Poaching is a global problem causing the decline of species worldwide. Optimizing the efficiency of ranger patrols to deter poaching activity at the lowest possible cost is crucial for protecting species with limited resources. We applied decision analysis and spatial optimization algorithms to allocate efforts of ranger patrols throughout a national park. Our objective was to mitigate poaching activity at or below management risk targets for the lowest monetary cost. We examined this trade-off by constructing a Pareto efficiency frontier using integer linear programming. We used data from a ranger-based monitoring program in Nyungwe National Park, Rwanda. Our measure of poaching risk is based on dynamic occupancy models that account for imperfect detection of poaching activities. We found that in order to achieve a 5% reduction in poaching risk, 622 ranger patrol events (each corresponding to patrolling 1-km² sites) were needed within a year at a cost of US$49,760. In order to attain a 60% reduction in poaching risk, 15,560 patrol events were needed at a cost of US$1,244,800. We evaluated the trade-off between patrol cost and poaching risk based on our model by constructing a Pareto efficiency frontier and park managers found the solution for a 50% risk reduction to be a practical trade-off based on funding constraints (comparable to recent years) and the diminishing returns between risk mitigation and cost. This expected reduction in risk required 8,558 patrol events per year at a cost of US$684,640. Our results suggest that optimal solutions could increase efficiency compared to the actual effort allocations from 2006 to 2016 in Nyungwe National Park (e.g., risk reductions of ~30% under recent budgets compared to ~50% reduction in risk under the optimal strategy). The modeling framework in this study took into account imperfect detection of poaching risk as well as the directional and conditional nature of ranger patrol events given the spatial adjacency relationships of neighboring sites and access points. Our analyses can help to improve the efficiency of ranger patrols, and the modeling framework can be broadly applied to other spatial conservation planning problems with conditional, multilevel, site selection.

中文翻译：

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优化分配执法巡逻工作以减少偷猎活动

偷猎是一个全球性问题，导致世界范围内物种的减少。优化护林员巡逻的效率以尽可能低的成本阻止偷猎活动对于保护资源有限的物种至关重要。我们应用决策分析和空间优化算法来分配整个国家公园的护林员巡逻工作。我们的目标是以最低的货币成本在管理风险目标或低于管理风险目标的情况下减少偷猎活动。我们通过使用整数线性规划构建帕累托效率边界来检验这种权衡。我们使用了卢旺达 Nyungwe 国家公园中基于护林员的监测计划的数据。我们对偷猎风险的衡量基于动态占用模型，该模型解释了对偷猎活动的不完美检测。我们发现，为了将偷猎风险降低 5%，²站点）在一年内需要花费 49,760 美元。为了将偷猎风险降低 60%，需要 15,560 次巡逻活动，成本为 1,244,800 美元。我们基于我们的模型通过构建帕累托效率边界来评估巡逻成本和偷猎风险之间的权衡，公园管理者发现风险降低 50% 的解决方案是基于资金限制的实际权衡（与近年来相比） ) 以及风险缓解和成本之间的收益递减。这种预期的风险降低需要每年进行 8,558 次巡逻，成本为 684,640 美元。我们的结果表明，与 Nyungwe 国家公园 2006 年至 2016 年的实际努力分配相比，最佳解决方案可以提高效率（例如，在最近的预算下风险降低了约 30%，而在最佳策略下风险降低了约 50%）。鉴于相邻站点和接入点的空间邻接关系，本研究中的建模框架考虑了对偷猎风险的不完善检测以及护林员巡逻事件的定向和条件性质。我们的分析可以帮助提高护林员巡逻的效率，并且建模框架可以广泛应用于其他有条件、多层次、站点选择的空间保护规划问题。