OPTIMAL DYNAMIC HARVEST OF A MOBILE RENEWABLE RESOURCE

We present a mathematical model for the growth, movement, and harvesting of a renewable resource, and characterize the spatiotemporal distribution of harvest effort which maximizes the present value of harvest (yield) over a finite time horizon. We derive the optimality system for this model and show that the yield-maximizing solution often includes one or more no-take reserves that change in size over time. We explore how the results change with varying parameter values. The results inform ongoing debate about the use of reserves, and are increasingly relevant as technology enables enforcement of spatially structured harvest constraints.