The Effects and Value of a Resistant Perennial Variety: An Application to Pudrición del Cogollo Disease

This article develops a forestry model to obtain the optimal control strategy and optimal rotation length after a disease attacks in a perennial variety. Three cases are considered: a benchmark consisting of a disease-free field, an identical field with the disease present but no resistant variety with which to replant, and an identical field with the disease present and a resistant variety with which to replant. We determine general decision rules and then apply the model to the case of Pudrición del Cogollo, a major disease threat to the Colombian oil palm industry. In the application, we compare the optimal rotation length between the three scenarios and determine the optimal level of control in each period for the disease scenarios. The singular solution involves complete control of the disease, and in the absence of a resistant variety, the presence of the disease increases the rotation length. With these solutions, we then determine the value of developing a resistant variety. This value depends heavily on the age distribution of the current trees and decreases as the average tree age decreases. The value further declines when the resistance variety has negative attributes such as higher replanting and maintenance costs than the original variety.