Maximum sustainable yield with continuous age structure and density-dependent recruitment

The problem addressed is that of finding the harvesting policy that will maximize the yield and maintain a given population in a steady state. It is assumed that the equations describing the evolution of the population and the yield are linear but that the equation describing reproduction is nonlinear (density dependence). The optimal strategy consists in harvesting two age classes only: a younger age class is partially harvested, and an older age class is completely harvested as in the linear case. This problem is a particular case of a general abstract maximization problem in which, for example, nonlinear mortality or nonlinear value of the individuals can also be introduced. The appropriate compactness for this problem is obtained from the fact that maximizing sequences are decreasing.