A Bayesian approach to analysing distance sampling data with application to large-scale experimental studies

Background/Question/Methods

Large-scale experimental studies are often needed to assess the effects of some intervention on numbers of species of conservation interest. Buckland et al. 2009 developed a two-stage approach for analysing count data from such studies. In a first step, a detection function is fitted to the distance data and the effective area estimated. In a second step, the effective area is included in a log-linear count model to adjust for imperfect detectability. A beneficial effect of the experiment would be indicated by a positive coefficient for counts on treated plots compared to untreated plots. Precision estimates are obtained using a nonparametric bootstrap.

For our Bayesian approach, we combine the likelihoods from both steps into an integrated likelihood that allows simultaneous estimation of parameters and associated precision in one step. A random effect is included in the count model to account for correlated counts between repeated measures at the same sites. A reversible Jump MCMC algorithm is used to explore model and parameter space simultaneously.

Results/Conclusions

We illustrate the method using a large-scale point-transect study of birds where the interest lies in the effect of establishing conservation buffers along field margins. The data originates from the National CP-33 Monitoring Program coordinated by the Mississippi State University, Department of Wildlife and Fisheries. Analysed data included counts of indigo buntings in 2006 and 2007 on 446 sites of paired points (one buffered and one adjacent non-buffered) that were located in nine Southeastern and Midwestern states. Highest model probabilities were scored by a hazard-rate detection function and a count model including type (buffered or not) and Julian day as covariates. Results revealed a positive effect of buffers on indigo bunting densities. A coefficient of 0.3 for type indicated that densities were on average 35% larger on buffered fields than on non-buffered fields (exp(0.3) = 1.35). Strong similarities of results from our Bayesian approach with those from a maximum likelihood approach provided validity to our newly developed methods.