” Journal of Applied Ecology, 45(1), 204–217.Google Scholar
  50. Wang, H., and Ranalli, M. G. (2007), “Low-Rank Smoothing Splines on Complicated Domains,” Biometrics, 63(1), 209–217.Google Scholar
  51. Williams, R., Kaschner, K., Hoyt, E., Reeves, R., and Ashe, E. (2011), “Mapping large-scale spatial patterns in cetacean density: Preliminary work to inform systematic conservation planning and MPA network design in the northeastern Pacific,”, Report for WDCS, the Whale and Dolphin Conservation Society.Google Scholar
  52. Williams, R., Krkošek, M., Ashe, E., Branch, T. A., Clark, S., Hammond, P. S., Hoyt, E., Noren, D. P., Rosen, D., and Winship, A. (2011), “Competing conservation objectives for predators and prey: Estimating killer whale prey requirements for Chinook salmon,” PloS one, 6(11).Google Scholar
  53. Williams, R., Lusseau, D., and Hammond, P. ( 2006), “Estimating relative energetic costs of human disturbance to killer whales (Orcinus orca),” Biological Conservation, 133, 301–311.Google Scholar
  54. Wood, A., Naef-Daenzer, B., Prince, P., and Croxall, J. (2000), “Quantifying habitat use in satellite-tracked pelagic seabirds: application of kernel estimation to albatross locations,” Journal of Avian Biology, 31(3), 278–286.Google Scholar
  55. Wood, S. N. (2006), Generalized Additive Models: An Introduction with R Chapman & Hall/CRC.Google Scholar
  56. Wood, S. N., Bravington, M. V., and Hedley, S. L. ( 2008), “Soap Film Smoothing,” Journal of the Royal Statistical Society, Series B, 70(5).Google Scholar
  57. Zorn, C. (2006), “Comparing GEE and robust standard errors for conditionally dependent data,” Political Research Quarterly, 59(3), 329–341.Google Scholar

Copyright information

© International Biometric Society 2015

Authors and Affiliations

  • Lindesay A. S. Scott-Hayward
    • 1
  • Monique L. Mackenzie
    • 1
  • Erin Ashe
    • 2
  • Rob Williams
    • 2
  1. 1.Centre for Research into Ecological and Environmental Modelling (CREEM), School of Mathematics and StatisticsUniversity of St. AndrewsSt. AndrewsUK
  2. 2.Sea Mammal Research Unit (SMRU), School of BiologyUniversity of St. AndrewsSt. AndrewsUK

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