Sigmoids are described within the range XP ± 5 years (yr) , since all sigmoids 

 are estimated to be fully expressed therein. Use of a constant maximum range, such as 

 XP ± 5 years, keeps descriptor components to a minimum for the sigmoidal time effects, 

 yet permits satisfactory matching of the objective curves in this case. Restated in 

 general terms, the whole descriptor is as follows: 



Mortality percent = Int + Lsc (Lsig) + Rsc (Rsig) 



where 



Lsig = left sigmoid = f^(Ln, LI, XP, Yr)...see the basic sigmoid parameters 

 defined in Matchacurve-1 , page 3. 



Ln = Lsig power = fj (d.b.h.) 



LI = Lsig inflection point as a proportion of the range in years from 

 XP-5 to XP, = f 2 (d.b.h.) 



XP = point in time where surface peaks = f 3 (d.b.h.) 



Rsig = right sigmoid = f D (Rn, RI, XP, Yr) 



K 



Rn = Rsig power = f^fd.b.h.) 



RI = Rsig inflection point as a proportion of the range in years from XP+5 

 to XP, = f 5 (d.b.h.) 



Int = intercept, left edge = f 6 (d.b.h.) 



Rsc = Rsig scalar = ridgetop = fy(d.b.h.) 



Lsc = Lsig scalar = ridgetop-Int 

 Segmental constraints: 



Left side; 66 <^ Yr <^ XP, discrete values only 



Right side; XP < Yr 5.71, discrete values only 



Either side; 8 <_ d.b.h. <_ 18, midpoints of 2-inch d.b.h. classes 



only... 8, 10, 12, etc. 



The model, refitted by least squares to smoothed mortality percent at 36 control 

 points on the original data cross-sections over time resulted in an R 2 of 0.96. Used 

 as a goodness-of-f it index, this high R 2 value attests to the fact that the descriptor 

 duplicates the objective graph with reasonable accuracy. 



4 



