Linking individual-tree and whole-stand models for forest growth and yield prediction

Forest Ecosystems

Table 3 Stand-level and tree-level evaluation statistics for three methods

Statistic^1/	Unadjusted tree model	Disaggregation method	Combination method
Stand level
Stand density (trees/ha)
MD	28.1	*−3.5* ^2/	4.1
MAD	176.1	*148.8*	149.4
FI	0.765	0.825	*0.830*
Stand basal area (m²/ha)
MD	2.05	*0.06*	1.89
MAD	3.99	*2.17*	3.87
FI	0.676	*0.862*	0.699
Tree level
Tree survival probability
MD	0.019	*−0.014*	0.019
MAD	0.239	*0.206*	0.239
−2ln(L)	5167	*4615*	4976
Tree diameter (cm)
MD	0.16	*−0.13*	0.27
MAD	0.94	*0.84*	1.03
FI	0.939	*0.952*	0.927

^1/ Notations:
MD = $\sum (y_{i} - {\hat{y}}_{i}) / n$ ; MAD = $\sum |y_{i} - {\hat{y}}_{i}| / n$ ; FI = $\sum {(y_{i} - {\hat{y}}_{i})}^{2} / {(y_{i} - \bar{y})}^{2}$ ; − 2 ln(L) = − 2[∑p _i ln(p _i) + ∑(1 − p _i)ln(1 − p _i)], where y _i and ${\hat{y}}_{i}$ = observed and predicted values at the end of the growth period of stand variables (stand survival and basal area) or tree variables (tree diameter and survival probability); $\bar{y}$ = average of y _i; n = number of observations, and p _i = predicted survival probability of tree i.
^2/ For each evaluation statistic, the bold italic number denotes the best among three methods.