Optimal allocation of law enforcement patrol effort to mitigate poaching activities

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 tradeoff by constructing a Pareto efficiency frontier using integer linear programing. 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 which 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 $49,760 USD. In order to attain a 60% reduction in poaching risk, 15,560 patrol events were needed at a cost of $1,244,800 USD. We evaluated the tradeoff 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 tradeoff 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 $684,640 USD. Our results suggest that optimal solutions could increase efficiency compared to the actual effort allocations from 2006 – 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, multi-level, site selection.

Methods
Data on poaching risk and ranger patrol cost were originally collected from the ranger-based monitoring program in Nyungwe National Park (NNP), Rwanda. These data are published and discussed in:  Moore, J. F., Mulindahabi, F., Masozera, M. K., Nichols, J. D., Hines, J. E., Turikunkiko, E., & Oli, M. K. (2017). Are ranger patrols effective in reducing poaching-related threats within protected areas? Journal of Applied Ecology, 99–107. https://doi.org/10.1111/1365-2664.1296. We used the fitted dynamic occupancy model and data from this publication to predict the probability of poaching (poaching risk) in each grid cell in the park under different levels of ranger patrol effort. 

The grid cell neighbors, and upstream/downstream relationships of grid cells along each straight line path between terminal grid cells and their nearest access point (e.g. ranger station, road) were calculated using ArcMap 10.1 (see corresponding manuscript for more details).