Reconsidering compact measures: A multiobjective framework for ecological reserve design

This study aims to develop a refined compactness measure, a key spatial attribute in reserve design that impacts both ecological and economic efficiency. Designing ecological reserves often involves conflicting objectives, necessitating the simultaneous consideration of spatial attribute and ecological diversity. We introduce a novel metric that accounts for both size and shape in measuring reserve compactness. Additionally, we employ multiobjective optimization to generate Pareto-optimal solutions, offering stakeholders a range of high-quality reserve configurations. Our focus on compactness is particularly relevant when clusters represent distinct habitats with limited biological interactions. We compare various compactness measures, such as boundary length and pairwise distance and evaluate their suitability for inclusion in optimization models. This approach addresses diverse stakeholder priorities, leading to more balanced reserve selections. We demonstrate the shortcomings of single-objective approaches, which often yield suboptimal, non-compact reserves, and highlight the advantages of optimizing across multiple metrics to better capture the complexities of reserve design.