Functional Differential Equations in Sustainable Forest Harvesting

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This article deals with the dynamics of the volume control method in forest regulation. The sustainability of harvesting a given constant volume in a simplified forest model is studied. Depending on the initial age distribution, the cut can lead to the forest exhaustion, or to an asymptotic steady-state uniform age distribution. A continuous model is formulated in terms of various kinds of partial differential equations, delay differential equations, and non-linear integral equations. Equilibrium solutions and their stability properties are determined. Discrete models are also obtained, both by direct reasoning and as approximations to the continuous case. These are used for simulation and graphical exploration of the system behavior. In addition, contrasting various discrete and continuous versions was found useful in clarifying some issues, in particular, ambiguity/redundancy problems in the relation between integral equations and delay differential equations derived from them. The basic problem of evaluating sustainability for an initial distribution remains unsolved, however. Further progress is linked to the asymptotic properties of a second-order recurrence relationship. It is hoped that the interplay between the theory of functional differential equations and this concrete and easily interpretable problem in forest management might prove fruitful in both fields.
森林計画学会の論文
2001-02-00