Accounting for spatial habitat and management boundaries when estimating forest bird population distribution and density: inferences from a soap film smoother

Birds are often obligate to specific habitats which can result in study areas with complex boundaries due to sudden changes in vegetation or other features. This can result in study areas with concave arcs or that include holes of unsuitable habitat such as lakes or agricultural fields. Spatial models used to produce species' distribution and density estimates need to respect such boundaries to make informed decisions for species conservation and management. The soap film smoother is one model for complex study regions which controls the boundary behaviour, ensuring realistic values at the edges of the region. We apply the soap film smoother to account for boundary effects and compare it with thin plate regression spline (TPRS) smooth and design-based conventional distance sampling methods to produce abundance estimates from point-transect distance sampling collected data on Hawai'i 'Akepa Loxops coccineus in the Hakalau Forest Unit of the Big Island National Wildlife Refuge Complex, Hawai'i Island, USA. The soap film smoother predicted zero or near zero densities in the northern part of the domain and two hotspots (in the southern and central parts of the domain). Along the boundary the soap film model predicted relatively high densities where 'Akepa occur in the adjacent forest and near zero elsewhere. The design-based and soap film abundance estimates were nearly identical. The width of the soap film confidence interval was 16.5% and 0.8% wider than the width of the TPRS smooth and design-based confidence intervals, respectively. The peaks in predicted densities along the boundary indicates leakage by the TPRS smooth. We provide a discussion of the statistical methods, biological findings and management implications of applying soap film smoothers to estimate forest bird population status.