Optimization Model and Algorithm for the Design of Connected and Compact Conservation Reserves

Conservation planning is fundamental to guarantee the survival of endangered species and to preserve the ecological values of some ecosystems. Planning land acquisitions increasingly requires a landscape approach to mitigate the negative impacts of spatial threats such as urbanization, agricultural development, and climate change. In this context, landscape connectivity and compactness are vital characteristics for the effective functionality of conservation reserves. Connectivity allows species to travel across landscapes, facilitating the flow of genes across populations from different protected areas. Compactness measures the spatial dispersion of protected sites, which can be used to mitigate risk factors associated with species leaving and re-entering the reserve. This research proposes an optimization model to identify areas to protect while enforcing connectivity and compactness. In the suggested projected area, this research builds upon existing methods and develops an alternative metric of compactness that penalizes the selection of patches of land with few protected neighbors. The new metric is referred as leaf because it intends to minimize the number of selected areas with 1 neighboring protected area. The model includes budget and minimum selected area constraints to reflect realistic financial and ecological requirements. Using a lexicographic approach, the model can improve the compactness of conservation reserves obtained by other methods. The use of the model is illustrated by solving instances of up to 1100 patches.