An optimization approach to selecting Research Natural Areas in national forests

The USDA Forest Service has a long-established program to identify areas in national forests for designation as protected Research Natural Areas (RNAs). One of the goals is to protect high quality examples of regional ecosystems for the purposes of maintaining biological diversity, conducting nonmanipulative research and monitoring, and fostering education. When RNA designation conflicts with other land uses, difficult choices must be made about the best number and location of sites. We addressed this problem by adapting a classic optimization formulation from the location science literature. The formulation was an integer optimization model for selecting the set of RNAs that maximized the number of regional ecosystems and natural communities represented subject to an upper bound on the total area covered by the sites in the selected set. We applied the formulation using 33 potential RNAs in the Superior National Forest in northeastern Minnesota. The 33 potential RNAs were chosen for our case study because they had been mapped and field-surveyed for the presence of natural communities. The use of those sites does not imply that other areas in the Superior National Forest do not merit further study as RNA candidates. The model quickly generated information about the trade-offs between different protection goals. We found multiple sets of potential RNAs, ranging from all 33 sites to a much smaller set of 21 sites, that attained the specified goals for natural community representation. Thus, the decision-maker can choose among sets of sites with a wide range of total areas without compromising the representation goal. We also found that requirements to choose a set of sites that represents a range of locally defined ecosystems or priority natural communities can limit the total number of natural communities that can be represented within a set of sites of a given area. Average solution times for different problems were less than 5 seconds on a personal computer, suggesting that integer optimization can readily facilitate investigation of the impacts of RNA selection goals.