The use of Markov optimization models in the economic and ecological management of forested landscapes under risk

Abstract

Markov chains and Markov decision process models are very powerful approaches to simulate or optimizing forest systems under risk. The method consists first in transforming the initial system, possibly represented with a complex stochastic simulator, in a table of transition probabilities, as in a Markov chain, and then bringing the power of optimization to this simplified model. Markov chain models are tables of probabilities signifying the chances that a particular system changes from one state to another within a specified amount of time. They have wide and effective applications in forestry. Even the simplest results of Markov chains can give insights on forest growth dynamics. In particular, they can help predict the effects of natural or human disturbances on forest landscapes. They can also be used to project the evolution of a forest stand over time, through specific succession phases. The results of Markov chain theory, such as mean recurrence time and mean residence time help clarify the dynamics of forest stands, and its consequences for landscape diversity. Markov chains are also useful to predict the effects of management policies under risk, for both economic and ecological criteria. Markov decision process models introduce decision making in forest systems that evolve according to a Markov chain. A policy is a rule that specifies a decision fore each stand state. Mathematical programming can be used here to optimize the present value of expected returns from a stand state over an infinite horizon. Decisions that maximize a long-term expected value criterion, such as the long-term expected biodiversity of a stand, or the long-term expected periodic income, can also be found. We report on an application of these methods to the mixed loblolly pine (Pinus taeda L.) and hardwood forests in the southern United States. The results showed that natural catastrophes enhanced the diversity of the landscape, but impaired the tree diversity. Following current management would generate high landscape diversity, but low timber productivity. A highly diverse landscape could be maintained while keeping the tree diversity near the achievable maximum. But managing to maximize tree size diversity or species diversity would much decrease landscape diversity. The opportunity cost of preserving a highly diverse landscape was high in terms of foregone timber production.