Developing spatially explicit critical loads for herbaceous species across the United States using convex hulls.

Atmospheric deposition of nitrogen and sulfur, after land use change, is one of the most impactful stressors to terrestrial biodiversity. Deposition effects on ecosystems are pervasive, impacting species distributions and disrupting natural communities and associated ecosystem services. Decision makers in particular areas have in the past been limited to using critical loads from faraway research sites or from networks of plots that may or may not overlap with or represent their particular management area. That potential mismatch between the management area and available data presents scientific and possibly legal challenges. Here, we develop spatially explicit critical loads using convex hulls to fill this key knowledge gap in the translation of science to decision making. Specifically, we used convex hulls to understand how representative critical loads are to the broader landscape by comparing the environmental conditions from a set of roughly 15,000 sampled locations with critical loads to a broader landscape for which there is no direct sampling. We performed separate analyses for critical loads of forest and grassland biodiversity and of individual herbaceous species. We found that the sampled plots, though unevenly distributed across the landscape, represented forest and grassland canopy communities very well across the contiguous United States aside from areas in the Southeast and the coastal Pacific Northwest. For the 198 species assessed, 161 species (81%) had 50% or more of their historical range inside the convex hull, and 197 species (99%) had 50% or more of their historical range within 1 SD of the convex hull. These results indicate that most critical loads may be used with confidence across species' ranges to support decision making. These results also can guide future sampling efforts in strategic areas. Further, the use of convex hulls as a general tool for other efforts may greatly increase the utility of various existing datasets to support land managers and decision makers charged with protecting ecosystems.