Optimal harvesting of a plant-hervibore system: lichen and reindeer in northern Finland

The optimal harvesting policy for a plant-herbivore system consisting of lichen and reindeer in Finnish Lapland is investigated. Using a discrete time model with no age structure it is shown that the optimal procedure to reach target levels for lichen and reindeer involves a possible initial harvest of reindeer and then a sequence of no-harvesting years until the lichen has recovered. After two adjusting harvests the system will settle to an equilibrium. The optimal solution is compared with the fastest possible approach to the target levels. The two solutions coincide if future yields are sufficiently discounted. With a discount factor near one there will be a heavier initial harvest in the optimal solution. It is seen that allowing some harvesting also in the no-harvesting years has no marked effect on the total yield. The target levels for lichen and reindeer are not unique but depend both on discounting and on the length of the planning period.