A two-agent dynamic model with an invasive weed diffusion externality: an application to Yellow Starthistle (Centaurea solstitialis L.) in New Mexico

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.

Using economic instruments to develop effective management of invasive species: insights from a bioeconomic model

Economic growth is recognized as an important factor associated with species invasions. Consequently, there is increasing need to develop solutions that combine economics and ecology to inform invasive species management. We developed a model combining economic, ecological, and sociological factors to assess the degree to which economic policies can be used to control invasive plants. Because invasive plants often spread across numerous properties, we explored whether property owners should manage invaders cooperatively as a group by incorporating the negative effects of invader spread in management decisions (collective management) or independently, whereby the negative effects of invasive plant spread are ignored (independent management). Our modeling approach used a dynamic optimization framework, and we applied the model to invader spread using Linaria vulgaris. Model simulations allowed us to determine the optimal management strategy based on net benefits for a range of invader densities. We found that optimal management strategies varied as a function of initial plant densities. At low densities, net benefits were high for both collective and independent management to eradicate the invader, suggesting the importance of early detection and eradication. At moderate densities, collective management led to faster and more frequent invader eradication compared to independent management. When we used a financial penalty to ensure that independent properties were managed collectively, we found that the penalty would be most feasible when levied on a property's perimeter boundary to control spread among properties. At the highest densities, the optimal management strategy was "do nothing" because the economic costs of removal were too high relative to the benefits of removal. Spatial variation in L. vulgaris densities resulted in different optimal management strategies for neighboring properties, making a formal economic policy to encourage invasive species removal critical. To accomplish the management and enforcement of these economic policies, we discuss modification of existing agencies and infrastructure. Finally, a sensitivity analysis revealed that lowering the economic cost of invader removal would strongly increase the probability of invader eradication. Taken together, our results provide quantitative insight into management decisions and economic policy instruments that can encourage invasive species removal across a social landscape.