Parametric distance weighting of landscape influence on streams

We present a parametric model for estimating the areas within watersheds whose land use best predicts indicators of stream ecological condition. We regress a stream response variable on the distance-weighted proportion of watershed area that has a specific land use, such as agriculture. Distance weighting functions model the declining influence of landscape elements as a function of their flowpath distances, first to the stream channel (to-stream distance), and then down the channel to the location at which stream condition was sampled (in-stream distance). Model parameters specify different distance scales over which to-stream and in-stream influences decline. As an example, we predict an index of biotic integrity (IBI) for the fish communities in 50 small streams of the Willamette Basin of Oregon, USA, from distance-weighted proportions of agricultural or urban land use in their watersheds. The weighting functions of best-fitting models (R-2 = 0.57) represent landscape influence on IBI as extending upstream tens of kilometers along the stream channel network, while declining nearly to zero beyond a distance of 30 m from the channel. Our example shows how parametric distance weighting can identify the distance scales, and hence the approximate areas within watersheds, for which land use is most strongly associated with a stream response variable. In addition, distance-weighting parameters offer a simple and direct language for comparing the scales of landscape influence on streams across different land uses and stream ecosystem components.