Sustainable Continuous Cover Forestry Dynamics, Optimal Decisions, and Empirical Estimations

Department of Forest and Wood Technology, Faculty of Technology, Linnaeus University, Vaxjo, Sweden
peter.lohmander@icloud.com
*Corresponding author
Manuscript received December 4, 2023; accepted March 13, 2024; published June 27, 2024.

Abstract—Sustainable continuous cover forestry is defined and analyzed in several ways. The differential equation representing growth of the basal areas of individual trees, motivated by fundamental biological production theory by Lohmander, is analyzed and extended in different directions. From the solution of the differential equation, the basal areas and the tree diameters are obtained as explicit functions of time. The diameter is a strictly increasing function of time. In the absence of competitors, the diameter increment is shown to be a strictly decreasing function of time. Hence, the diameter increment can also be interpreted as a strictly decreasing function of the diameter. Alternative forms of adjustment of the differential equation, with consideration of competition, are defined. If the competition is strong, with large trees in the vicinity of a particular tree, then the basal area increment, and the diameter increment, are reduced. The growth of a large tree is less sensitive than the growth of a small tree, to competition from other trees. Under strong competition, the basal area increment, and the diameter increment, are strictly concave functions of the size of the tree. The unique maximum of the diameter increment occurs at a higher diameter, if the competition increases. In dynamic equilibrium, the tree size frequency distribution is stationary. If natural tree mortality can be avoided via the harvest strategy, the tree size frequency distribution is a function of the size and competition dependent growth function, and the harvest strategy. Empirical tree size frequency data are used to simultaneously estimate parameters of a size and competition dependent growth function and the applied harvest strategy, via nonlinear optimization. The properties of the estimated growth function are consistent with the corresponding properties of the production theoretically motivated hypothetical function, and the properties of the estimated harvest strategy confirm the corresponding hypotheses. The R2 of the nonlinear regression exceeds 0.97. With access to an empirically estimated equilibrium tree size distribution, it is possible to: 1. Estimate size frequency relevant parameters of tree size and competition dependent growth functions for individual trees. 2. Estimate the applied harvest strategy. 3. Explain and reproduce the empirically estimated tree size equilibrium distribution.

Keywords—continuous cover forestry, sustainability, optimization, growth parameter estimation

Cite: Peter Lohmander, "Sustainable Continuous Cover Forestry Dynamics, Optimal Decisions, and Empirical Estimations," International Journal of Sustainability in Energy and Environment, vol. 1, no. 1, pp. 65-76, 2024.

Copyright © 2024 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).