Table 1.

Parameters from linear and generalized additive models associating mean annual rain days with mean percentage tree cover measured at each of the 12 spatial scales, for all of the climate stations in the dataset. The partial regression coefficient (±s.e.) associating rainfall with tree cover is shown; for linear models only so too is the R² of the model. Bold type indicates the scale at which the largest value of a particular parameter was observed. Linear models were of the form RAIN=TC+LLA1+LLA2+LLA3, where RAIN is log(mean annual rain days), TC is arcsine square root transformed percentage tree cover and LLA1–3 are the three variables generated from a PCA of longitude, latitude and altitude (see text for details). GAMs took the form RAIN=TC+s₁(LLA1)+s₂(LLA2)+s₃(LLA3), where RAIN, TC and LLA1–3 are as before, and s_i indicates an optimally derived smooth function of the variable in question (see text for details).

scale of tree cover measurement (km2)	linear model		GAM
tree cover coefficient±s.e.	model R2	tree cover coefficient±s.e.
9	0.36±0.063	0.64	0.19±0.068
25	0.40±0.069	0.64	0.22±0.076
49	0.45±0.073	0.65	0.26±0.081
81	0.50±0.076	0.66	0.30±0.086
121	0.54+0.078	0.66	0.34±0.090
225	0.58±0.081	0.67	0.37±0.097
361	0.62±0.083	0.67	0.41±0.103
625	0.66±0.087	0.67	0.46±0.112
1369	0.70±0.092	0.67	0.51±0.125a
2401	0.70±0.097	0.67	0.50±0.136a
5329	0.72±0.103	0.66	0.54±0.155
9409	0.77±0.109	0.66	0.62±0.173

^aAt these two scales only, the optimal GAM suggested a nonlinear relationship between tree cover and rainfall (i.e. the estimated degrees of freedom for the tree cover parameter were greater than 1). However, EDFs did not greatly exceed 1, and models in which tree cover was included as a linear predictor did not have a significantly higher residual deviance than models which included the optimal smooth function of tree cover (F-test of deviance, p>0.05 in both cases). The coefficient from GAMs in which tree cover was included as a linear predictor is therefore shown for all scales.