Accounting for non-random samples with distance sampling to estimate population density

1. A critical assumption of standard distance sampling is that sampling lines are located such that animals are uniformly distributed as a function of distance from the line. Failure to meet this assumption can introduce bias in the estimator.
2. Many studies have used landscape features, such as roads or rivers, as lines, which can violate assumptions of distance sampling in two ways. First, animals may be attracted or repelled by the landscape feature due to human activity (e.g. along roads) or habitat characteristics associated with the feature (e.g. rivers). Second, sampling along landscape features may not be representative of the larger area of interest.
3. We used auxiliary data to generalize the distance sampling estimator and relax assumptions of a uniform distribution of animals relative to distance from the line (i.e. density gradient) and to allow the distribution of animals to differ by habitat type. The generalized estimator provides unbiased estimates of density within the area sampled but may not be representative of the study area.
4. To address the problem of landscape features providing unrepresentative sampling, we used a resource selection model to estimate the proportion of the population that occurred within the surveyed area to obtain an estimate of abundance for the desired area of inference.
5. We demonstrate our modified distance sampling estimator using white-tailed deer (Odocoileus virginianus) in a 972-km2 study area. We conducted infrared surveys of deer from roads to collect distance-to-transect data. We used locations of radio-collared deer to model the distribution of deer relative to the transects and to develop a resource selection model of deer based on distance to roads, habitat type, elevation and slope to account for roads being a non-representative sample of the study area.
6. Synthesis and applications. When using landscape features as survey lines, the density gradient and deer distribution can introduce either positive or negative bias, which makes it impossible to assess the bias introduced without auxiliary data. The estimator we developed can improve precision because we obtained a better fit to distance observations and accounts for non-random placement of transects with minimal loss of precision.