A problem of optimal harvesting policy in two-stage age-dependent populations

The optimal equilibrium harvesting policy is investigated for an age-dependent population of females whose life history consists of two stages termed eggs (or juveniles) and adults. Using a continuous-time linear model, we consider admissible harvesting policies in which a certain fraction of individuals of fixed ages is harvested per unit time in both stages to bring the population to an equilibrium level. Determination of the harvest rate that maximizes the sustainable yield, subject to a linear ecological or economic constraint, leads to a nonlinear, nonconvex optimization problem. The optimal policy is shown to consist of harvesting at most three ages. Thus, we say that the harvest is trimodal. In one stage, at most two ages are harvested, with the oldest being harvested completely; in the other, at most one age is harvested completely. In each stage, the age totally removed, if present, is older than the surplus age, which is the age at which the proportion of the expected number of eggs multiplied by the proportion of the expected number of adults first exceeds one. The three harvesting ages are dependent on the birth, maturation, and death rates and on the economic parameters of the problem. A simple algorithm to find the optimum harvesting strategy is described.