Bayesian Clustering of Animal Abundance Trends for Inference and Dimension Reduction
- 247 Downloads
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 WordsDistance-dependent Chinese restaurant process Gaussian Markov random fields Ecological trends Northern fur seal Model-based clustering Dirichlet process prior Spatio-temporal model
Unable to display preview. Download preview PDF.
- 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
- Gentry, R. L. (1998), Behavior and Ecology of the Northern fur Seal, Princeton: Princeton University Press. Google Scholar
- MacEachern, S., and Muller, P. (1998), “Estimating Mixture of Dirichlet Process Models,” Journal of Computational and Graphical Statistics, 7 (2), 223–238. Google Scholar
- (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
- Royle, J. A., and Dorazio, R. M. (2008), Hierarchical Modeling and Inference in Ecology, San Diego: Academic Press-Elsevier. Google Scholar
- 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
- 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