Optimal Harvesting of Size-Structured Biological Populations

The question of harvesting size-structured biological resources is generic in resource economics but purely understood. This study is based on a well known density-dependent size-structured population model that includes an age-structured model as a special case. Harvest from each size class can be chosen independently. Mathematically the model is an any number of state and control variables discrete-time optimization problem. While earlier studies have analysed the Maximum Sustainable Yield (MSY) steady states using problem-specific optimization procedures, this study applies non-linear programming and analyses the dynamic economic problem. It is shown that with two size classes, there may exist six steady state regimes. The optimal steady state is shown to be either unique or a continuum implying that earlier MSY-theorems are not entirely correct. Given a unique steady state the optimal solution converges toward a saddle point steady state or a stationary cycle. Optimal harvest of single individuals deviates from Faustmann-type timing, and a higher interest rate may cause a shift to harvesting older age classes. For the general specification with any number of size classes, equations for optimal steady states and a stability result are obtained.