Optimising management against dynamic threats: A spatially explicit approach based on integer programming

Abstract Defining strategies to control dynamic threats is a highly complex problem that is defined by the biological characteristics of the threatening agents (e.g. invasive species), the landscape context and the management objective within the constraints of limited financial resources. While different optimisation models have focussed on finding frameworks capable of incorporating complex dynamics between species and threats, they often overlook the spatial aspect of management plans or address it at a very coarse resolution. Here, we develop a framework based on a Mixed Integer Programming (MIP) methodology to design multi‐period management planning strategies that account for the dynamic nature of threats and abatement actions. The model is capable of dealing with different types of threats, depending on their nature and propagation rate. The allocation of management actions in space and time is prioritised to maximise the area where all species are free from threats at the end of the planning period. Employing a Warm‐start algorithmic strategy ensures rapid generation of feasible solutions, enhancing the model's practical applicability and scalability. To demonstrate the effectiveness of our methodology, we apply it to two case studies. The first case simulates a threat's appearance and radial spread within a 10 × 10 grid, where two species are spatially distributed. The second case focusses on a portion of the Mitchell River catchment in northern Australia, where 31 freshwater fish species are affected by one simulated threat, using a wide range of management budgets. The results demonstrate how the methodology allows giving a guide on the best use of the resources considering trade‐offs among the ecological, spatial and cost criteria, enabling decision‐makers to explore and analyse a broad range of conservation strategies and to select the one exhibiting the best quantitative and qualitative strategic and operational outcomes. Our model and resolution approach enable decision‐makers to explore and analyse a broad range of strategies to concurrently halt, eliminate or contain the propagation of multiple threats. The ability to optimally deal with large‐scale, realistic scenarios makes our approach an important contribution to the field of invasive species control.