In this paper, the following type of harvesting problem is considered. An animal population is divided into two stocks: an 'underlying' population and a 'surface' population. It is assumed that there is a natural exchange between the two population levels. The predator or harvestor affects only the 'surface' population and does not influence the 'underlying' population directly. Such a situation occurs, for example, in the off-shore Eastern Tropical Tuna Fishery. In this case, tuna associate with porpoise schools. The fishery harvests only those tuna associated with porpoise. Consequently, the underlying population of tuna is not sampled by the fishery. One may wonder what information measurements on the surface, harvested population provides about the unobservable underlying population. Furthermore, it is interesting and important to know if the standard, linear relationship between harvest and effort is valid in an aggregating population.