Optimum Age-specific Harvesting Policy For A Population Growing According To The Leslie Matrix Model

Abstract

Under favorable conditions, natural animal population has a tendency to increase in numbers. It is, however, possible to remove some animals and still maintain a constant population size. This type of removal is known as harvesting. The word "harvesting" is not necessarily a euphemism for "slaughtering"; the animals may be removed from the population for other reasons. To harvest a population in an optimal way we must understand the factors regulating the abundance of that population. That man so frequently mismanages exploited population like the pacific sardine and the Nile perch is partly a measure of his ignorance of population dynamics. Management of forestry, fishery and wildlife resources is presently based more on rules of thumb and empirical results than on scientific knowledge and forecasting; and one of the great challenges of modem ecology is to place resource management on a scientific basis. Indeed, we can all be very good at managing yesterday's population. The questions is; when will we be equally adept at managing tomorrow's? In this project we are concerned with the best way to harvest a renewable natural resource without destroying it or reducing it to a level where further exploitation is fruitless. In particular, we examine the problem of removing the maximum harvest in terms of number of animals or biomass or any linear combination of the proportions harvested from various age-groups or.stages in the life-cycle of the population subject to various conservation constraints. One of the most important constraints is the fact that a fixed population size and age structure be maintained after every time interval. In this respect we have restricted ourselves to what is called sustainable harvesting policy. In this policy an animal population is periodically harvested in such a way that the yield of each harvest is the same and the age-distribution of the population remaining after each harvest is also the same. Thus, the animal population is not completely depleted by a sustainable harvesting policy; only the excess growth is exploited.