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Optimal Rotation Age in Fast Growing Plantations: A Dynamical Optimization Problem.
Alex Altamirano-Fernández1, Alejandro Rojas-Palma2, Sergio Espinoza-Meza3
1Departamento de Matemática, Física y Estadística, Universidad Católica del Maule, Av San Miguel 3605, 3460000, Talca, Chile. alex.altamirano@alu.ucm.cl.
Bulletin of Mathematical Biology
|April 6, 2024
Summary
Climate change impacts forest plantations. This study models optimal timber rotation ages, finding 24 years for realistic scenarios and 19 years for pessimistic fire-prone conditions to maximize economic benefits.
Area of Science:
- Forestry science
- Environmental economics
- Mathematical modeling
Background:
- Forest plantations are vital for timber and carbon capture, but climate change may alter growth and optimal harvest timing.
- Existing mathematical models for climate change effects on timber rotation age are limited.
- Understanding these impacts is crucial for sustainable forest management and economic viability.
Purpose of the Study:
- To determine the optimal rotation age for timber production that maximizes net economic benefits under a negative climate change scenario.
- To develop and apply a bioeconomic optimal control model incorporating forest growth, fire risk, and management strategies.
- To analyze the influence of climate change and fire incidence on rotation age and economic returns for Pinus radiata plantations.
Main Methods:
- Formulated a bioeconomic optimal control problem using a system of Ordinary Differential Equations (ODEs).
- Incorporated state variables: live biomass volume, intrinsic growth rate, and fire-affected area.
- Utilized control variables for felling, thinning, reforestation, and fire prevention, solved numerically via the Forward-Backward Sweep method.
Main Results:
- Optimal strategies involve simultaneous management of felling, thinning, and reforestation based on biomass and harvest levels.
- Fire prevention spending is reduced in realistic scenarios but increased in pessimistic, high-fire-risk scenarios.
- Optimal rotation ages were determined as 24 years for realistic and 19 years for pessimistic scenarios for Pinus radiata.
Conclusions:
- The optimal rotation age is significantly influenced by fire incidence, directly impacting net economic benefits.
- Integrated forest management strategies, including fire prevention, are essential for maximizing economic returns under climate change.
- The model provides valuable insights for adaptive forest management in response to changing environmental conditions.
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