Abundance estimation from point counts when replication is spatially intensive but temporally limited: comparing binomial N-mixture and hierarchical distance sampling models

We investigated the performance of hierarchical distance sampling (HDS) versus binomial N-mixture (binmix) models, both aiming at abundance (or, equivalently, density) estimation. We tested the accuracy of density estimates using simulated data and compared them to the estimates coming from a Red-breasted Flycatcher (Ficedula parva) point count survey in the Darilubie Forest (N Poland). In both the simulations and the actual data, we mimicked varying plot size (i.e., radius length, and site area) and song loudness from quiet to loud by modifying detection functions. We found that the resolution at which distance detection data are collected (i.e., the number and width of distance classes) had essentially no effect on estimates and their precision in HDS, even when birds were only assigned into two, wide distance classes, such as close and far. Both site size (radius length) and song loudness affected density estimates in HDS only slightly: a positive bias (by 5%-l7%) occurred when sites were small and a lower precision occurred for quiet singers. In general, however, estimates from HDS were accurate. In contrast, under binmix, density was heavily overestimated at smaller sites, but apparently correct at large sites. The latter may stem from the counterbalancing effects of overestimation at close distances and underestimation at large distances that cancel each other out on average. both of which are a function of song loudness and arise always when the observer is stationary. When applied to point count results, binmix models must be used with care, as the song loudness in relation to site size seems to affect abundance estimates. We suggest that when density (or population size) estimation is of interest, and with a limited number of visits, a study using point counts would profit from applying HDS models by using additional information on detection distances, even at low resolution. This cost-effective option represents an attractive alternative to be considered vs. simpler counts during which just the number of birds is noted.