Modeling abundance effects in distance sampling

Distance-sampling methods are commonly used in studies of animal populations to estimate population density. A common objective of such studies is to evaluate the relationship between abundance or density and covariates that describe animal habitat or other environmental influences. However, little attention has been focused on methods of modeling abundance covariate effects in conventional distance-sampling models. In this paper we propose a distance-sampling model that accommodates covariate effects on abundance. The model is based on specification of the distance-sampling likelihood at the level of the sample unit in terms of local abundance (for each sampling unit). This model is augmented with a Poisson regression model for local abundance that is parameterized in terms of available covariates. Maximum-likelihood estimation of detection and density parameters is based on the integrated likelihood, wherein local abundance is removed from the likelihood by integration. We provide an example using avian point-transect data of Ovenbirds (Seiurus aurocapillus) collected using a distance-sampling protocol and two measures of habitat structure (understory cover and basal area of overstory trees). The model yields a sensible description (positive effect of understory cover, negative effect on basal area) of the relationship between habitat and Ovenbird density that can be used to evaluate the effects of habitat management on Ovenbird populations.