A Monte Carlo appraisal of plot and distance sampling for surveys of black grouse and rock ptarmigan populations in alpine protected areas

We used distance sampling to assess density and the detectability of male black grouse (Tetrao tetrix) and rock ptarmigan (Lagopus muta) in 2 protected areas of the Italian Alps. Our sampling effort was not sufficient to provide reliable inference for monitoring projects. Therefore, we used our field results to structure a simulation study to compare the performance of plot-based and distance sampling estimators of density. These 2 methods have different assumptions: plot sampling assumes a perfect detection of animals within the surveyed plots, whereas distance sampling assumes a decrease in detectability as the distance between observer and animal increases. The density and the detectability conditions adopted in the simulation were designed to be similar to those observed in our 2 studies, whereas the spatial patterns presumed for the simulated populations described a wide range of possible scenarios. Sampling points were allocated according to both random and stratified distributions. Simulation results showed that plot sampling underestimated density with bias invariably greater than 30% and confidence intervals with coverage lower than the nominal level of 95%. Conversely, distance sampling estimators provided bias levels invariably smaller than those obtained using plot sampling and bootstrap confidence intervals with empirical coverage near to or greater than 95%. Based on our simulations, the distance sampling estimator was superior to the plot sampling estimator for these grouse species on our study areas in terms of precision and accuracy and the stratified allocation was superior to the random allocation. However, distance sampling would be very costly to implement. Based on our simulations, 4-5 points per km2 would be necessary to achieve reliable estimates of density and density changes. If distance sampling cannot be completed at this intensity, other sampling methods should be adopted.