A mixed integer programming approach to address cumulative threats in multi action management plans for biodiversity recovery

Traditionally, most of the prioritization models used by researchers and practitioners, rely on spatially dichotomous settings for threats, for species and for actions’ benefit; i.e., threats and species are present with equal intensity in some territorial units (while in the other units are not present at all), and actions have impact only on those units where they are applied. However, when dealing with ecological phenomena on large and complex territories, characterized by different areas (such as multiple realms or large river basins) and different spatial connectivity patterns among them, such a dichotomous setting does not capture the spatial (cumulative) diffusion of threats and thus actions’ benefits. Hence, common conservation planning tools are likely to misestimate the benefits of actions and the impact of threats, yielding less effective solutions. In order to address this issue, we develop a framework for designing multi-action prioritization plans featuring threats and actions’ benefit spatial diffusion. Our framework relies on a mathematical programming model that identifies priority areas for the implementation of management actions for multiple threats across a complex and large landscape. We consider the particular case an ecological setting characterized by different realms, multiple threats, and multiple species. We use the Tagus River (Iberian Peninsula) as a case study, including four realms (terrestrial, freshwater, estuary, and marine), where we integrate three different types of spatial connectivity: longitudinal along rivers, and multidimensional in the estuary and marine realms. We simulate the spatial diffusion of threats across the study area using four types of decay models (dispersal kernels): one exponential kernel, two negative triangular kernels (medium and high), and no dispersal. The results show how the MIP-based methodology offers a flexible and practical strategy for incorporating the cumulative effects of threats into action management planning. Furthermore, the primal-MIP heuristic was demonstrated to be a noteworthy alternative for finding good bounds of the original MIP model.