On the Optimal Policy for Combined Harvesting of Independent Species

By a combination of analytical reasoning and numerical experiment it is demonstrated that, for the combined harvesting of two ecologically independent species which grow logistically and are harvested at a rate proportional to both stock level and effort, there is a unique attainable equilibrium which yields positive revenue and to which the approach path satisfies all of Pontryagin's necessary conditions for maximizing the harvest's present value. A simple feedback law governs this approach and is conjectured to be the optimal policy. On that basis, criteria are found for the survival of the less productive species, as a function of the system parameters and initial stocks. An economic interpretation of the equilibrium is also given.