# Assessment of the Mass and Surface Area of the Scots Pine (_Pinus sylvestris_ L.) Needles
## 3 Results
### Characteristics of the Sample Trees
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & **FMN** & **SN** & **DBH** & **H*** \\  & & **(kg)** & **(m2)** & **(cm)** & **(m)** & **(m)** \\ \hline SN (m2) & Pearson’s r & 0.9384 & - & & & \\  & \(p\)-value & **<0.0001** & - & & & \\ DBH (cm) & Pearson’s r & **0.8481** & **0.7267** & - & & \\  & \(p\)-value & **<0.000** & **<0.001** & - & & \\ H (m) & Pearson’s r & **0.5870** & **0.4808** & **0.6276** & - & \\  & \(p\)-value & **<0.010** & **<0.043** & **<0.005** & - & \\ H* (m) & Pearson’s r & **0.6956** & **0.6774** & **0.7002** & 0.2012 & - \\  & \(p\)-value & **<0.001** & **<0.002** & **<0.001** & **<0.423** & - \\ \hline \hline \end{tabular} DBH—diameter breast height; H—tree height; H’—crown length; FMN—fresh mass of needles; SN—surface of the needles.  
\end{table} 
Table 1: [PERSON]’s correlation matrix between needle weight results and needle area and biometric features of 18 sample trees. Significant results (\(p<0.05\)) in bold. Figure 2: The dendrogram illustrating structures composed of the points with coordinates defined by the scaled sample tree parameters (DBH, H, H*, FMN, FMN\({}_{1000}\), LN). the changes. This observation was confirmed by the correlation coefficients presented in the section above (Table 1). The data, obtained from actual measurements of the sample trees, were used for deriving linear allometric equations, enabling the calculation of the mass and surface area of needles if the DBH of the given tree is known. Structural parameters \(\beta\) of the relationship \(\mathrm{FMN}=\beta_{\mathrm{OFMN}}+\beta_{\mathrm{IFMN}}\cdot\mathrm{DBH}\) (Figure 4a) and \(\mathrm{SN}=\beta_{\mathrm{OSN}}+\beta_{\mathrm{ISN}}\cdot\mathrm{DBH}\) (Figure 4b). Their standard errors (FMN) and \(p\)-values (\(p\)) for H\({}_{0}\): \(\beta_{\mathrm{i}}=0\) {i = 0,1} were calculated [59]. For normality assessment of the model residuals distribution, the Anderson-Darling and the Kolmogorov-Smirnov tests were used. To test heteroskedasticity, the Breusch-Pagan and the Goldfeld-Quandt tests were applied. Table 2 presents the estimated parameters of the models. It shows the values of intercepts (\(\beta_{0}\)) and slopes (\(\beta_{1}\)) with their standard errors (SE\({}_{\beta 0}\), SE\({}_{\beta 1}\) respectively) and \(p\)-values for H\({}_{0}\): \(\beta_{\mathrm{i}}=0\) {i = 0,1}. Additionally, the limits of the parameter's 95% confidence interval (CI\({}_{\beta 1}\) {i = 0,1}) and coefficient of determination (R\({}^{2}\)) were calculated. Taking into account the calculated \(p\)-values concerning structural parameters in the models, the null hypotheses can be rejected. The soundness of this conclusion is weaker for \(\beta_{\mathrm{OSN}}\) since within the CI range, the 0 value is included. To verify the normal distribution of the model, residual Anderson-Darling and Kolmogorov-Smirnov tests were used. The results obtained for both models (\(p\)-value > 0.05) indicate retaining the null hypotheses. For heteroskedasticity tests, similar conclusions were drawn, the null hypothesis concerning homogeneity of the model variance cannot be rejected. The equations were derived based on data for the studied population; therefore, they can be successfully used in calculating the FMN and SN of all the trees in the research plots. Figure 3: Biplot illustrating PCA-derived relationships between the scaled sample tree parameters (DBH, H, H\({}^{*}\), FMN, FMN\({}_{1000}\), LN). They can also be used for calculating the FMN and SN for other tree stands of a similar age that grow in comparable habitat conditions.