Optimal harvesting in forestry: steady-state analysis and climate change impact

Abstract

We perform the steady-state analysis of a nonlinear partial differential equation model that describes the dynamics of a managed size-structured forest. The harvesting policy is to maximize the net benefits from timber production over an infinite planning horizon. The existence and uniqueness of the steady-state trajectories are analysed. Closed-form steady states are obtained in meaningful special cases and are used to estimate how climate change affects the optimal harvesting regime, diameter of cut trees, number of logged trees, and net benefits in the long run.

Keywords:

• sustainable forestry
• optimal control of nonlinear partial differential equations
• size-structured forest
• climate change

Acknowledgements

The authors express their deep gratitude to Prof. Saber Elaydi for organizing the 3rd International Conference on Mathematical Modeling and Analysis of Populations in Biological Systems, San Antonio, TX, October 7–9, 2011; participants of the conference for their useful remarks on the presented topic; Editor in Chief Dr J. M. Cushing and two anonymous reviewers for their valuable comments. The work is supported by the NSF DMS grant 1009197 and the Ministerio de Ciencia e Innovación grant Econ2010-17020.