Hierarchical distance‐sampling models to estimate population size and habitat‐specific abundance of an island endemic

Population size and habitat‐specific abundance estimates are essential for conservation management. A major impediment to obtaining such estimates is that few statistical models are able to simultaneously account for both spatial variation in abundance and heterogeneity in detection probability, and still be amenable to large‐scale applications. The hierarchical distance‐sampling model of J. A. Royle, D. K. Dawson, and S. Bates provides a practical solution. Here, we extend this model to estimate habitat‐specific abundance and rangewide population size of a bird species of management concern, the Island Scrub‐Jay (Aphelocoma insularis), which occurs solely on Santa Cruz Island, California, USA. We surveyed 307 randomly selected, 300 m diameter, point locations throughout the 250‐km² island during October 2008 and April 2009. Population size was estimated to be 2267 (95% CI 1613–3007) and 1705 (1212–2369) during the fall and spring respectively, considerably lower than a previously published but statistically problematic estimate of 12 500. This large discrepancy emphasizes the importance of proper survey design and analysis for obtaining reliable information for management decisions. Jays were most abundant in low‐elevation chaparral habitat; the detection function depended primarily on the percent cover of chaparral and forest within count circles. Vegetation change on the island has been dramatic in recent decades, due to release from herbivory following the eradication of feral sheep (Ovis aries) from the majority of the island in the mid‐1980s. We applied best‐fit fall and spring models of habitat‐specific jay abundance to a vegetation map from 1985, and estimated the population size of A. insularis was 1400–1500 at that time. The 20–30% increase in the jay population suggests that the species has benefited from the recovery of native vegetation since sheep removal. Nevertheless, this jay's tiny range and small population size make it vulnerable to natural disasters and to habitat alteration related to climate change. Our results demonstrate that hierarchical distance‐sampling models hold promise for estimating population size and spatial density variation at large scales. Our statistical methods have been incorporated into the R package unmarked to facilitate their use by animal ecologists, and we provide annotated code in the Supplement.