Advertisement

Bayesian Clustering of Animal Abundance Trends for Inference and Dimension Reduction

  • Devin S. Johnson
  • Rolf R. Ream
  • Rod G. Towell
  • Michael T. Williams
  • Juan D. Leon Guerrero
Article

Abstract

We consider a model-based clustering approach to examining abundance trends in a metapopulation. When examining trends for an animal population with management goals in mind one is often interested in those segments of the population that behave similarly to one another with respect to abundance. Our proposed trend analysis incorporates a clustering method that is an extension of the classic Chinese Restaurant Process, and the associated Dirichlet process prior, which allows for inclusion of distance covariates between sites. This approach has two main benefits: (1) nonparametric spatial association of trends and (2) reduced dimension of the spatio-temporal trend process. We present a transdimensional Gibbs sampler for making Bayesian inference that is efficient in the sense that all of the full conditionals can be directly sampled from save one. To demonstrate the proposed method we examine long term trends in northern fur seal pup production at 19 rookeries in the Pribilof Islands, Alaska. There was strong evidence that clustering of similar year-to-year deviation from linear trends was associated with whether rookeries were located on the same island. Clustering of local linear trends did not seem to be strongly associated with any of the distance covariates. In the fur seal trends analysis an overwhelming proportion of the MCMC iterations produced a 73–79 % reduction in the dimension of the spatio-temporal trend process, depending on the number of cluster groups.

Key Words

Distance-dependent Chinese restaurant process Gaussian Markov random fields Ecological trends Northern fur seal Model-based clustering Dirichlet process prior Spatio-temporal model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Blei, D. M., and Frazier, P. I. (2011), “Distance Dependent Chinese Restaurant Processes,” Journal of Machine Learning Research, 12, 2461–2488. MathSciNetGoogle Scholar
  2. Call, K. A., Ream, R. R., Johnson, D., Sterling, J. T., and Towell, R. G. (2008), “Foraging Route Tactics and Site Fidelity of Adult Female Northern fur Seal (Callorhinus Ursinus) Around the Pribilof Islands,” Deep-Sea Research. Part 2. Topical Studies in Oceanography, 55, 1883–1896. CrossRefGoogle Scholar
  3. Chapman, D. G., and Johnson, A. M. (1968), “Estimation of fur Seal Pup Populations by Randomized Sampling,” Transactions of the American Fisheries Society, 97 (3), 264–270. CrossRefGoogle Scholar
  4. Dorazio, R. M. (2009), “On Selecting a Prior for the Precision Parameter of Dirichlet Process Mixture Models,” Journal of Statistical Planning and Inference, 139 (9), 3384–3390. MathSciNetCrossRefzbMATHGoogle Scholar
  5. Dorazio, R. M., Mukherjee, B., Zhang, L., Ghosh, M., Jelks, H. L., and Jordan, F. (2008), “Modeling Unobserved Sources of Heterogeneity in Animal Abundance Using a Dirichlet Process Prior,” Biometrics, 64 (2), 635–644. MathSciNetCrossRefzbMATHGoogle Scholar
  6. Escobar, M., and West, M. (1995), “Bayesian Density-Estimation and Inference Using Mixtures,” Journal of the American Statistical Association, 90 (430), 577–588. MathSciNetCrossRefzbMATHGoogle Scholar
  7. Ferguson, T. S. (1973), “A Bayesian Analysis of Some Nonparametric Problems,” The Annals of Statistics, 1, 209–230. MathSciNetCrossRefzbMATHGoogle Scholar
  8. Gentry, R. L. (1998), Behavior and Ecology of the Northern fur Seal, Princeton: Princeton University Press. Google Scholar
  9. Johnson, D. S., and Hoeting, J. A. (2011), “Bayesian Multimodel Inference for Geostatistical Regression Models,” PLoS ONE, 6 (11), e25677. CrossRefGoogle Scholar
  10. MacEachern, S., and Muller, P. (1998), “Estimating Mixture of Dirichlet Process Models,” Journal of Computational and Graphical Statistics, 7 (2), 223–238. Google Scholar
  11. Muller, P., and Quintana, F. A. (2004), “Nonparametric Bayesian Data Analysis,” Statistical Science, 19, 95–110. MathSciNetCrossRefGoogle Scholar
  12. Neal, R. (2000), “Markov Chain Sampling Methods for Dirichlet Process Mixture,” Journal of Computational and Graphical Statistics, 9 (2), 249–265. MathSciNetGoogle Scholar
  13. Pitman, J. (2006), Combinatorial Stochastic Processes, Berlin: Springer. zbMATHGoogle Scholar
  14. (R Core Team) (2012), R: A Language and Environment for Statistical Computing, Vienna: R Foundation for Statistical Computing. ISBN:3-900051-07-0 Google Scholar
  15. Ross, B. E., Hooten, M. B., and Koons, D. N. (2012), “An Accessible Method for Implementing Hierarchical Models with Spatio-Temporal Abundance Data,” PLoS ONE, 7, e49395. CrossRefGoogle Scholar
  16. Royle, J. A., and Dorazio, R. M. (2008), Hierarchical Modeling and Inference in Ecology, San Diego: Academic Press-Elsevier. Google Scholar
  17. Rue, H., and Held, L. (2005), Gaussian Markov Random Fields: Theory and Applications. Monographs on Statistics and Applied Probability, Vol. 104, London: Chapman & Hall. CrossRefGoogle Scholar
  18. Stein, M. L. (2005), “Space-Time Covariance Functions,” Journal of the American Statistical Association, 100 (469), 310–321. MathSciNetCrossRefzbMATHGoogle Scholar
  19. Towell, R., Ream, R., and York, A. (2006), “Decline in Northern fur Seal (Callorhinus Ursinus) Pup Production on the Pribilof Islands,” Marine Mammal Science, 22 (2), 486–491. CrossRefGoogle Scholar
  20. Ward, E. J., Chirakkal, H., Gonzalez-Suarez, M., Aurioles-Gamboa, D., Holmes, E. E., and Gerber, L. (2010), “Inferring Spatial Structure from Time-Series Data: Using Multivariate State-Space Models to Detect Metapopulation Structure of California Sea Lions in the Gulf of California, Mexico,” Journal of Applied Ecology, 47 (1), 47–56. CrossRefGoogle Scholar
  21. York, A., and Kozloff, P. (1987), “On the Estimation of the Numbers of Northern fur Seal, Callorhinus Ursinus Pups Born on St. Paul Island, 1980–86,” Fisheries Bulletin, 85, 367–375. Google Scholar
  22. Zeppelin, T. K., and Ream, R. R. (2006), “Foraging Habitats Based on the Diet of Female Northern fur Seals (Callorhinus Ursinus) on the Pribilof Islands, Alaska,” Journal of Zoology, 270 (4), 565–576. CrossRefGoogle Scholar

Copyright information

© International Biometric Society 2013

Authors and Affiliations

  • Devin S. Johnson
    • 1
  • Rolf R. Ream
    • 1
  • Rod G. Towell
    • 1
  • Michael T. Williams
    • 2
  • Juan D. Leon Guerrero
    • 2
  1. 1.National Marine Mammal LaboratoryNOAA National Marine Fisheries ServiceSeattleUSA
  2. 2.Alaska RegionNOAA National Marine Fisheries ServiceAnchorageUSA

Personalised recommendations