# Modeling Production Processes in Forest Stands: An Adaptation of the Solow Growth Model
## 4 Discussion  
Table 2 gives the values of the ESM parameters for different stands in the Siberian taiga forests, where the maximal values of coefficient \(A\) are characteristic of such deciduous species as larch and birch. For the Scots pine and the Siberian fir, parameters of the EcoSolow model are similar for forest stands growing under different climatic conditions. As can be seen from the data in Table 2, for all tree species the elasticity (\(1-\alpha\)) in changing the photosynthesisizing phytomass is significantly higher than the non-photosynthesizing phytomass elasticity. Thus, the NPP of the trees is less influenced by changes in the value of \(K\) than by changes in the mass of the photosynthesisizing apparatus, \(ML\). If, initially, we assumed that \(\alpha+\beta\
eq 1\), results of calculations showed that in this version of the model, \(\alpha+\beta=1.05\), and this is very close to \(1\) (Table 2). Thus, we do not need to introduce the additional free parameter, \(\beta\), into the model. Figure 4 shows the age dynamics of the NPP of forest stands calculated from the values obtained for coefficients \(A\), \(\alpha\), and \(s\). The graph shows that the age trends of the NPP of pine stands (with the NPP maximum at the age of \(40\) years and NPP minimum at older ages up to \(300\) years) are similar for the stands growing in different geographical zones. However, the absolute NPP values of the pine stands of all ages are higher for the stands growing in more favorable climatic conditions. The age dynamics of NPP were also similar for the single-species even-aged stands of various tree species in Siberia (Figure 5). Note that for the dominant Siberian taiga species fir and larch, the NPP values are quite close in the same age group, although the characteristic lifespans of their needles differ considerably. Since we know the values of GPP and NPP, we can characterize the effectiveness of the photosynthetic process as \(\eta=\frac{NPP(T)}{GPP(T)}\). It is obvious that \(0\leq\eta(T)<1\), and that the closer the value of \(\eta(T)\) to unity, the more effectively photosynthesis produces energy. Figure 6 shows the dynamics of parameters of photosynthesis effectiveness for pine stands in different geographical regions of Siberia. The effectiveness of photosynthesis monotonically decreases with the stand age. Interestingly, the highest effectiveness of photosynthesis was shown by the stands in the north taiga zone and the lowest by the stands in South Siberia. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Woody Species, Location**} & \multicolumn{3}{c}{**ESM Parameters**} \\ \cline{2-4}  & \(A\) & \(\alpha\) & \(s\) \\ \hline _Pinus sylvestris_ L., \(53^{\circ}50^{\prime}\) N \(92^{\circ}\) E & 0.72 & 0.23 & 0.54 \\ _Pinus sylvestris_ L., \(51^{\circ}45^{\prime}\) N \(94^{\circ}30^{\prime}\) E & 0.56 & 0.27 & 0.50 \\ _Larix sibirica_ Ledeb., \(54^{\circ}\) N, \(91^{\circ}\)E & 1.60 & 0.09 & 0.23 \\ _Larix sibirica_ Ledeb., \(52^{\circ}\) N, \(95^{\circ}30^{\prime}\) E & 1.39 & 0.17 & 0.70 \\ _Pica obovata_ Ledeb., \(56^{\circ}35^{\prime}\) N, \(57^{\circ}40^{\prime}\) E & 1.10 & 0.11 & 0.70 \\ _Pica obovata_ Ledeb., \(59^{\circ}\) N, \(61^{\circ}\) E & 0.73 & 0.28 & 0.39 \\ _Abies sibirica_ Ledeb., \(59^{\circ}\) N, \(93^{\circ}\) E & 0.67 & 0.24 & 0.28 \\ _Betula pendula_ Roth., \(57^{\circ}\) N, \(93^{\circ}\) E & 2.03 & 0.33 & 0.94 \\ _Betula pendula_ Roth., \(55^{\circ}10^{\prime}\) N, \(92^{\circ}\) E & 1.83 & 0.31 & 0.67 \\ _Pinus sylvestris_ L., \(59^{\circ}30^{\prime}\) N, \(101^{\circ}50^{\prime}\) E & 0.61 & 0.25 & 0.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: ESM parameters for forest stands with different woody species in Siberia [10; 11]. Figure 4: Age dynamics of the NPP of single-species even-aged pine stands (**1**) South Siberia, (**2**) Middle Siberia). Figure 5: Age dynamics of the NPP of forest stands in the taiga zone of Siberia [11].