Table 3. Relationships in spatial mixed models between the rate at which habitat diversity, measured with a broad habitat classification, increases with area from 10 km to 290 km quadrats and log10 transformed human population density using linear, square, and cubic terms of the latter. Two sets of analyses were conducted using predictors measured at either the 10 km or the 290 km spatial grain. Model fit is measured by Akaike Information Criteria (AIC), and here we report ΔAIC values, i.e., the difference between the focal model’s AIC and that of the best fitting model, i.e., that with the smallest AIC. Model weights are provided in brackets and represent the probability that the model provides the most parsimonious fit to the data out of those created. Following Johnson and Omland (2004) we present the best set of competing models, i.e., that with a cumulative model weight of 0.9. Parameter estimates for the intercept and predictor variables are provided, with positive and negative effects indicated by + and – respectively. Note that r² values cannot be calculated from these spatial models, but are reported for nonspatial equivalents solely to give an indication of explanatory power. Spatial grain Intercept Log10 human density Log10 human density² Δ AIC (model weight) model r² 10 km 0.574 -0.282 +0.040 0.0 (0.900) 0.02 290 km 0.162 +0.044 0.0 (0.544) 0.01 " -0.405 +0.728 -0.185 1.1 (0.314) 0.01