Optimal age-dependent sustainable harvesting of natural resource populations: Sustainability value

We studied the optimal age-dependent harvesting of a natural resource population that achieves a maximum income under the constraint of sustainability, i.e. the reproductive adults numbers must exceed a given minimum. The resource species is assumed to be semelparous (a single reproduction over a life). The economic value and natural mortality coefficient can vary with age. The optimal age-dependent harvesting under the sustainability constraint is obtained using Pontryagin’s maximum principle. The constraint of resource sustainability can be treated as an additional term measured in the same units as economic income. Specifically, three terms: (1) current harvesting value, (2) future harvesting value, and (3) sustainability value, are calculated for each age, and the resources should be harvested at the maximum rate when their current harvesting value is greater than the sum of future harvesting value and sustainability value, and should not be harvested otherwise. Numerical analyses of several cases demonstrated that the optimal harvesting schedule depends critically on the natural mortality coefficient and the functional form of the economic value of the resource.