Lohmander, P. Sustainable Continuous Cover Forestry Dynamics, Optimal Decisions, and Empirical Estimations. Preprints2024, 2024021250. https://doi.org/10.20944/preprints202402.1250.v1
APA Style
Lohmander, P. (2024). Sustainable Continuous Cover Forestry Dynamics, Optimal Decisions, and Empirical Estimations. Preprints. https://doi.org/10.20944/preprints202402.1250.v1
Chicago/Turabian Style
Lohmander, P. 2024 "Sustainable Continuous Cover Forestry Dynamics, Optimal Decisions, and Empirical Estimations" Preprints. https://doi.org/10.20944/preprints202402.1250.v1
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 (2017a), is analyzed and extended in different directions.
From the solution of the differential equation, the basal area and the tree diameter 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.
Environmental and Earth Sciences, Sustainable Science and Technology
Copyright:
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