Spread externalities and the implications of heterogeneous ecological capacity constraints

We develop a spatial-dynamic model of resource management in the presence of externalities, such as the spread of harmful invasive species, and show that ecological capacity constraints influence optimal management strategies across space. We use integer-programming methods to solve for optimal control strategies in both homogeneous and heterogeneous landscapes. Using the spread of gypsy moths as an application, our results show that optimal levels of control vary over space in landscapes with heterogeneous capacity constraints. Optimal outcomes depend on the marginal costs and damages associated with the externality and the emergence of spread externalities from relative differences in population levels between adjacent patches. In models with high degrees of heterogeneity, we show that a naïve policy assuming homogeneous carrying capacity results in a significantly higher welfare losses from the externality.