Ecological Modelling 131 (2000) 79 – 95 Optimal control of spatially distributed process models Craig Loehle * National Council of the Paper Industry for Air & Stream Improement, Suite 224, 552 S. Washington Street, Naperille, IL 60540, USA Received 10 December 1999; received in revised form 5 April 2000; accepted 7 April 2000 Abstract Increasingly, forest management practices are being evaluated from a watershed or landscape perspective. Currently, few tools are available for incorporating the impact of spatial patterns of management on spatially distributed dynamic processes. A new algorithm is presented for scheduling that can maximize timber harvest while meeting spatial constraints. Beginning with a candidate list of stands available for harvest, the algorithm swaps stands that cause the most environmental impact with stands where less impact will occur. It then tries to add more stands for harvest if the swap has reduced landscape level impacts below the environmental restriction. This process repeats as long as swapping is successful. A test case demonstrated that the algorithm could minimize impact of timber harvest on an edge-sensitive bird species. In a second example using water quality (sediment production) restrictions, SWAP generated flexible buffers where width was determined by both clear cut size and landscape position variables. A third example tested the ability of SWAP to control storm runoff from a watershed. A simple watershed was simulated with peak flow the landscape attribute to be controlled. SWAP found a solution that controlled peak flow while maintaining high timber harvest levels. Stand selection based on rankings of stand impact on peak flow did not produce as good a result as SWAP. While the examples explored here are simplistic in their treatment of watershed and landscape factors, the algorithm is easily linked to more sophisticated simulation models. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Optimization; Spatial models; Wildlife habitat; Timber management; Landscape management www.elsevier.com/locate/ecolmodel 1. Introduction Natural resource management is becoming in- creasingly dependent on optimization techniques. Ecosystems can be modeled with varying degrees of accuracy. It is natural to build on such models to achieve economic or conservation goals (or both). When a single ecosystem is to be managed, the optimal control problem is to determine the set of control parameters over time that will con- trol the system trajectory to meet the specified goals (e.g. Williams, 1996; Batabyal, 1999; Sep- pelt, 1999). This is a difficult nonlinear problem. When multiple spatial units comprise the system to be managed, complexity goes up considerably. In forest management analyses, the first step is to decouple the simulation by generating yield tables as a function of age, stocking, fertilizer input, etc. * Tel.: +1-630-5791190; fax: +1-630-5791195. 0304-3800/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S0304-3800(00)00274-X