Optimal two-species harvesting policy with price and size (biomass) of the fish population dependent catch rate function

This paper develops an optimal combined harvesting policy for a Lotka–Volterra ecosystem of prey–predator populations with both ameliorating and deterioration effects. Here, the rates of growth and decay are assumed to be constant and the catch rates of the items are linear functions of their respective selling prices and available biomasses. The withdrawal of the species from bhery depends on the respective catch rate. The optimal amounts of the species for one-time harvesting are evaluated in order to maximize the profit over a fixed time period using a gradient-based optimization technique. The model has been illustrated with some numerical data. As particular cases, results have been obtained for both biomass dependent/independent withdrawals in the presence of predator. Optimal harvesting quantity of one species (i.e. prey) is also obtained in the absence of another species (i.e. predator).