Development of a well-behaved site-indes equation: Jack pine in north-cental Ontario: Comment

Bailey and Clutter (1974) introduced base-age invariance as a property of site-index curves and defined it as curves that are "...invariant under choices of base age." The word invariant means "unaffected by the group of mathematical operations under consideration" (Webster's New Collegiate Dictionary 1977 edition). The definition of base-age invariance in Goelz and Burk (1992) is inconsistent. Moreover, site-index curves generated with their model 16, labeled as base-age invariant in that article, are not invariant to (i.e., unaffected by) choice of base age. To illustrate this point, we generated example predictions with that model using the coefficients given in their article. Their Ontario jack pine (Pinus banksiana Lamb.) data are for ages up to 150 years. With a base age of 20 years, we specified a site index of 13 m and predicted heights (m) for ages 20-150 years in 10-year increments using model 16 (Table 1). We then specified the predicted value for height at age 150 years (24.2 m) as site index and 150 years as the base age. With the same model and coefficients we again predicted heights (m) for the same ages; the values are also given in Table 1.