There, along 4 radii, the sapwood border was recorded in order to calculate the sapwood area. In a first step we compared the predictive power of crown surface area (CSA), crown projection area (CPA), and basal area (BA) with that of other often used substitutes for leaf area, e.g., sapwood area at crown base (SAPcb), at breast height (SAPdbh), and at three tenth of the tree height (SAP03), for each stand separately by using log-linear regression models of the following form: equation(11) ln LA=a+b⋅ln Xln LA=a+b⋅ln Xwith LA the leaf area, a the intercept and b the coefficient for the respective
substitute variable X. The coefficients were estimated by log-linear regression in order to avoid heteroscedasticity. Further on, analysis of covariance was used to test Small molecule library solubility dmso if (i) the assumption of a common slope for all stands was justified, (ii) the relation between LA and X was proportional (b = 1), and (iii) the intercepts did not differ between the stands. Here should be mentioned that, if b = 1 the intercept a represents the proportionality factor of LA to X in the delogarithmized form of Eq. (11). In a next step the same procedures were used to test if the estimation of leaf area within the stands can be improved by including more variables into the above equation (11). Finally, we investigated if the leaf area models can be generalized by using tree and stand variables in the
mixed model equation (12). equation(12) ln(LA)=a+b⋅ln(X)+cT⋅STANDVAR+u+eln(LA)=a+b⋅ln(X)+cT⋅STANDVAR+u+eAdditionally N-acetylglucosamine-1-phosphate transferase to the variables and Doxorubicin in vivo coefficients of Eq. (11) following variables
were included: cT a vector of the coefficients of STANDVAR which is a vector of the stand variables ( Table 2) and a dummy variable for the thinning treatment. In the models the natural logarithm of each variable in Table 2 has been used. Finally, u, and e are the random effects of the stands and the trees, respectively. All statistical analysis were performed with Microsoft® Office Excel 2003 (2003) and the statistical software package SPSS for Windows – Rel. 13.0 (2004). The mixed models were analysed and parameterized with the procedure “MIXED” of SPSS for Windows. In all models only variables with significant coefficients (p ≤ 0.05) were included. For comparing the models and finding the final ones, following goodness of fit criteria were used: R2 for log-linear regression models with the same number of predictor variables, adjusted R2 for log-linear regression models with a different number of predictor variables, and the Akaike Information Criterion (AIC) for mixed models according to Demidenko (2004). Judged from the average R2 and the standard error of estimate of the natural logarithm of leaf area, the sapwood areas at crown base and at three tenth of the tree height are the best predictors for leaf area ( Table 3).