Modelling environmental variation in Young's modulus for Pinus radiata and implications for determination of critical...

Although density-specific stiffness, E/rho, (where E is Young's modulus and rho is wood density) is often assumed constant by the elastic similarity model, and in determination of critical buckling height (H(crit)), few studies have tested this assumption within species. Here this assumption is tested for Pinus radiata growing across an environmental gradient, and theory is combined with data to develop a model of Young's modulus.

Analyses use an extensive series of environmental plots covering the range of climatic and edaphic conditions over which P. radiata is grown in New Zealand. Reduced major axis regression was used to determine scaling exponents between log-log plots of H(crit) vs. groundline diameter (D), and E/rho vs. D. Path analysis was used to identify significant direct and indirect (through stem slenderness) edaphic and climatic influences on E.

Density-specific stiffness exhibited 3-fold variation. As E/rho scaled positively with D, the exponent of 0.95 between H(crit) and D exceeded the assumed value of 0.67 under constant E/rho. The final path analysis model included mean air temperature in early autumn (T(aut)) and slenderness as significant (P < 0.05) positive direct influences on E. Tree leaf area index and T(aut) were indirectly associated with E through their significant (P < 0.05) positive direct relationship with stem slenderness. Young's modulus was most sensitive to T(aut), followed by stem slenderness then leaf area index, and the final model explained 76 % of the variance in E.

The findings suggest that within species E/rho variation may influence H(crit) and the scaling exponent between D and H(crit) so important in assumptions regarding allometric relationships. The model presented may provide a useful means of determining variation in E, E/rho and H(crit) across environmental gradients.