Environmental and Ecological Statistics

, Volume 10, Issue 2, pp 201–219 | Cite as

A Bayesian hierarchical model for monitoring harbor seal changes in Prince William Sound, Alaska

  • Jay M. Ver Hoef
  • Kathryn J. Frost


Bayesian hierarchical models were used to assess trends of harbor seals, Phoca vitulina richardsi, in Prince William Sound, Alaska, following the 1989 Exxon Valdez oil spill. Data consisted of 4–10 replicate observations per year at 25 sites over 10 years. We had multiple objectives, including estimating the effects of covariates on seal counts, and estimating trend and abundance, both per site and overall. We considered a Bayesian hierarchical model to meet our objectives. The model consists of a Poisson regression model for each site. For each observation the logarithm of the mean of the Poisson distribution was a linear model with the following factors: (1) intercept for each site and year, (2) time of year, (3) time of day, (4) time relative to low tide, and (5) tide height. The intercept for each site was then given a linear trend model for year. As part of the hierarchical model, parameters for each site were given a prior distribution to summarize overall effects. Results showed that at most sites, (1) trend is down; counts decreased yearly, (2) counts decrease throughout August, (3) counts decrease throughout the day, (4) counts are at a maximum very near to low tide, and (5) counts decrease as the height of the low tide increases; however, there was considerable variation among sites. To get overall trend we used a weighted average of the trend at each site, where the weights depended on the overall abundance of a site. Results indicate a 3.3% decrease per year over the time period.

trend analysis abundance estimation population monitoring Markov Chain Monte Carlo Poisson regression aerial surveys Exxon Valdez oil spill harbor seal Phoca vitulina richardsi Prince William Sound 


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  1. Craig, B.A., Newton, M.A., Garrott, R.A, Reynolds III, J.E., and Wilcox, J.R. (1997) Analysis of aerial survey data on Florida manatee using Markov chain Monte Carlo. Biometrics, 53, 524–41.Google Scholar
  2. Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap. Chapman and Hall, New York, pp. 436.Google Scholar
  3. Frost, K.F., Lowry, L.F., and Ver Hoef, J.M. (1999) Monitoring the trend of harbor seals in Prince William Sound, Alaska, after the Exxon Valdez oil spill. Marine Mammal Science, 15, 494–506.Google Scholar
  4. Frost, K.F., Lowry, L.F., Sinclair, E., Ver Hoef, J., and McAllister, D.C. (1994) Impacts on distribution, abundance, and productivity of harbor seals. In Marine Mammals and the Exxon Valdez, T.R. Loughlin (ed.), Academic Press, Inc., San Diego, pp. 97–118.Google Scholar
  5. Gelman, A., Carlin, J.B., Stern, H.S., and Rubin, D.B. (1995) Bayesian Data Analysis. Chapman and Hall, London, pp. 526.Google Scholar
  6. Gilks, W.R., Richardson, S., and Spiegelhalter, D.J. (1996) Markov Chain Monte Carlo in Practice. Chapman and Hall, London, pp. 486.Google Scholar
  7. Harvey, J.T. (1987) Population dynamics, annual food consumption, movements, and dive behaviors of harbor seals, Phoca vitulina richardsi, in Oregon. Ph.D. Thesis, University of Oregon, pp. 177.Google Scholar
  8. Harvey, J.T., Brown, R.F., and Mate, B.R. (1990) Abundance and distribution of harbor seals (Phoca vitulina) in Oregon, 1975–1983. Northwestern Naturalist, 71, 65–71.Google Scholar
  9. Huber, H.S. (1995) The abundance of harbor seals (Phoca vitulina richardsi) in Washington, 1991–1993. MS Thesis, University of Washington, pp. 56.Google Scholar
  10. Lowry, L.F., Frost, K.J., and Pitcher, K.W. (1994) Observations of oiling of harbor seals in Prince William Sound, in Marine Mammals and the Exxon Valdez, T.R. Loughlin (ed.), Academic Press, Inc., San Diego, pp. 209–26.Google Scholar
  11. Manly, B.F.J. (1997) Randomization, Bootstrap and Monte Carlo Methods in Biology, Second Edition, Chapman and Hall, London, pp. 399.Google Scholar
  12. McCullagh, P. and Nelder, J.A. (1989) Generalized Linear Models, second edition, Chapman and Hall, London, pp. 511.Google Scholar
  13. Morris, B.F. and Loughlin, T.R. (1994) Overview of the Exxon Valdez oil spill, 1989–1992. In Marine Mammals and the Exxon Valdez, T.R. Loughlin (ed.), Academic Press, Inc., San Diego, pp. 1–22.Google Scholar
  14. Moss, J. (1992) Environmental and biological factors that influence harbor seal (Phoca vitulina richardsi) haulout behavior in Washington and their consequences for the design of population surveys. MS Thesis, University of Washington, pp. 127.Google Scholar
  15. Olesiuk, P.F., Bigg, M.A., and Ellis, G.M. (1990) Recent trends in the abundance of harbour seals, (Phoca vitulina richardsi) in British Columbia. Canadian Journal Fisheries and Aquatic Science, 47, 992–1003.Google Scholar
  16. Pauli, B.D. and Terhune, J.M. (1987) Tidal and temporal interaction on harbour seal haul-out patterns. Aquatic Mammals, 13, 93–5.Google Scholar
  17. Pitcher, K.W. (1990) Major decline of harbor seals, Phoca vitulina richardsi, on Tugidak Island, Gulf of Alaska. Marine Mammal Science, 6, 121–34.Google Scholar
  18. Schneider, D.C. and Payne, P.M. (1983) Factors affecting haul-out of harbor seals at a site in southeastern Massachusetts. Journal of Mammalogy, 64, 518–20.Google Scholar
  19. Stewart, B.S. (1984) Diurnal hauling patterns of harbor seals at San Miguel Island, California. Journal of Wildlife Management, 48, 1459–61.Google Scholar
  20. Thompson, P.M. and Harwood, J. (1990) Methods for estimating the population size of common seals, Phoca vitulina. Journal of Applied Ecology, 27, 924–38.Google Scholar
  21. Thompson, P.M., Tollit, D.J., Wood, D., Corpe, H.M., Hammond, P.S. and MacKay, A. (1997) Estimating harbour seal abundance and status in an estuarine habitat in north-east Scotland. Journal of Applied Ecology, 34, 43–52.Google Scholar
  22. Yochem, P.K., Stewart, B.S., DeLong, R.L. and DeMaster, D.P. (1987) Diel hauling patterns and site fidelity of harbor seals (Phoca vitulina richardsi) on San Miguel Island, California, in autumn. Marine Mammal Science, 3, 323–332.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Jay M. Ver Hoef
    • 1
  • Kathryn J. Frost
    • 1
  1. 1.Alaska Department of Fish and GameFairbanksU.S.A.

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