Optimizing strategies for slowing the spread of invasive species.

Invasive species are spreading worldwide, causing damage to ecosystems, biodiversity, agriculture, and human health. A major question is, therefore, how to distribute treatment efforts cost-effectively across space and time to prevent or slow the spread of invasive species. However, finding optimal control strategies for the complex spatial-temporal dynamics of populations is complicated and requires novel methodologies. Here, we develop a novel algorithm that can be applied to various population models. The algorithm finds the optimal spatial distribution of treatment efforts and the optimal propagation speed of the target species. We apply the algorithm to examine how the results depend on the species' demography and response to the treatment method. In particular, we analyze (1) a generic model and (2) a detailed model for the management of the spongy moth in North America to slow its spread via mating disruption. We show that, when utilizing optimization approaches to contain invasive species, significant improvements can be made in terms of cost-efficiency. The methodology developed here offers a much-needed tool for further examination of optimal strategies for additional cases of interest.