A mathematical model for zoning of protected natural areas

When formulated in mathematical terms, the problem of zoning a protected natural area subject to both box and spatial constraints results in a combinatorial optimization problem belonging to the NP-hard class. This fact and the usual dimension of the problem (regularly in the tens of thousands order) suggest the need to apply a heuristic approach. In this contribution we describe a quantitative method for zoning protected natural areas based on a simulated annealing algorithm. Building upon previous work by Bos, we introduce three main innovations (a quadratic function of distance between land units, a non-symmetric matrix of compatibilities among uses, and a spatial connection constraint) that make the approach applicable for ecological purposes. When applied to solving small-size simulated problems, the results were indistinguishable from those obtained via an exact, enumerative method. A coarse-scale zoning of Talampaya National Park (Argentina) rendered maps remarkably similar to those produced by subject area experts using a non-quantitative consensus-seeking approach. Results are encouraging and show particular potential for the periodical update of zoning of protected natural areas. Such a capability is crucial for application in developing countries where both human and financial resources are usually scarce but still critical for updating zoning and management plans.