Bayesian Methods for Hierarchical Distance Sampling Models
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The few distance sampling studies that use Bayesian methods typically consider only line transect sampling with a half-normal detection function. We present a Bayesian approach to analyse distance sampling data applicable to line and point transects, exact and interval distance data and any detection function possibly including covariates affecting detection probabilities. We use an integrated likelihood which combines the detection and density models. For the latter, densities are related to covariates in a log-linear mixed effect Poisson model which accommodates correlated counts. We use a Metropolis-Hastings algorithm for updating parameters and a reversible jump algorithm to include model selection for both the detection function and density models. The approach is applied to a large-scale experimental design study of northern bobwhite coveys where the interest was to assess the effect of establishing herbaceous buffers around agricultural fields in several states in the US on bird densities. Results were compared with those from an existing maximum likelihood approach that analyses the detection and density models in two stages. Both methods revealed an increase of covey densities on buffered fields. Our approach gave estimates with higher precision even though it does not condition on a known detection function for the density model.
Key WordsDesigned experiments Hazard-rate detection function Heterogeneity in detection probabilities Metropolis–Hastings update Point transect sampling RJMCMC
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- Bates, D. (2009a), “Adaptive Gauss–Hermite Quadrature for Generalized Linear or Nonlinear Mixed Models. R Package Version 0.999375-31,” Technical Report. http://lme4.r-forge.r-project.org/. Google Scholar
- Bates, D. (2009b), “Computational Methods for Mixed Models. R Package Version 0.999375-31,” Technical Report. http://lme4.r-forge.r-project.org/. Google Scholar
- Cañadas, A., and Hammond, P. S. (2006), “Model-Based Abundance Estimates for Bottlenose Dolphins off Southern Spain: Implications for Conservation and Management,” Journal of Cetacean Research and Management, 8 (1), 13–27. Google Scholar
- Chelgren, N. D., Samora, B., Adams, M. J., and McCreary, B. (2011), “Using Spatiotemporal Models and Distance Sampling to Map the Space Use and Abundance of Newly Metamorphosed Western Toads (Anaxyrus Boreas),” Herpetological Conservation and Biology, 6 (2), 175–190. Google Scholar
- Gelman, A., Roberts, G. O., and Gilks, W. R. (1996), “Efficient Metropolis Jumping Rules,” in Bayesian Statistics, Vol. 5, eds. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Oxford: Oxford University Press, pp. 599–608. Google Scholar
- Gimenez, O., Bonner, S. J., King, R., Parker, R. A., Brooks, S. P., Jamieson, L. E., Grosbois, V., Morgan, B. J. T., and Thomas, L. (2009), “WinBUGS for Population Ecologists: Bayesian Modeling Using Markov Chain Monte Carlo Methods,” in Modeling Demographic Processes in Marked Populations. Environmental and Ecological Statistics, Vol. 3, eds. D. L. Thomson, E. G. Cooch, and M. J. Conroy, Berlin: Springer, pp. 883–915. CrossRefGoogle Scholar
- King, R., Morgan, B. J. T., Gimenez, O., and Brooks, S. P. (2010), Bayesian Analysis for Population Ecology, London/Boca Raton: Chapman & Hall/CRC Press. Google Scholar
- Marcot, B. G., Holthausen, R. S., Raphael, M. G., Rowland, M. M., and Wisdom, M. J. (2001), “Using Bayesian Belief Networks to Evaluate Fish and Wildlife Population Viability Under Land Management Alternatives from an Environmental Impact Statement,” Forest Ecology and Management, 153, 29–42. CrossRefGoogle Scholar
- Royle, J. A., and Dorazio, R. M. (2008), Hierarchical Modeling and Inference in Ecology: The Analysis of Data from Populations, Metapopulations and Communities, San Diego: Academic Press. Google Scholar
- Thomas, L., Buckland, S. T., Rexstad, E. A., Laake, J. L., Strindberg, S., Hedley, S. L., Bishop, J. R. B., Marques, T. A., and Burnham, K. P. (2010), “Distance Software: Design and Analysis of Distance Sampling Surveys for Estimating Population Size,” Journal of Applied Ecology, 47, 5–14. CrossRefGoogle Scholar