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Citation: Wang Y, Önal H, Fang W (2018) How large spatially-explicit optimal reserve design models can we solve now? An exploration of current models' computational efficiency. AbstractSpatially-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. A peer-reviewed open-access journalYicheng Wang et al. / Nature Conservation 27: 17-37 (2018) 18 Keywords nature reserve design, mixed integer programming, computational efficiency, contiguity, compactness, spatial optimisation

Conservation planning often involves multiple species occupying large areas including habitat sites with varying characteristics. For a given amount of financial resources, designing a spatially coherent nature reserve system that provides the best possible protection to targeted species is an important ecological and economic problem. In this paper, we address this problem using optimization methods. Incorporating spatial criteria in an optimization framework considering spatial habitat needs of multiple species poses serious challenges because of modeling and computational complexities. We present a novel linear integer programming model to address this issue considering spatial contiguity and compactness of the reserved area. The model uses the concept of path in graph theory to ensure contiguity and minimizes the sum of distances between selected sites and a central site in individual reserves to promote compactness. We test the computational efficiency of the model using randomly generated data sets. The results show that the model can be solved quite efficiently in most cases. We also present an empirical application of the model to simultaneous protection of two cohabiting species, Gopher Tortoise and Gopher Frogs, in a military installation in Georgia, USA.

Agency theory suggests that conflict interests between managers and owners cause management shirking and associated agency costs. An audit is a monitoring mechanism that provides an independent check on accounting information and reduces agency costs (Jensen and Meckling, 1976). Therefore, given severe owner-manager agency problems, higher audit quality should be associated with lower client company owner-manager agency costs. The purpose of this study is to empirically test this relation.In China, owner-manager agency problems are severe given extremely low or no management ownership. Moreover, there is a lack of variations in management holdings across Chinese public companies. Such an environment allows us to examine the role of audits in reducing owner-manager agency costs.Using a sample of Chinese listed companies, we find that observations with higher quality audits show lower owner-manger agency costs. Such a result suggests that in an emerging market, higher quality audits more effectively reduce agency costs.

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