Optimal harvesting of stochastic spatial resources

We characterize the optimal harvest of a renewable resource in a generalized stochastic spatially explicit model. Despite the complexity of the model, we are able to obtain sharp analytical results. We find that the optimal harvest rule in general depends upon dispersal patterns of the resource across space, and only in special circumstances do we find a modified golden rule of growth that is independent of dispersal patterns. We also find that the optimal harvest rule may include closure of some areas to harvest, either on a temporary or permanent basis (biological reserves). Reserves alone cannot correct open access, but may, under sufficient spatial heterogeneity and connectivity, increase profits if appropriate harvest controls are in place outside of reserves.