Table 4. Multiple regression spatial mixed models of the slopes of SARs (a) with, and (b) without species richness as a predictor. All predictor variables, except the rate of increase in habitat heterogeneity, are measured at the 10km scale. 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 (that with the smallest AIC). Model weights are provided in brackets and represent the probability that the model provides the best fit to the data out of those created. We provide each best fitting model until a cumulative model weight of 0.9 is achieved and this set of models represents the best candidate set of models (Johnson and Omland 2004). Parameter estimates for the intercept and predictor variables are provided. Note that r^{2} values cannot be calculated from these spatial models, but are reported for nonspatial equivalents solely to give an indication of explanatory power. We provide both the model r^{2} value and partial r^{2} values for each predictor, the latter being in square brackets.
(a)


response 
intercept 
species richness 
summer temp 
annual NDVI 
rate of increase in habitat diversity 
Δ
AIC (model weight) 
model r^{2} 

z  from power SAR 
0.299 
0.002 [0.62] 
0.002 [0.01] 
0.032 [0.03] 

0.0 (0.89) 
0.893 
" 
0.306 
0.002 [0.62] 
0.003 [0.02] 
0.007 [0.03] 
0.003 [0.010] 
5.0 (0.08) 
0.899 
m  from semilog SAR 
25.402 
0.111 [0.58] 
0.076 [0.03] 
0.891 [0.002] 

0.0 (0.70) 
0.889 
" 
25.273 
0.111 [0.57] 
0.068 [0.03] 
0.878 [0.004] 
+0.057 [0.002] 
2.5 (0.20) 
0.891 


(b)


response 
intercept 
summer temp 
annual NDVI 
rate of increase in habitat diversity 
log_{10} human density 
Δ
AIC (model weight) 
model r^{2} 

z  from power SAR 
0.308 
0.012 [0.152] 
0.054 [0.025] 
+0.032 [0.011] 

0.0 (0.91) 
0.284 
m  from semilog SAR 
26.347 
0.832 [0.183] 
2.118 [0.013] 
+2.413 [0.018] 

0.0 (0.76) 
0.325 
" 
26.541 
0.856 [0.048] 
2.051 [0.014] 
+2.465 [0.010] 
0.057 [0.007] 
2.8 (0.19) 
0.332 


