Harvesting and Conversation in a Predator-Prey System

Abstract

Optimal harvesting of prey in a predator-prey ecosystem is studiedunder 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 harvesting rates are identified for particular ecosystem characteristics, harvesting costs, the discount rate value, and value functions for birds. These optimal harvest rates are constant harvesting, at levels possibly leading to the extinction of birds, or oscillating harvesting, giving rise to oscillating stocks of birds and shellfish. The approach path towards an optimal regime is shown qualitatively and consists of alternating between harvesting maximally and not harvesting at all