Improving distance sampling: accounting for covariates and nonindependency between sampled sites

1. There is currently much interest in replacing the design-based component of conventional distance sampling methods by a modelling approach where animal densities are related to environmental covariates. These models allow identification of relationships between density and covariates. One of the uses of such models is to assess the effects of some intervention on numbers for species of conservation interest in designed distance sampling experiments. 2. In this context, we use an integrated likelihood approach for modelling sample counts, adopting a Poisson model and allowing imperfect detectability on the sample plots. We use the method of Royle, Dawson & Bates (2004, Ecology, 85, 1591), extended to model heterogeneity in detection probabilities using either multiple covariate distance sampling methods or stratification. Moreover, we include a random effect for site in the plot abundance model to accommodate correlation in repeat counts at a single site. 3. These developments were motivated by a large-scale experimental study to assess the effects of establishing conservation buffers along field margins on indigo buntings in several US states. We analyse the data using an integrated likelihood and include model selection for both the Poisson rate of counts and detection probabilities. We assess model performance by comparing our results with those using a two-stage approach (Buckland et al. 2009, Journal of Agricultural, Biological, and Environmental Statistics, 14, 432) which we extended by including a random effect for site in the plot abundance model. 4. The two methods led to the same selected models and gave similar results for parameters, which revealed significant beneficial effects of buffers on indigo bunting densities. Densities on buffered fields were on average 35% higher than on unbuffered fields. Using a detection function stratified by state captured some of the heterogeneity in detection probabilities between the nine states included in the analyses. 5. Synthesis and applications. We develop and compare two methods for analysing data from large-scale distance sampling experiments with imbalanced repeat measures. By including a random site effect in the plot abundance model, we relax the assumption of independent sample counts which is generally made for distance sampling methods, and we allow inference to be drawn for the wider region that the sites represent.