New methods for quantifying the effects of catchment spatial patterns on aquatic responses

Context Previous studies developed distance-weighted regression to describe how land use effects on aquatic systems attenuate with arrangement of source areas within catchments. Objectives We clarify and extend the conceptual foundations of this approach, enhance the spatial and statistical methods, and provide new tools to interpret the results. Methods We derive the framework from first principles to resolve conceptual issues with how weighting is applied to source area versus total area, and we formalize the requirements for an ideal weighting function. We quantify the spatial distributions of land areas in a way that integrates with model fitting. We adapt non-linear optimization to simultaneously fit regression and weighting parameters. We quantify the spatial distribution of source effects with arrangement and document how different weighting functions alter that distribution. Results To verify their utility, we applied these methods to a published analysis relating polychlorinated biphenyls in fish to developed land use in catchments. We identified a stronger distance-weighted model and more completely characterized the effects of weighting on where aquatic impacts originate. Conclusions Our methods enable more comprehensive analyses of the effects of spatial arrangement to better inform a wide range of scientific investigations and applications. Our methods can relate almost any spatially distributed source or driver to an integrated response at a point or along a boundary; and alternate hypotheses about the effects of pattern or proximity on processes can be tested with alternative weighting functions. New applications will generate additional weighting functions that enhance the general approach.