# Modeling Production Processes in Forest Stands: An Adaptation of the Solow Growth Model
## 3 Results  
In the adaptation of the Solow model--the EcoSolow model (ESM)--proposed in this study, the process of phytomass growth in a forest stand is regarded as analogous to a manufacturing process. Capital, \(K\), consists of the non-photosynthesizing components of the phytomass--tree stem, roots, and branches, and labor force, \(L\), is represented by leaves (or needles), which carry out photosynthesis. Figure 1 shows estimations of growth dynamics of pine stands in Siberia calculated with the EcoSolow model. Inventory data and model calculations are evidently in good agreement (coefficients of determination R\({}^{2}\) are higher than 0.98). The ESM can be used to describe the nonmonotonic phytomass change observed in forest ecosystems, when, having reached its peak value at a certain age, the phytomass begins decreasing. How do the calculations with the EcoSolow model differ from the NPP calculations with the balanced model (5)? Figures 2 and 3 show the curves of the temporal growth dynamics of forest \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Age, Years**} & \multirow{2}{*}{**Density, Trees/ha**} & \multicolumn{5}{c}{**Pityomass, \(\boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{ \boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{ \boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{ \boldsymbol{ }}}}}}}}}}}}}\)**} \\ \cline{2-6}  & **Stem with Bark** & **Needles** & **Branches** & **Roots \({}^{*}\)** \\ \hline
10 & 13,522 & 7.4 & 3.13 & 2.5 & 4.3 \\
20 & 7528 & 25.7 & 3.64 & 4.2 & 8.9 \\
40 & 3604 & 61.2 & 3.8 & 6.2 & 14.9 \\
60 & 2167 & 85.4 & 3.71 & 7.4 & 18.0 \\
80 & 1477 & 100.2 & 3.56 & 8.1 & 19.6 \\
100 & 1075 & 108.3 & 3.41 & 8.6 & 20.4 \\
120 & 827 & 113.1 & 3.27 & 8.9 & 20.8 \\
140 & 656 & 114.4 & 3.13 & 9.1 & 20.8 \\
160 & 542 & 113.8 & 3.0 & 9.2 & 20.6 \\
180 & 453 & 112.6 & 2.89 & 9.3 & 20.4 \\
200 & 382 & 110.7 & 2.78 & 9.4 & 20.1 \\
220 & 331 & 107.7 & 2.68 & 9.4 & 19.7 \\
240 & 289 & 104.5 & 2.59 & 9.4 & 19.2 \\
260 & 255 & 101.5 & 2.51 & 9.4 & 18.7 \\
280 & 226 & 97.8 & 2.42 & 9.3 & 18.3 \\
300 & 202 & 94.7 & 2.35 & 9.3 & 17.9 \\ \hline \hline \end{tabular} \({}^{*}\) Estimated—Appendix A.  
\end{table} 
Table 1: Middle Siberia, south taiga. Figure 1: Phytomass of pine stands. (**1**) inventory data, Middle Siberia; (**2**) calculation with the ESM; (**3**) inventory data, South Siberia; (**4**) calculation with the ESM; (calculations were based on the data of different authors systematized [10; 11]). stand phytomass (including the root phytomass) and the NPP calculated with the balance model and the EcoSolow model. Calculations of the NPP by different methods yielded very similar results (particularly for older ages). However, in contrast to the nonparametric balance method of NPP calculation, the EcoSolow model provides estimations of three free parameters, \(A,\alpha\), and \(s\). By analyzing the relationships between these parameters and the tree species and environmental conditions, one can obtain more information on the photosynthetic processes in woody plants. We certainly do not know the \"true\" NPP curve, which could be compared to the ESM. The data in Figure 3 show that calculations based on the ESM and on the balanced model yield similar results. We did not attempt to force the ESM to fit the balanced model. Figure 3 shows that the NPP curves are similar. However, the main difference between the balanced model and the ESM is that the balanced model is a nonparametric one and it cannot be used to estimate changes in the NPP depending on the species and habitat. The ESM is a parametric model with parameters A, \(\alpha\), s and can be used to compare different tree stands using these parameters and correlate the parameters with the tree  
Figure 3: NPP calculation with the balanced Equation (**1**), taking into account root phytomass, and with the EcoSolow Equation (**2**). _Larix gmelini_ Rupr., Middle Siberia ([10], p. 589).