Harvesting and conservation in a predator-prey system

Optimal harvesting of prey in a predator-prey ecosystem is studied under the condition that the existence of the predator has value. Predators (birds) and humans (fishers) compete for prey (shellfish). The behavior of the system is studied and conditions for optimal control are deduced. Various optimal harvest rates are identified for particular ecosystem and economic parameters. We discuss optimal harvest rates, focusing on system characteristics that lead to the survival of birds. The approach path towards an optimal regime is shown qualitatively for different types of optimal harvest regimes.