where 



= number of trees living after n"* years 



V = number of trees living today 



o ^ ' 



P = mortality rate based on an n year interval 

 n 



n = number of years used as basis for estimating 



- number of years for which prediction is desired. 



Algebraic manipulation of formula (3) produces the following formula that converts an 

 n-year mortality rate to an n'^-year mortality rate: 



^ ^ ^/ 

 -ill = n P 



o 



= > ^ ^ 1 _ (i.p )^Vn 



o 



= > P ^= 1-(1-P )'^''/" (4) 



Continuing with the grand fir example, the mortality probability prediction 

 model from RISK is as follows: 



P^ = 1.0/{1.0 + exp[4. 89819 - 0. 0047554 (%DEF^) - . 222746 (CC^) ]} 



where 



P^ = predicted annual mortality rate for tree i 



%DEF . - percent defect in tree i 

 CC . - crown class of tree i. 



In this model, the qualitative variable crown class is used as if it were a con- 

 tinuous variable. Because we would expect a constant increase in mortality rate as 

 crown class changes from dominant to suppressed (1 to 4) , using crown class in this 

 manner should cause few problems. 



This model predicts the probability that an individual grand fir tree will die in 

 a given year as a function of percent defect and crown class. Thus, for codominant 

 grand fir [CC . = 2) with 25 percent defect, the probability of mortality in the follow- 

 ing year is: 



P^ = 1.0/{1.0 + exp[4. 89819 - 0.0047554(25.0) ^ 0.222746(2)]} 

 = 1.0(1.0 + exp[4. 89819 - 0.11888 - 0.44549]} 

 = 1.0/[1.0 + exp(4. 33382)] 

 = 1.0/77.23494 

 = 0.01295 



This tree would have a 1.29 percent chance of dying during a 1-year period. This 

 yearly mortality rate will change as the tree parameters, percent defect and crown 



9 



