On Optimal Harvesting in Age-Structured Populations

Abstract

The problem of optimal harvesting (in a fish population as a benchmark) is stated within a model that takes into account the age-structure of the population. In contrast to models disregarding the age structure, it is shown that in case of selective harvesting mode (where only fish of certain sizes are harvested) the optimal harvesting effort may be periodic. It is also proved that the periodicity is caused by the selectivity of the harvesting. Mathematically, the model comprises an optimal control problem on infinite horizon for a McKendrick-type PDE with endogenous and non-local dynamics and boundary conditions.