Linearizing this function gives: 

 c 



Generalizing this function further to provide for an even wider range of potential model forms: 

 Jn(y) = bQ + biln x + b2X , i'2<0 



Therefore, the inclusion of In(D) and D in the log of basal area growth model would 

 allow for a wider range of "peaking" functions. The values of c chosen were 1, 1.5, 2, 2.5, 

 3, 3.5, and 4. These values cover a wide range of forms from the Weibull function (Bailey and 

 Dell 1973) . 



The measure of productivity in this study is Minor's (1964) site index. It is expected 

 that, when site index (S) is zero, growth would be zero, and, as site increases, growth would 

 also increase. To model this effect, the proposed independent variable is the log of site 

 index, in other words, ln(S) . This choice of independent variable is supported by the findings 

 of Cole and Stage (1972). 



Because of the findings of Fritts and others (1965) and Pearson and Wadsworth (1941), I 

 decided to express precipitation in two fashions: average annual 5-year growth period rainfall 

 (GRF) , and average annual 5-year rainfall (ARF) . Growth period rainfall is defined as the 

 rain that fell in the interval from September through May previous to the given growing period. 

 Based on a reasoning similar to that for site index, I decided that the log of GRF and the log 

 of ARF were the appropriate independent variables. 



There are several different expressions of total stand density, including the following: 

 total stand basal area per acre (BA) , total number of trees per acre (T) , and crown competition 

 factor (CCF) (Larson and Minor 1968) . In all cases, growth should maximize when the stand 

 density values are near zero, and growth should decline as the values increase. An appropriate 

 form for modeling this behavior is: 



, d 



y = bQe 



where 



y = predicted growth 

 X = measure of stand density 

 iiQ, ill = model parameters 

 d = a power on x 



Linearizing this form produces the following independent variables: BA^, T*^, and CCF*^. 

 Three potentially suitable values of d are 2, 3, and 4 (d could take on any positive value). 

 These particular values were chosen because any one of them would provide for a slow decline 

 in y when x is near zero, which is also an expected effect (that is, low stand densities 

 will not influence growth) . 



The vigor differences between blackjack pine and yellow pine were handled by simply 

 modeling each of them separately. 



54 



