Faculty Publications


A mathematical model of tree harvesting in age-structured forests subject to beetle infestations

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Maria Conceição A. Leite

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In this paper, we investigate a mathematical model for age-structured forest–beetle interactions that includes harvesting of trees. The aim is to broaden the understanding of the synergistic effects of harvesting and insect infestation on the age structure of the forests and the harvesting benefit. In the first part of this study, we consider different scenarios of the forest infestation by beetles and observe that the quantitative age profile of the forest depends significantly on whether the beetle population is in its endemic or epidemic states. In the second part, we also include harvesting of the forest trees and analyze two different harvesting strategies: cutting all trees older than a certain age, and cutting a fixed proportion of trees older than a certain age. Numerical simulations are implemented to determine the optimal cutting age for both harvesting strategies. The numerical simulations reveal that, independent of the steady state of the beetle population (that is, no beetles, endemic or epidemic state) clear cutting all trees older than a given age provides a higher harvesting benefit. Our numerical simulations further indicate that to obtain a fixed harvesting yield, a forest under a beetle epidemic state has to be cut at a younger age than if the forest were at an endemic beetle state or a no-beetle state.


Springer International Publishing