Spatially varying rules of landscape change: lessons from a case study

Land-cover and land-use change modeling have become increasingly common, and myriad different modeling techniques are now available. Many techniques assume that the rules of landscape change are the same everywhere within the study area, an assumption that contrasts with reality in many municipal regions, which have spatially varying development restrictions. In this paper, we provide a case study from the Raleigh–Durham area of North Carolina (USA) showing the consequences of using a model with a spatially homogeneous form when the rules of landscape change are spatially heterogeneous. Using classified Thematic Mapper images of 1990 and 2000, we fit two models relating probability of deforestation to a large set of potentially explanatory variables. Potential autocorrelation in the error term of our models was avoided by sampling outside the zone of spatial autocorrelation. The first model, a logistic regression (GLM), was used as an example of a simple, spatially homogeneous model, where the probability of deforestation is a function of a set of explanatory variables. The second model was a classification and regression tree analysis (CART), a spatially heterogeneous model in which the data were recursively partitioned on the same explanatory variables plus spatially explicit indicator variables, to create a binary decision tree that adequately captured the pattern in deforestation. Overall, the CART model (15.2% misclassification rate) performed significantly better than the GLM model (33.1% misclassification rate). When the residuals of both models were examined spatially, the CART model appears to perform better, more accurately predicting hotspots of development and predicting the baseline proportion of deforested pixels more accurately. Our results lend support to the importance of spatial heterogeneity in the rules of landscape change, and suggest that models that attend local variability in the forces driving landscape change can provide more useful predictions than models that assume these forces operate similarly throughout the landscape.