Designing compact, connected and gap-free reserves with systematic reserve site selection models.

Protected areas play a crucial role in current global policies to mitigate the erosion of biodiversity and systematic reserve site selection models are increasingly involved in their design. These models address the optimisation problem that seeks to cover spaces hosting biodiversity features with nature reserves at a minimum cost for human activities. To increase the likelihood of a successful implementation, reserves need to be spatially consistent. Widely used decision support tools such as Marxan and PrioritizR commonly enforce compactness indirectly by penalising the reserve perimeter in the objective function. Few other optimisation models explicitly consider spatial properties such as limited fragmentation, connectivity of selected sites, and buffer zones around them, etc. So far, no reserve site selection model can guarantee the production of a connected, compact, and gap-free reserve all at once. The impossibility of designing reserve solutions with desirable spatial properties using existing models makes it difficult to implement such solutions in the real world. Therefore, we propose a mixed-integer linear program to build a reserve that is connected, compact, and gap-free. To enforce these spatial attributes within a reserve site selection model, we used a multicommodity flow approach. We tested the computational feasibility of our model on generated instances and the real instance of Fernando de Noronha. The results indicate that a single model can be used to enforce compactness, connectivity, and the absence of gaps. Using this optimisation model, conservation practitioners can design reserve solutions with desirable spatial properties, thereby increasing the likelihood of a successful implementation. • We provide a mixed-integer linear program that allows the explicit designing of compact, connected and gap-free reserves. • These spatial characteristics are essential for the successful implementation of protected areas in the real world. • We propose several variations in the formulation to give greater control over the geometric characteristics of the reserves. • Compact, connected, and gap-free reserves do not result in a significant increase in socio-economic costs. • Our model can solve instances of 500 planning units within a realistic timeframe, although larger instances may be addressed. [ABSTRACT FROM AUTHOR]