APPLICATIONS OF 

 MODIFIED PROGRAM 



Mortality 



The program has been used in two independent situations to estimate the probabil- 

 ity of individual tree mortality. Permanent sample plots established in western white 

 pine (Pinus monticola Dougl.) on the Deception Creek Experimental Forest and on the 

 Kaniksu National Forest were measured at 5-year intervals for 20 years. A preliminary 

 analysis of these data produced the following model for predicting mortality of indi- 

 vidual trees : 



P = {1 + exp[-0.2735 + 0.2746(67?) + 2 . 3054 (PCT) ] }~ 1 



where 



CR = crown ratio 



PCT = position in the tree basal area distribution 



Lee (1971) tabulated mortality rates for lodgepole pine by 2-inch-diaineter classes. 

 A functional expression describing this relationship must be developed if it is to be 

 used in a computer program. Such an expression demonstrates another use for this 

 analysis and illustrates the versatility of the logistic function. 



The logistic function is expressed graphically as a sigmoid shaped curve. Because 

 Lee's data indicate that a U-shaped curve describes the relationship between mean stand 

 d.b.h. and mortality, the independent variable must be transformed to fit the relation- 

 ship. The sets of transformed variables x and x 2 , x and 1/x, and x and In x have the 

 potential of fitting either this U-shaped distribution or a bell-shaped distribution. 

 For Lee's data the model is 



P = {1 + exp[3.002 + 0.30775 (DBH) - . 1 74 (DBH) 2 ] } " 1 



where 



DBH = mean stand d.b.h. 



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