Accounting for location uncertainty in distance sampling data

Ecologists use distance sampling to estimate the abundance of plants and animals while correcting for undetected individuals. By design, data collection is simplified by requiring only the distances from a transect to the detected individuals be recorded. Compared to traditional design-based methods that require restrictive assumption and limit the use of distance sampling data, model-based approaches enable broader applications such as spatial prediction, inferring species-habitat relationships, unbiased estimation from preferentially sampled transects, and integration into multi-type data models. Unfortunately, model-based approaches require the exact location of each detected individual in order to incorporate environmental and habitat characteristics as predictor variables. We modified model-based methods for distance sampling data by including a probability distribution that accounts for location uncertainty generated when only the distances are recorded. We tested and demonstrated our method using a simulation experiment and by modeling the habitat use of Dickcissels (Spiza americana) using distance sampling data collected from the Konza Prairie in Kansas, USA. Our results showed that ignoring location uncertainty can result in biased coefficient estimates and predictions. However, accounting for location uncertainty remedies the issue and results in reliable inference and prediction. Like other types of measurement error, hierarchical models can accommodate the data collection process thereby enabling reliable inference. Our approach is a significant advancement for the analysis of distance sampling data because it remedies the deleterious effects of location uncertainty and requires only distances be recorded. In turn, this enables historical distance sampling data sets to be compatible with modern data collection and modeling practices.