DERIVING THE FUNCTIONAL FORM 

 FOR THE PREDICTION EQUATIONS 



A set of height/diameter curves for three even-aged stands of grand fir is shown 

 in figure 3. These curves are plotted solutions of a nonlinear equation for predicting 

 tree height from diameter, site quality, and age of the stand. Analysis of these data 

 confirmed that the allometric relation: 



ln(ff) = a + b ln(Z?) 



CD 



does indeed apply to the development of trees as age increases, but that the coefficients 

 a and b depend upon the competitive status of the trees. Competitive status can be 

 defined by the distance of the (H 3 D) point for a particular tree from the curve of 

 relation (1) for dominant trees (Perkal and Battek 1955) . The dashed line shows the 

 trend followed by the average for the dominant and codominant trees in the stand. 

 Trees in lower crown classes move more steeply upward. Conversely, dominants move 

 along lines of lower slope. 



110 r 



100 



30 



60 



40 



20 



In H = 2.447 +0.8 In D 



16 



DIAMETER (b.h. inches) 



Figure 3. Sequenae of height/ diameter curves for even-aged stands of grand fir. 



8 



