A mathematical model to investigate the effects of fishing zone configurations and mass dependent rates on biomass yield: Application to brown shrimp in Gulf of Mexico

Abstract

A mathematical model is developed to investigate the effect of harvesting zone configuration upon total biomass yield of a resource species with size dependent continuum spatiotemporal population dynamics. Size (with the interpretation of average mass per individual at each spatiotemporal point) is modeled as an additional state variable along with population density in contrast to the traditional approach of viewing size as a structure parameter. The model takes a form of a coupled system of partial differential equations (PDE) of reaction–diffusion type for the population density and first-order hyperbolic transport type for the mass state variable. The model was investigated both analytically and numerically and is illustrated by applying it to the harvesting of a brown shrimp population in the Gulf of Mexico distributed within a patched network of hypothesized marine protection areas (MPAs) and fishing zones. The results highlight the critical role that size dependent mobility plays in determining optimal MPA network configurations.