Placing invasive species management in a spatiotemporal context

Invasive species are a worldwide issue, both ecologically and economically. A large body of work focuses on various aspects of invasive species control, including how to allocate control efforts to eradicate an invasive population as cost effectively as possible. There are a diverse range of invasive species management problems, and past mathematical analyses generally focus on isolated examples, making it hard to identify and understand parallels between the different contexts. In this study, we use a single spatiotemporal model to tackle the problem of allocating control effort for invasive species when suppressing an island invasive species, and for long-term spatial suppression projects. Using feral cat suppression as an illustrative example, we identify the optimal resource allocation for island and mainland suppression projects. Our results demonstrate how using a single model to solve different problems reveals similar characteristics of the solutions in different scenarios. As well as illustrating the insights offered by linking problems through a spatiotemporal model, we also derive novel and practically applicable results for our case studies. For temporal suppression projects on islands, we find that lengthy projects are more cost effective and that rapid control projects are only economically cost effective when population growth rates are high or diminishing returns on control effort are low. When suppressing invasive species around conservation assets (e.g., national parks or exclusion fences), we find that the size of buffer zones should depend on the ratio of the species growth and spread rate.