Modelling within-field spatial variability of crop biomass - weed density relationships using geographically weighted regression

The objective of this study is to offer a new framework for exploring and modelling the spatial variation in crop biomass - weed density relationships, adapting geographically weighted regression (GWR) to include a non-linear regression model. The relationship between crop biomass and weed density is usually modelled by non-linear regression models, in which the spatial heterogeneity of the relationship is ignored, although the effect of weeds on crop can differ in relation to topographic and edaphic variability. GWR attempts to capture spatial variability by calibrating a regression model to each location in space. We show the application of the method in different cereal cropping systems, with one or two weed species. The results indicate that GWR can significantly improve model fitting over non-linear least squares (NLS) in some situations. Furthermore, the parameter estimates can be mapped to illustrate local spatial variations in the regression relationship under study and eventually to relate the spatial variability of the model to the environmental heterogeneity. We discuss the value of the GWR for analysing the observed spatial variability and for improving model development and our understanding of spatial processes.