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Statistics and Mathematics of General Control Function Optimization for Continuous Cover Forestry, with a Swedish Case Study based on Picea abies
Optimal Solutions, Sweden.ORCID iD: 0000-0003-2013-2580
Linnaeus University, Faculty of Technology, Department of Forestry and Wood Technology.
2022 (English)In: Asian Journal of Statistical Sciences, ISSN 2582-9912, Vol. 2, no 1, p. 1-35Article in journal (Refereed) Published
Abstract [en]

Continuous cover forests contain large numbers of spatially distributed trees of different sizes. The growth of a particular tree is a function of the properties of that tree and the neighbor trees, since they compete for light, water and nutrients. Such a dynamical system is highly nonlinear and multidimensional. In this paper, a particular tree is instantly harvested if a control function based on two local state variables, S and Q, is satisfied, where S represents the size of the particular tree and Q represents the level of local competition. The control function has two parameters. An explicit nonlinear present value function, representing the total value of all forestry activities over time, is defined. This is based on the parameters in the control function, now treated as variables, and six new parameters. Explicit functions for the optimal values of the two parameters in the control function are determined via optimization of the present value function. Two equilibria are obtained, where one is a unique local maximum and the other is a saddle point. An equation is determined that defines the region where the solution is a unique local maximum. Then, a case study with a continuous cover Picea abies forest, in southern Sweden, is presented. A new growth function is estimated and used in the simulations. The following procedure is repeated for five alternative levels of the interest rate: The total present value of all forest management activities in the forest, during 300 years, is determined for 1000 complete system simulations. In each system simulation, different random combinations of control function parameters are used and the total present value of all harvest activities is determined. Then, the parameters of the present value function are estimated via multivariate regression analysis. All parameters are determined with high precision and high absolute t-values. The present value function fits the data very well. Then, the optimal control function parameters and the optimal present values are analytically determined for alternative interest rates. The optimal solutions found within the relevant regions are shown to be unique maxima and the solutions that are saddle points are located far outside the relevant regions. 

Place, publisher, year, edition, pages
ARF India , 2022. Vol. 2, no 1, p. 1-35
National Category
Forest Science Probability Theory and Statistics
Research subject
Technology (byts ev till Engineering), Forestry and Wood Technology; Statistics/Econometrics
Identifiers
URN: urn:nbn:se:lnu:diva-125725Scopus ID: 2-s2.0-85168221481OAI: oai:DiVA.org:lnu-125725DiVA, id: diva2:1813230
Available from: 2023-11-20 Created: 2023-11-20 Last updated: 2023-11-20Bibliographically approved

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Lohmander, PeterFagerberg, Nils

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