Incorporating spatial non-stationarity of regression coefficients into predictive vegetation models

The results of predictive vegetation models are often presented spatially as GIS-derived surfaces of vegetation attributes across a landscape or region, but spatial information is rarely included in the model itself. Geographically weighted regression (GWR), which extends the traditional regression framework by allowing regression coefficients to vary for individual locations ('spatial non-stationarity'), is one method of utilizing spatial information to improve the predictive power of such models. In this paper, we compare the ability of GWR, a local model, with that of ordinary least-squares (OLS) regression, a global model, to predict patterns of montane ponderosa pine (Pinus ponderosa) basal area in Saguaro National Park, AZ, USA on the basis of variables related to topography (elevation, slope steepness, aspect) and fire history (fire frequency, time since fire). The localized regression coefficients exhibited significant non-stationarity for four of the five environmental variables, and the GWR model consequently described the vegetation-environment data significantly better, even after accounting for differences in model complexity. GWR also reduced observed spatial autocorrelation of the model residuals. When applied to independent data locations not used in model development, basal areas predicted by GWR had a closer fit to observed values with lower residuals than those from the optimal OLS regression model. GWR also provided insights into fine-scale controls of ponderosa pine pattern that were missed by the global model. For example, the relationship between ponderosa pine basal area and aspect, which was obscured in the OLS regression model due to non-stationarity, was clearly demonstrated by the GWR model. We thus see GWR as a valuable complement to the many other global methods currently in use for predictive vegetation modeling.