The relationship between Reineke's stand-density index and physical stem mechanics

Data from 358 plots from long-term, growth-and-yield studies established in loblolly pine plantations were used to test the hypothesis that the value of Reineke's stand-density index (SDI) represents the amount of bending stress generated in the stems by wind action on the canopy. By assuming constant bending stress in stems as a function of height and a linear relationship between canopy depth and mean tree spacing, SDI can be expressed in terms of foliage density (leaf area per unit volume of space, F), mean live-crown ratio (C-r), and canopy depth (C-d). The equation is SDI = a[F(1/C-r - 0.5)](0.53) C-d(0.12) where a is a constant. Foliage density was calculated as leaf area index divided by canopy depth. An initial test of the equation was conducted by fitting the model SDI = beta(O)[F(1/C-r - 0.5)](beta 1) to the growth-and-yield data. The factor C-d was not included in the model because of its mathematical relationship to F. The fitted equation explained 76% of the variation in SDI and estimated beta(1) as 0.51, which was not significantly different from the derived exponent, 0.53. Residuals from the fitted equation were unbiased with respect to foliage density and mean live-crown ratio. Further analysis revealed that species variation in maximum values of SDI increased linearly with decreasing wood specific gravity, providing additional evidence that density indexes are related to physical stem mechanics.