index, age, transformations of age and site index, and 

 environmental variables explained 87 to 99 percent of 

 the variation in tree height, with standard deviation 

 about regression ranging from 3.4 to 8.2 feet. We are 

 able to explain 77 to 92 percent of the variance in height 

 of other species (table 3) from white pine site index and 

 the age of the predicted species without employing 

 environmental variables as additional predictors; 

 standard deviation about regression ranged from 6.4 to 

 10.7 feet. 



Wiant and Porter (1966) used simple linear regression 

 to predict site index of Douglas-fir (Pseudotsuga 

 menziesii), redwood (Sequoia sempervirens), and 

 associated hardwoods from site indexes of other tree 

 species in northern California. They used eight to 

 33 plots per regression and obtained explained variances 

 from 13 to 55 percent. Carmean (1979), Carmean and 

 Hahn (1983), and Carmean and Vasilevsky (1971) 

 compared site indexes in several areas of the Midwest 

 and upper Midwest and found linear relations between 

 each species pair. Seven to 278 plots were used for the 

 comparisons (notably larger than our sample size range), 

 with one to five trees of each species on a plot. Their 

 equations explained 40 to 91 percent of the variation in 

 site index; standard deviation from the regression line 

 ranged from 2.5 to 11.3 feet. Our results (table 2) show 

 explained variarices ranging from a low of 33 percent 

 (Douglas-fir/ponderosa pine comparison) to a high of 84 

 percent (Douglas-fir/subadpine fir comparison); deviations 

 about regression ranged from 3.1 feet (predicted lodge- 

 pole pine site index from western larch) to 12.1 feet 

 (predicted grand fir site index from lodgepole pine). 



Using Regression Models 



The site index regression models are displayed in 

 figures 1 through 9. The independent variable (the site 

 index of the species used to predict) is plotted on the 

 X-axis versus the dependent variable (the predicted site 

 index of the specific species) on the Y-axis. For instance, 

 to use figure 1, obteiin a mean site index for Douglas-fir, 

 say 60. Locate this value on the X-axis £ind read up to 

 the weatern larch line and then directly across to the 

 Y-£Lxis, the predicted western larch site index being 63. 

 The user is warned not to extrapolate beyond the range 

 of the independent variable (as denoted by the length of 

 the line) because these are empirically derived equations. 

 Extrapolation beyond the range of the data may lead to 

 gross errors of over- or underestimation. 



The direct comparison of site index of one species to 

 that of another must consider their respective index 

 ages, whether it is age at breast height, or total age. 

 Curves based on breast height age, in essence, regard 

 the site tree to be years old at the time it reaches 

 breast height, whereas curves based on total age assume 

 the tree to be some fixed number of years old by the 

 time it reaches breast height. Thus, the site index of two 

 different species that are 50 years old at breast height 

 and of equal height will not be equal if the number of 

 years added to reach breast height is not equal. Table 1 

 shows the number of years added to breast height age to 

 obtain total age for those curves requiring total age. A 



further consideration when comparing tree heights at 

 ages other than the index age is the shape of the site 

 index curves. None of the curves employed in this study 

 are identical; these curves reflect species-specific growth 

 patterns. Consequently, when comparing species at ages 

 other than 50, different heights may be registered for 

 trees that are of equal height at the index age. The 

 magnitude of these differences may be appreciable at 

 older ages. 



Use of Site Index Graphs 



Examination of site index comparison graphs (figs. 1 

 through 9) reveals that the relationship of one species 

 site index to that of its associates may change differen- 

 tially in response to site quality, even when a 1:1 

 correspondence is observed over part of the range of site 

 index. For example, Douglas-fir responds strongly to 

 differences in site quality; the increase in its height 

 growth rate from poor to good sites is comparatively 

 greater than that exhibited by some of its associates. 

 This observation is reflected in the steeper slopes of the 

 Douglas-fir regression lines (compare figs. 2, 3, 7, 8, and 

 9). Western white pine also demonstrates a similar sensi- 

 tivity to site quality (figs. 1, 4, and 8). Engelmann 



30 I — I — I — 1 — I — I — 4 — I — I — I I I — 1 I I 



30 40 50 60 70 80 90 100 



OBSERVED DOUGLAS-FIR SITE INDEX. FT 



Figure 1.— Using Douglas-fir site 

 index (x-axis) to predict that of 

 associated species (y-axis). The 

 diagrammed example case shows 

 an observed Douglas-fir site Index 

 of 60 predicts a western larch site 

 index of 63. In this and all following 

 figures the species abbreviations 

 are: ES, Engelmann spruce; GF, 

 grand fir; DF, Douglas-fir; PP, 

 ponderosa pine; WL, western larch; 

 SAF, subalpine fir; LPP, lodgepole 

 pine; WWP, western white pine; MH, 

 mountain hemlock. 



5 



