Because of the data restrictions, the only "recruitment" model possible at this time is 

 an ingrowth model. In this study, ingrowth is defined as the number of new trees growing into 

 the 4- or 5-inch diameter classes during a growth period. Ingrowth, therefore, includes not 

 only those factors influencing the amount of established seedlings, but also includes those 

 factors influencing the growth and mortality rate of seedlings as they advance to ingrowth 

 size. Conditions providing for a large, established seedling crop and allowing favorable 

 seedling growth and low mortality will ultimately result in a large ingrowth rate at some 

 point in the future. 



For uneven-aged stands, ingrowth can be expected at any time, but in even-aged stands, 

 ingrowth would only be expected during the early, and possibly the late, stand development 

 phase. Unfortunately, the Taylor Woods even-aged data represent only stands in relatively 

 early stand development. As a result, any ingrowth model developed using just the Taylor 

 Woods data would be applicable only to stands in the same stand development phase. Such a 

 restriction would give the model little utility for predicting even-aged stand development 

 through all phases of development. Therefore, it was decided that the ingrowth model would be 

 developed only for uneven-aged stands. An alternative method for even-aged stands by which 

 use of the basal area and mortality models are extended down into the 1-, 2-, and 3-inch 

 diameter classes is proposed and tested in the validation phase. 



Two equations were used to model uneven-aged ingrowth. The first predicts the total 

 number of ingrowth trees. The second predicts the proportion of the total ingrowth trees that 

 will grow through the 4-inch diameter class and into the 5-inch diameter class during the 

 growth period. 



TOTAL INGROWTH 



After examining prior silvicultural and mensurational findings, I hypothesized that the 

 factors possibly influencing the rate of ingrowth for uneven-aged stands included potential 

 of the stand to produce cones, level and structure of competition, site index, mean stand 

 diameter, and quadratic mean stand diameter. Based on these factors, appropriate independent 

 variables were defined. The following is a summary of the process used to develop the total 

 ingrowth model. Further details are in appendix G. 



Two factors influenced the development of a strategy for modeling total, ingrowth. First, 

 while a nonlinear total ingrowth model is most likely, it was not known whether the residuals 

 about the model are multiplicative (implying that taking the log of the model could linearize 

 the data) or additive. Second, the form and specification of the applicable independent 

 variables in the final ingrowth model had not been rigorously defined. Therefore, a good deal 

 of screening was necessary before the final model could be determined. Given these conditions, 

 the following strategy was used to develop a total ingrowth model: 



Phase l .--The total ingrowth data were separated into two sets: virgin uneven-aged and 

 managed uneven-aged. For each set, a preliminary all -combinations screening run using linear 

 regression was made on the variables linearized by applying logarithms, and selected models 

 were chosen for further analysis. 



Phase 2 . --A second screening run combined the two basic data sets through use of the 

 time-since-last-cutting transforms. Because the sign on site index was not considered reason- 

 able, a new dependent variable was formed by dividing total ingrowth by site index and taking 

 the log of the quotient. A new set of screening runs was then made and the final independent 

 variables were chosen. 



Phase 3. --An examination of the residuals of the preceding model indicated that the error 

 structure of total ingrowth divided by site index might not be best represented by a log 

 model. Therefore, the antilog of the model was fitted with a linear, least squares slope 

 correction. An examination of these residuals revealed that the error structure of total 

 ingrowth divided by site index was better represented by a weighted, nonlinear model with an 

 additive error. 



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