Ingrowth = t-ii^e 



to + 5 



to 



(to ^ 5).ie^2Q^^^ - to.ie^2QMD 



and 



Ingrowth = igt + ij^BA 



to + 5 



to 



= 5i>o + SijjBA 



= i3* + 25*BA (4) 

 Ek's (1974) model predicts the total number of ingrowth trees directly by the equation: 

 Ingrowth = biT -^e ^ (5) 



where 



T = total number of trees 



BA = total stand basal area. 



Moser used nonlinear regression to fit model (1) and linear regression to fit model (2). 

 Ek also used nonlinear regression to fit model (5) . Both are assuming, therefore, that the 

 error term is additive, but neither provided evidence to support this assumption. 



Total Ingrowth Model Development 



The previously discussed literature review for ponderosa pine in the Southwest indicated 

 that ingrowth might be influenced by the potential of the stand to produce cones, the level 

 and structure of competition, and the time since the last good seedling year. 



From the data presented by Larson and Schubert (1970), the following equation was devel- 

 oped to predict the number of cones a tree in a given diameter class (greater than or equal to 

 12 inches) would produce in a year: 



Number of cones per tree per year = 0.94993974(0-12) + 0.61427282(0-12)2 



D > 12 



where 



D = diameter class size. 



Using this equation, the predicted number of cones (C) for the stand was computed and 

 used as an independent variable. The number of cones is expected to be positively 

 correlated with ingrowth. 



To represent level and structure of competition, six diameter classes were created (4 to 

 6 inches, 7 to 9 inches, 10 to 15 inches, 16 to 21 inches, 22 to 27 inches, 28+ inches), and 

 the number of trees and basal area in each was determined. These classes can then be combined 

 in numerous ways to produce various measures of the level and structure of competition. 



78 



