Abstract --- We discuss two types of partial differential equation models of fishery
harvesting problems. We consider steady state spatial models and diffusive
spatial-temporal models. We characterize the distribution of harvest
effort which maximizes the harvest yield, and in the steady state case,
also minimizes the cost of the effort. We show numerical results to
illustrate various cases. The results inform ongoing debate about the use
of reserves (regions where fishing is not allowed), and are increasingly
relevant as technology enables enforcement of spatially structured harvest
constraints.
Suzanne Lenhart is Assoc. Director of the National Insitute for Mathematical and Biological Synthesis.
