Addition of site index to the variables of equation 2 further raised the amount 

 of variation accounted for to 80.3 percent (equation 1, table 1). With the exception 

 of tree age, none of the other basic variables mentioned contributed appreciably to 

 explained variation when in multiple regression with the variables presented 'in 

 equations 1 and 2. Equations 1 and 2 are usable for future growth prediction in un- 

 managed stand situations. We also believe that equations 1 and 2 may be applied in 

 managed stands as an interim guide under conditions where changes resulting from 

 treatment or natural causes w£uld be reflected in corresponding changes in measured 

 values of d.b.h., CCF, and d/D. 



Age has been shown to be a significant variable in predicting past periodic 

 diameter and volume growth of ponderosa pine (Pinus ponderosa Laws.) (Lemmon and 

 Schumacher 1962) and past volume growth of lodgepole pine stands (Dahms 1966) . To 

 assess the effect of tree age on prediction of future basal area growth of individual 

 lodgepole pine trees, the reciprocal of tree age at breast height was added to the 

 variables involved in equations 1 and 2 of table 1. Equation 4, table 1, shows that an 

 additional 6.7 percent of variation is accounted for by the inclusion of tree age with 

 the variables of equation 2; but equation 3 reveals that the further inclusion of site 

 index only accounts for an additional 0.3 percent of variation. It is interesting to 

 compare this small addition to the 3.9 percent increase in explained variation that is 

 accounted for by site index in the presence of the same variables without age as shown 

 for equations 1 and 2. Apparently, in these undisturbed stands, d.b.h. and age in- 

 directly represent the influence of site index on diameter gro\rth to an extent that 

 further inclusion of site index itself has little additional value in predicting basal 

 area growth of individual trees. Lemmon and Schumacher (1962) reported a similar effect 

 in regard to diameter growth prediction of ponderosa pine trees. Subsequent elimination 

 of both site index and elevation from the equations including age resulted in a very 

 small reduction in variation explained, as shown by equation 5, table 1, in comparison 

 to equation 3. Hence, if age is to be measured, equation 5 gives virtually the same 

 accuracy in prediction of basal area growth as do equations requiring the additional 

 measurement of site index and elevation. 



The usefulness of prediction equations containing age is limited by two factors. 

 First, by the practical consideration of whether the value of the 2.6 percent increase 

 in explained variation (equation 5 versus equation 1) offsets the additional expense 

 of increment boring to obtain tree age. Second, tree age in the presence of d.b.h. 

 indirectly functions as a past diameter growth rate and can be expected to be highly 

 corrolutod with future growth rate unless stand growing conditions change significantly. 

 Since a common objective of management is to increase growth rates, obviously the past 

 growth rate implied by d.b.h. and tree age will not be representative of that expected 

 to follow cultural operations. Accordingly, we do not recommend using these prediction 

 equations involving age in disturbed stands, because no such stands were included in 

 our data, and we doubt that the influence of age would be independent of past treatment. 



In view of the high percentage of accounted-for variation, the reduction in 

 increment boring, and its application to both managed and unmanaged stand situations, 

 equation 1 seems most practical for predicting future basal area growth of lodgepole 

 pine trees. 



6 



