Accounting for animal density gradients using independent information in distance sampling surveys

Distance sampling is extensively used for estimating animal density or abundance. Conventional methods assume that location of line or point transects is random with respect to the animal population, yet transects are often placed along linear features such as roads, rivers or shorelines that do not randomly sample the study region, resulting in biased estimates of abundance. If it is possible to collect additional data that allow an animal density gradient with respect to the transects to be modelled, we show how to extend the conventional distance sampling likelihood to give asymptotically unbiased estimates of density for the covered area. We illustrate the proposed methods using data for a kangaroo population surveyed by line transects laid along tracks, for which the true density is known from an independent source, and the density gradient with respect to the tracks is estimated from a sample of GPS collared animals. For this example, density of animals increases with distance from the tracks, so that detection probability is overestimated and density underestimated if the non-random location of transects is ignored. When we account for the density gradient, there is no evidence of bias in the abundance estimate. We end with a list of practical recommendations to investigators conducting distance sampling surveys where density gradients could be an issue.