Table 2 Performance of models when applied to data not used in model fitting

Model	Cross-validation (interpolation)			Spatial cross-validation (extrapolation)
	RMSE	Correlation	Coefficient of determination	RMSE	Correlation	Coefficient of determination
Dataset	0.105	0.011	−1.091	0.105	0.061	−1.574
RF - spatial	0.051	0.749	0.536	0.069	0.055	−0.192
RF – environment	0.051	0.736	0.539	0.077	0.132	−0.449
RF – both	0.049	0.755	0.567	0.070	0.153	−0.253
GAM – spatial	0.054	0.701	0.480	0.081	0.149	−0.809
GAM – environment	0.057	0.618	0.369	0.070	0.212	−0.515
GAM – both	0.053	0.704	0.474	0.071	0.219	−0.388
Ensemble	0.049	0.759	0.567	0.068	0.272	−0.132

Model performance has been assessed using k-fold cross-validation (presumed to reflect interpolation performance) and spatial cross-validation (where an entire region was removed for model testing, presumed to reflect extrapolation performance).
Model performance has been assessed as (1) root mean square error (RMSE), which indicates the average prediction error (g cm^-3), (2) the correlation coefficient between observed and predicted values and (3) the coefficient of determination [1-(residual sum of squares/ total sum of squares)]. Negative coefficient of determination values indicate that the difference between model predictions and the testing data are greater than the difference between the testing data mean and the testing data. Median values across cross-validation folds are presented.

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