Optimal Fishery Modelling Population Dynamics with Optimal Harvest Strategies

Abstract: Determining sustainable harvest strategies are of interest in order to avoid overexploitation of ecosystems. In this report the dynamics of sh populations a ected by shery is studied. The aim is to nd an optimal catch policy under which shery shall be performed in order to obtain maximum catch without the sh population facing extinction. By formulating this as an optimal control problem, Pontryagin's principle can be used in order to nd optimal harvest strategies. The numerical results show that for a spatially independent model of a single population, there is an optimal population size which gives maximum yield. For interdependent species, interference by shery may change the qualitative behaviour of the dynamical system. The majority of the studied dynamical systems had a stationary optimal strategy.