Advantages of Geographically Weighted Regression for Modeling Benthic Substrate in Two Greater Yellowstone Ecosystem Streams

Stream habitat assessments are commonplace in fish management, and often involve nonspatial analysis methods for quantifying or predicting habitat, such as ordinary least squares regression (OLS). Spatial relationships, however, often exist among stream habitat variables. For example, water depth, water velocity, and benthic substrate sizes within streams are often spatially correlated and may exhibit spatial nonstationarity or inconsistency in geographic space. Thus, analysis methods should address spatial relationships within habitat datasets. In this study, OLS and a recently developed method, geographically weighted regression (GWR), were used to model benthic substrate from water depth and water velocity data at two stream sites within the Greater Yellowstone Ecosystem. For data collection, each site was represented by a grid of 0.1 m² cells, where actual values of water depth, water velocity, and benthic substrate class were measured for each cell. Accuracies of regressed substrate class data by OLS and GWR methods were calculated by comparing maps, parameter estimates, and determination coefficient r ². For analysis of data from both sites, Akaike’s Information Criterion corrected for sample size indicated the best approximating model for the data resulted from GWR and not from OLS. Adjusted r ² values also supported GWR as a better approach than OLS for prediction of substrate. This study supports GWR (a spatial analysis approach) over nonspatial OLS methods for prediction of habitat for stream habitat assessments.