Harvesting a lichen-reindeer system in an uncertain environment

The optimal harvesting rule for a lichen-reindeer system with stochastic environmental variation is compared to a corresponding deterministic model. It is found that the optimal harvesting rule can be expressed as a function of lichen biomass only. The deterministic and stochastic solutions differ in three ways. Firstly, monality risk of the reindeer increases the discount rate. This results in a heavier use of the lichen resources and consequently the optimal target lichen biomass is in the stochastic model lower than in the deterministic case. Secondly, when the current lichen biomass is below the optimal target level, during lichen recovery more reindeer are left alive in the stochastic model, in order to avoid overharvesting the reindeer population. Thirdly, if the amount of lichen is greater than the optimal biomass value, more animals can be left alive in the deterministic model in order to reduce the lichen biomass back to the optimal value.