Table 1.— Sources of curves used for computing site index'' 





Estimated 





years 







to obtain 







breast 





Species 



hoinht 



ouurcc uT curve 



Subalpine fir (Abies lasiocarpa) 





Alexander (1967) 



Grand fir (Abies grand is) 



12 



Stage (1959) 



Western larch (Larix occidentalis) 



5 



Schmidt and others (1976) 



Engelnnann spruce (Picea engelmannii) 



(2) 



Alexander (1967) 



Lodgepole pine (Pinus contorta) 



7 



Brickell (1970) 



Western white pine (Pinus monticola) 



5 



Haig (1932) 



Ponderosa pine (Pinus ponderosa) 



5 



Lynch (1958) 



Douglas-fir (Pseudotsuga menziesii) 



(2) 



Monserud (1984b) 



Mountain hemlock (Tsuga mertensiana) 



(2) 



Alexander (1967) 



'All site curves based on a 50-year index age. 

 ^Curves based on age at breast height were used. 



Daubenmire (1961) and Lynch (1958) have warned 

 against adding a constant number of years to breast 

 height age to obtain total age for use with site curves 

 requiring total age. They also indicated that the better 

 the site, the fewer the years required to reach breast 

 height. But, we lacked concrete data to indicate what 

 variable number of years would be appropriate and 

 therefore adopted the values specified by Pfister and 

 others (1977) for western white pine, Stage (1959) for 

 grand fir {Abies grandis), Schmidt and others (1976) for 

 western larch (Larix occidentalis). Fiedler (1982) for 

 lodgepole pine (Pinus contorta), and Daubenmire (1961) 

 for ponderosa pine (Pinus ponderosa). 



ANALYSIS 



The data set was cleaned by discarding trees that were 

 considerably shorter or older than the rest of the site 

 trees in a stand. In a few cases, entire stands were 

 rejected because of extreme variation in height or age of 

 the site trees. First, we correlated site index between 

 species. Scatter diagrams and least squares regressions 

 were examined for all species combinations for which 

 concomitant observations on six or more stands were 

 available. A paired sample was composed of the mean 

 site index of one species and the mean site index of an 

 associated species. Examination of residuals indicated all 

 associations were linear and more than 90 percent were 

 statistically significant (95 percent confidence level). 



We then grouped our data according to the number of 

 site trees sampled in a stand. A minimum of two trees 

 of each species per stand was generally necessary to pro- 

 vide sufficiently precise estimates of mean stand site 

 indexes; a minimum of three site trees of each species 

 further improved the regressions. Clearly, a larger num- 

 ber of site trees improves the reliability of the estimate 

 of a stand's mean site index and consequently improves 

 the predictabUity of the regression equations. For spe- 

 cies combinations where enough pairs existed, regres- 

 sions were restricted to stands with at least three site 



trees of each species per stand. The regression equations 

 for the remaining species combinations were derived 

 from stands with at least two site trees of each species 

 per stand. 



Second, height projection equations were computed by 

 first considering the site index of species A and age of 

 species B as observed values to predict the height of 

 species B. It was assumed that the site index curves 

 used to compute the site index of the observed species 

 (species A) estimate site quality with neghgible error. 

 Without the assumption of measuring the age and site 

 index with no error, the regression produces biased 

 results. 



The majority of the data was obtained from stands 45 

 to 120 years in age. The primary emphasis was to 

 develop simple, flexible, empirical models for this age 

 range, rather than biologically realistic models spanning 

 the Ufe span of a species. Thus, logarithmic, exponential, 

 and second-order polynomial functions of age and site 

 index were regressed on height. The general model form 

 was chosen to be height predicted as a function of site 

 index, age, and logarithmic function of age. Conformity 

 to model assumptions was checked by examining plots 

 of residuals versus predicted values. Coefficients of 

 determination (R-) and standard deviation about regres- 

 sion were calculated as measures of reUabUity; curves of 

 estimated values generated by the regression equations 

 were plotted over the site index curves of the dependent 

 species to observe model behavior. 



RESULTS AND DISCUSSION 



Table 2 presents the site index regression equations 

 intended for general use. Two equations are given for 

 each species combination because the mathematics of 

 least squares regression is such that the regression of A 

 on B is the same as- the regression of B on A only in 

 producing equivalent coefficients of determination; the 

 error term and the regression coefficients are almost 

 invariably different. 



2 



