Improving distance sampling: accounting for covariates and non‐independency between sampled sites

Abstract

Summary1. 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.

Maintained effects of fire on individual growth and survival rates in a spur-thighed tortoise population

“…This method employs the mean of a size distribution and S ∞ calculated previously (see ESM 2). We used a bootstrap to calculate the confidence interval (as in Oedekoven et al 2013) and a t test to calculate the difference.…”

Management factors affecting densities of common grassland birds of high elevation grasslands of eastern South Africa: Ingula as a case study

“…Furthermore, the detection probability varies across methods and different observers, changes with habitats and weather conditions (Petitot et al 2014). Hierarchical distance-sampling methods account for the detection process and are therefore commonly used to study animal density (Marques et al 2007;Oedekoven et al 2013). Improvements in distance sampling allow for the incorporation of environmental and habitat variables to fully explore variation in density of species across sites (Royle et al 2004; Thomas et al 2010).…”

Model-Based Distance Sampling

“…For example, if there are multiple lines or points within a plot or site, then a site random effect allows for spatial correlation in the observations; similarly, if there are repeat counts at any given location, we might allow for temporal correlation using random effects (Oedekoven et al 2013(Oedekoven et al , 2014. A further reason to consider random effects is if there is heterogeneity in the detection probabilities that is not modelled by the available covariates (Oedekoven et al 2015).…”

“…A significant interaction was detected between treatment (control or burning) and year, indicating strong evidence of reduced warbler densities in the year after burning, with moderate evidence of continuing lower densities a year later. Oedekoven et al (2013) considered a point transect experiment, to assess whether conservation buffers along field margins increased densities of indigo buntings in the United States. Many of the sampled sites were in common between the bunting survey and the bobwhite survey of our case study, although the bunting survey was carried out in the breeding season, while the bobwhite survey was conducted in the fall.…”

“…Royle and Dorazio (2008) also adopted this approach for line transect sampling. Plot abundance and plot count models were developed by Royle et al (2004), by Buckland et al (2009) and by Oedekoven et al (2013Oedekoven et al ( , 2014. These enabled data from designed distance sampling experiments to be analysed.…”