Optimal harvesting policy for an age-specific population

Abstract

The optimal equilibrium harvesting policy for an age-specific population of females is investigated. Using a Leslie growth model, we consider admissible harvesting policies in which a certain fraction of each age group is harvested in such a way that the population returns to an identical age configuration after each harvest. The optimal harvesting policy, that policy which maximizes the yield subject to a linear ecological or economic constraint, is found. It is shown to consist of harvesting a certain fraction of a primary age group and all of a secondary age group. The primary age group is younger than, or the same age as, the “surplus” age group, that age group during which the cumulative expected number of daughters born to a female first exceeds one. The secondary age group is older than the surplus age group, though in some cases it is absent from the problem. The two harvesting ages are dependent on the birth and death rates and the economic parameters of the problem.