Optimal stand management with endogenous risk of sudden destruction

Abstract

The optimal thinning and rotation age policy for a stand subject to risk of destruction by windthrow is investigated. In particular, risk is not assumed exogenous as in previous research, but is modelled as endogenous to stand management. It is shown that the optimal solution when risk is endogenous differs significantly from the optimal solution to a problem where risk is assumed absent or exogenous. We find that in spite of substantial fixed costs related to thinning, the optimal number of thinnings increases and the optimal intensity of each thinning decreases. Furthermore, we find that the shortening effect of risk on the optimal rotation age is reduced substantially, when the thinning strategy is optimized subject to the effect on the risk levels. We conclude that the presence of endogenous risk strongly affects the optimal management strategy, and that an ecologically better founded approach to stand management is optimal in such cases. A group of solutions centred around a local optimum was characterized by fewer, more intense thinnings and a drastic shortening of the rotation age. If fixed costs were to increase substantially, this local optimum may become global, but still result in a longer rotation and more frequent thinnings than in the case of exogenous risk. Finally, features of the model's risk dynamics allow an analysis of the effect of changing the stand's resistance to and ability to recover from (i.e. the stand's resilience) the disturbances caused by thinnings, measured as changes in the susceptibility to windthrow. We find that in spite of the fixed costs related to thinning, a decrease in resistance or resilience makes it optimal to increase the number of thinnings, while at the same time making each thinning less intense.