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Multi-Objective Sequential Forest Management Under Risk Using a Markov Decision Process-Pareto Frontier Approach

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Abstract

Forests play an important role in many different cycles (carbon sink, biodiversity, timber) and, consequently, in regulating the global climate system. Moreover, forests are the source of a wide range of goods and services to human societies and, as a result, the decisions made by forest owners affect forest ecosystems. Since forests are currently threatened by climate change, there is a need to provide support to forest owners for managing forests under risk, taking conflicting objectives into account. This study focuses on developing an explicit multiple-objective and sequential forest management model under risk. The multi-objective sequential optimization approach used here is based on the concept of Pareto optimality, and the computation of the Pareto frontier (the set of non-dominated solutions), instead of a single solution. We consider a Markov Decision Process (MDP) model to evaluate forest management policies under different criteria, and to generate the Pareto frontier. The framework is applied to the management of a private forest located in southwestern France. We identify optimal forest management practices for each objective separately and trade-off policies considering all objectives jointly. We analyze the forest management policies located on the Pareto frontier, yielding different trade-offs among the conflicting objectives. Our framework makes it possible to envision all possible trade-offs, and to understand how a trade-off policy takes each objective into account. It is hoped that this information will help in analyzing potential policy implications for forest management, taking the provision of multiple forest ecosystem services into consideration.

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Notes

  1. When the horizon is infinite, it can be shown that the value function of a stationary policy does not depend on time. For that reason, the time index does not appear in mathematical equations.

  2. As seen in Table 1, we assume that harvesting or fire occurs at the beginning of a period, and that the volume of timber is evaluated at the end of the period. In the case of harvesting, the carbon stored in harvested timber is considered as definitively lost.

  3. The model could be applied to any other forest species or area by simply modifying the parameters for all of the functions specified.

  4. The National Forest Inventory (NFI)’s purpose is to describe the surface of the national territory and the occupation of its soil, of elaborating and updating the permanent inventory of national forest resources (see https://inventaire-forestier.ign.fr/). It provides personalized data tables for specific queries that are useful for our purpose.

  5. All the Matlab codes to run and to reproduce the study are available on the on-line repository FigShare at the following address: https://doi.org/10.6084/m9.figshare.7707233.v2

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  1. UR 875 Applied Mathematics and Computer Science Laboratory, INRAE, 31326, Castanet-Tolosan, France

    Stéphane Couture, Marie-Josée Cros & Régis Sabbadin

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  1. Stéphane Couture
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  2. Marie-Josée Cros
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Couture, S., Cros, MJ. & Sabbadin, R. Multi-Objective Sequential Forest Management Under Risk Using a Markov Decision Process-Pareto Frontier Approach. Environ Model Assess 26, 125–141 (2021). https://doi.org/10.1007/s10666-020-09736-4

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