A bio-economic optimization model for sustainable and long-term control of Sericea Lespedeza (Lespedeza Cuneata) invasion in the Great Plains
Native grasslands in the Great Plains are threatened by the spread of sericea lespedeza (Lespedeza cuneata), a noxious weed brought from Asia, which can damage forage or hay production and result in substantial economic loss to landowners. Sericea has spread over 5,501,400 acres of the mid- to southern Great Plains and has led to $29 million average annual forage loss in the Flint Hills region of Kansas. Therefore, policy makers and farmers need to find effective decision strategies for controlling sericea invasion and reducing the related damages. In this research, we develop a dynamic nonlinear bio-economic optimization model that is structured based on age, density, and frequency of invasive species. This very complex nonlinear optimization model integrates biological models into a decision theory framework while accounting for seed production and loss rates for different age classes, seed dispersal, longevity and germination, seed bank dynamics, survival rate of seedlings, carrying capacity, treatment costs, budget, and relevant economic loss. The model minimizes the sum of damages to hay and forage caused by the invasion of sericea over time subject to two main constraints: (1) growth and spread dynamics of invasive species over space and time, and (2) budget restricting the total cost of labor and herbicides used to control sericea. The numerical results provide effective management strategies to land managers and government officials regarding where, when, and how much resources need to be allocated for controlling sericea, and provide insights into the biological growth and spread behavior of invasive species.