How large spatially-explicit optimal reserve design models can we solve now? An exploration of current models’ computational efficiency

Spatially-explicit optimal reserve design models select best sites from a set of candidate sites to assemble nature reserves to protect species (or habitats) and these reserves display certain spatial attributes which are desirable for species. These models are formulated with linear 0–1 programming and solved using standard optimisation software, but they were run on different platforms, resulting in discrepant or even conflicting messages with regard to their computational efficiency. A fair and accurate comparison of the convenience of these models would be important for conservation planners who use these models. In this article, we considered eight models presented in literature and tested their computational efficiency using randomly generated data sets containing up to 2000 sites. We focused on reserve contiguity and compactness which are considered crucial to species persistence. Our results showed that two of these models, namely Williams (2002) and Önal et al. (2016), stand out as the most efficient models. We also found that the relative efficiency of these models depends on the scope of analysis. Specifically, the Williams (2002) model solves more of the test problems when contiguity is the only spatial attribute and a large subset of the candidate sites needs to be selected. When compactness is considered also, the Önal et al. (2016) model generally performs better. Large scale models are found to be difficult to solve in a reasonable period of time. We discussed factors that may affect those models’ computational efficiency, including model size, share of selected sites, model structure and input data. These results provide useful insight and guidance to conservation practitioners and researchers who focus on spatial aspects and work with large-scale data sets.