# Modeling Production Processes in Forest Stands: An Adaptation of the Solow Growth Model

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The EcoSolow Model of Production Processes in the Forest Stand

^{2}is used to evaluate the quality of data approximation by model Equation (7).

#### 2.2. Model Data

## 3. Results

^{2}are higher than 0.98).

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

_{1}); M

_{i}is the phytomass of the rank i component; and b(T) is the coefficient characterizing percentages of phytomasses of different ranks.

**Figure A1.**Functions of phytomass distribution among components of the Siberian fir Abies sibirica Ldb. stand (the West Sayan Mountains, the upper reaches of the Kebezh River, 52°N, 89°E) at ages of 40 and 300 years. (

**1**) aboveground components of tree phytomass in the 300-year-old stand; (

**2**) calculated root phytomass in the 300-year-old stand; (

**3**) aboveground components of tree phytomass in the 40-year-old stand; (

**4**) calculated root phytomass in the 40-year-old stand [10].

^{2}> 0.99) by Equation (A2) (Figure A1). Knowing coefficients of regression Equation (A2), one can calculate root phytomass.

^{2}, for the data on the distribution of phytomass in forest stands among tree components.

**Figure A2.**The distribution of the coefficient of determination R

^{2}of the linearized Zipf-Pareto Equation (A2) for the phytomass distribution among tree components.

^{2}= 0.98. Thus, the theoretical Equation (A2) is in very good agreement with the field measurement data.

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**Figure 2.**Dynamics of the forest stand phytomass, including root phytomass of Larix gmelinii Rupr., Middle Siberia, (

**1**) field data ([10], p. 589); (

**2**) EcoSolow model calculations.

**Figure 3.**NPP calculation with the balanced Equation (

**1**), taking into account root phytomass, and with the EcoSolow Equation (

**2**). Larix gmelinii Rupr., Middle Siberia ([10], p. 589).

**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]. (

**1**) Larix sibirica Ledeb.; (

**2**) Abies sibirica Ledeb.; (

**3**) Picea obovata Ledeb.; (

**4**) Betula pendula Rotsch.; (

**5**) Pinus sylvestris L.

**Figure 6.**Changes in the effectiveness of photosynthesis in the Scots pine trees as related to the age of the stands (

**1**) South Siberia; (

**2**) Middle Siberia; (

**3**) North Siberia.

**Figure 7.**The relationship between coefficients (1 − α) and s of the EcoSolow model for forest stands of different species in the northern and southern regions of Siberia. (

**1**) in the southern regions of Siberia (Pinus sylvestris L., Larix sibirica Ledeb., Betula pendula Roth.); (

**2**) in the northern regions of Siberia (Larix sibirica Ledeb., Abies sibirica Ledeb., Picea obovata Ledeb.).

Age, Years | Density, Trees/ha | Phytomass, t/ha | |||
---|---|---|---|---|---|

Stem with Bark | Needles | Branches | Roots * | ||

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 |

Woody Species, Location | ESM Parameters | ||
---|---|---|---|

A | α | s | |

Pinus sylvestris L., 53°50′ N 92° E | 0.72 | 0.23 | 0.54 |

Pinus sylvestris L., 51°45′ N 94°30′ E | 0.56 | 0.27 | 0.50 |

Larix sibirica Ledeb., 54° N, 91°E | 1.60 | 0.09 | 0.23 |

Larix sibirica Ledeb., 52° N, 95°30′ E | 1.39 | 0.17 | 0.70 |

Picea obovata Ledeb., 56°35′ N, 57°40′ E | 1.10 | 0.11 | 0.70 |

Picea obovata Ledeb., 59° N, 61° E | 0.73 | 0.28 | 0.39 |

Abies sibirica Ledeb., 59° N, 93° E | 0.67 | 0.24 | 0.28 |

Betula pendula Roth., 57° N, 93° E | 2.03 | 0.33 | 0.94 |

Betula pendula Roth., 55°10′ N, 92° E | 1.83 | 0.31 | 0.67 |

Pinus sylvestris L., 59°30′ N, 101°50′ E | 0.61 | 0.25 | 0.50 |

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**MDPI and ACS Style**

Soukhovolsky, V.; Ivanova, Y.
Modeling Production Processes in Forest Stands: An Adaptation of the Solow Growth Model. *Forests* **2018**, *9*, 391.
https://doi.org/10.3390/f9070391

**AMA Style**

Soukhovolsky V, Ivanova Y.
Modeling Production Processes in Forest Stands: An Adaptation of the Solow Growth Model. *Forests*. 2018; 9(7):391.
https://doi.org/10.3390/f9070391

**Chicago/Turabian Style**

Soukhovolsky, Vlad, and Yulia Ivanova.
2018. "Modeling Production Processes in Forest Stands: An Adaptation of the Solow Growth Model" *Forests* 9, no. 7: 391.
https://doi.org/10.3390/f9070391