The following is a summary of the procedures used to obtain these models. Additional 

 information is in appendix E. 



Prior silvicultural and mensurational research in southwestern ponderosa pine showed that 

 noncatastrophic mortality in uneven-aged stands is often correlated to diameter size, severity 

 of cutting, and tree vigor as indicated by bark color (in other words, whether the tree is a 

 blackjack or yellow pine). For even-aged stands, site and total stand basal area are signifi- 

 cant in predicting total stand mortality. 



I selected a nonlinear logistic function for modeling the proportion of trees in a dia- 

 meter class succumbing to mortality. One reason for this is that the dependent variable of 

 the logistic can be properly limited to a value between zero and one. Second, characterizing 

 a dichotomous dependent variable such as mortality with the logistic function appears to 

 produce a model with improved statistical properties when compared to ordinary, linear least 

 squares models (Hamilton 1974; Hamilton and Edwards 1976). 



To model the proportion of the trees in a diameter class dying in a growth period, the 

 dependent variable was set to zero if the tree survived to the end of the growth period, and it 

 was set to one if the tree died. The independent variables used were transformations of 

 diameter class or stand attributes and incorporated not only the prior factors found to be 

 correlated to mortality, but also factors hypothesized to be correlated. Included in this 

 group were tirae-since-last-cutting and basal area growth predicted from the three completed 

 models. Appropriate transformations were formed based upon both prior silvicultural and 

 mensurational research findings-, and an examination of the particular behavior of the logistic 

 function . 



The development of finished mortality models required the use of nonlinear regression and 

 proceeded in three phases: 



Phase l .--For each vigor class, the data were separated into three sets: virgin uneven- 

 aged, managed uneven-aged, and managed even-aged. Preliminary nonlinear regression runs, 

 using the logistic function, were made to select those variables most highly correlated to 

 mortality. The two best variables proved to be diameter class size squared and predicted 

 basal area growth. 



Phase 2 . --The separated data sets were collapsed into two sets (uneven-aged, and even- 

 and uneven-aged) by modeling the change in model parameters between the separated data sets as 

 functions of time-since-last-cutting. An examination of a chi-square "goodness-of -f it" test 

 for the best models indicated that the uneven-aged yellow pine equation (table 10) and the 

 uneven-aged blackjack pine equations (tables 11 and 12) were satisfactory. The equations for 

 even- and uneven-aged blackjack pine were not satisfactory. 



Phase 3 . --To resolve the problems with the even- and uneven-aged blackjack pine data set, 

 another set of nonlinear regression runs was made. While these models were an improvement 

 over the previous models, the chi-square values still indicated a significant difference 

 between predicted and actual mortality (tables 13 and 14) . An examination of the causes for 

 mortality revealed that the even-aged data had incurred considerable snowbreak loss. Because 

 I could not decide whether snowbreak should be treated as a catastrophic or noncatastrophic 

 loss, these models were retained until the validation phase of the study could more closely 

 examine the predictive capabilities of the equations. 



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