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

Yulia Ivanova,Vlad Soukhovolsky

doi:10.3390/f9070391

Abstract

The model of forest stand growth proposed in this study is based on R. Solow’s model of economic growth. The variables introduced into the model are the “capital” (the phytomass of the non-synthesizing tree components in the stand—the stem, roots, and branches) and the “labor” (the phytomass of the photosynthesizing tree components in the stand—leaves or needles). Root phytomass is calculated with a special independent model. The process of energy production by the trees is described with the Cobb-Douglas equation. The proposed approach is used to describe growth processes in the forest stands comprising various species in Siberia and the age dynamics of net primary production. The model can explain a number of effects (such as death of the forest stand after the needles have been consumed by defoliating insects) that cannot be explained by standard logistic models.

Highlights

IntroductionThe growth of individuals and populations can be presented as the totality of all births (the birth of a new individual or a change in the population density, biomass of an individual, or biomass of the entire population) and dissipation (the death of an individual or a population).Growth processes are usually described by using logistic models, including the Verhulst, Gompertz, Mitscherlich, Chapman-Richards functions, etc. [1,2,3,4,5,6,7,8]
The growth of individuals and populations can be presented as the totality of all births and dissipation.Growth processes are usually described by using logistic models, including the Verhulst, Gompertz, Mitscherlich, Chapman-Richards functions, etc. [1,2,3,4,5,6,7,8]
Descriptions of processes observed in forest stands by growth models are not in complete agreement with the real processes occurring in the forest

Summary

Introduction

The growth of individuals and populations can be presented as the totality of all births (the birth of a new individual or a change in the population density, biomass of an individual, or biomass of the entire population) and dissipation (the death of an individual or a population).Growth processes are usually described by using logistic models, including the Verhulst, Gompertz, Mitscherlich, Chapman-Richards functions, etc. [1,2,3,4,5,6,7,8]. The growth of individuals and populations can be presented as the totality of all births (the birth of a new individual or a change in the population density, biomass of an individual, or biomass of the entire population) and dissipation (the death of an individual or a population). Growth processes are usually described by using logistic models, including the Verhulst, Gompertz, Mitscherlich, Chapman-Richards functions, etc. The death of the forest stand is as natural as its growth, and mortality processes should be described in the model too [9]. Consumption at an arbitrary time of any amount of phytomass that is smaller than its current value never causes the death of a forest stand. A fir tree (Abies sibirica Ledeb.) dies if larvae of the Siberian silk moth (Dendrolimus sibiricus Tschetv.) have consumed all its needles, the phytomass of the needles constitutes about 3% of the total phytomass of a 100-year-old tree [10,11]

Methods

Results

Discussion

Conclusion