Table 1.— Regression equations predicting age at top of root swell related to diameter (mm) at top of 

 root swell and diameter squared, by location and species. 



Maximum 



Predicted Oldest 



Location 



Species 



n 



Intercept 



bi (D) 



b 2 (D 2 ) 



R 2 



SD 



Diameter 



aae 



tree 



Paiai I 

 DUVv I 



Qi mar 























marjle 



47 



9.82 



.4398 



-.000380 



.47 



52 



550 



137 



175 





Rppp h 



46 



1 ^ 



"}841 





86 



25 



500 



206 



258 





Ypllnw 



1 CI 1 \J V V 























U 1 1 L I 1 



94 



*i 7Q 



^ois 





7Q 





710 





cJyj l 





ppH c nri irp 



1 \CU Opi UvC 



21 



19 06 





- 000641 



87 



30 



680 



228 



264 





Striped 























maple 



24 



11.60 



.2098 





.84 



8 



240 



62 



70 





Mountain 























maple 



15 



6.75 



.2177 





.73 



6 



110 



31 



40 





Hobblebush 



15 



3.98 



.3622 





.64 



3 



30 



15 



19 



Nancy 























Brook 



Red spruce 



56 



14.58 



1.1000 



-.001120 



.88 



42 



560 



279 



390 





Balsam fir 



50 



13.94 



.7966 



-.001204 



.67 



33 



300 



145 



202 





Mountain 























paper birch 



21 



3.33 



.4401 



.000123 



.75 



29 



360 



178 



212 





Mountain ash 



19 



4.58 



.7039 



-.002677 



.92 



6 



160 



49 



55 



SD = sample standard deviation from regression = 



Vmean square deviation 











Age was regressed over tree 

 diameter and tree diameter 

 squared. 1 The squared term was left 

 in the regression if there was any 

 statistical or visual evidence that it 

 contributed to the precision of the 

 equation. In a few equations, the 

 squared term causes a slight drop (5 

 to 6 years) in predicted age of the 

 largest trees below the maximum 

 predicted age. 



Results 



Research in cutover stands in 

 the Northeast has indicated that 

 tree age and size are poorly related 

 (Blum 1961; Gibbs 1963). However, 

 results from the Lake States 

 indicate that age and size are fairly 

 well correlated in managed uneven- 

 aged stands (Tubbs 1977). Our 

 results in old-growth hardwoods and 



' Because variance tends to be 

 proportional to diameter, some form of 

 weighted regression would be a 

 reasonable approach for certain species. 



spruce-fir also indicated that age 

 and size are fairly well correlated, 

 apparently because these old- 

 growth stands are stable popu- 

 lations with consistent stand 

 densities and diameter distribu- 

 tions. The R 2 values (proportion of 

 variation accounted for by the 

 regressions) range from .47 to .92, 

 and the standard deviations around 

 the regression range from 3 to 52 

 years (Table 1). In applying these 

 regressions, do not extrapolate 

 beyond the maximum diameters 

 shown in Table 1, especially with 

 equations containing a squared 

 term. The positive squared term for 

 mountain paper birch is reasonable 

 for a species that declines markedly 

 in growth rate as diameter 

 increases. Although the negative 

 squared term for several other 

 species would seem to indicate that 

 diameter growth increases as 

 diameter increases, the curve shape 

 may simply mean that the largest 

 trees in these stands are more 

 vigorous than average. 



Sugar maple in the Bowl had 

 the lowest R 2 and the highest 

 standard deviation. However, a plot 



of the actual points indicates that 

 the regression is quite well defined 

 (Fig. 1). All other species had 

 relatively less scatter, although a 

 few had occasional outliers 

 (retained in the data) that deviated 

 more than the observations for 

 sugar maple. 



The regressions for red spruce 

 in the Bowl and Nancy Brook are 

 not identical. A red spruce of 550 

 mm diameter in the Bowl has a 

 predicted age of 233 years, while a 

 comparable tree in Nancy Brook has 

 a predicted age of 281 years. The 

 site in the Bowl is better, and 

 elevation is lower. 



Because of the curve-fitting 

 procedure, the maximum predicted 

 ages in Table 1 are less than the 

 age of the oldest tree. Furthermore, 

 the oldest tree ages are much less 

 than the maximum ages reported for 

 any given species. For example, 

 maximum predicted age for sugar 

 maple in the Bowl is about 137 

 years; age of the oldest tree is 

 about 175 years; but maximum age 

 for the species is about 400 years. 



2 



