Study on Single Species One Sex Age-structured Fish Population Model with Restricted Harvesting

A discrete age-structured Bernardelli, Lewis and Leslie (BLL) population model for a single species is formulated under age dependent harvesting condition. Here, after an initial period during which the growth of the species is not much, harvesting is performed. Its rate is proportional to the available bio-mass (number of species) of different age group population and decreases with the age of the species by considering monotonic decreasing catch per unit effort parameter. The modified Leslie matrix for the present models is derived. Stability of the system is studied from the ratio of the population densities with respect to times. This kind of study is very important in population biology as to get an idea about the future biomass and sustainability of the species.