Ecological Applications, 18(3), 2008, pp. 748–761 Ó 2008 by the Ecological Society of America A STATE-DEPENDENT MODEL FOR THE OPTIMAL MANAGEMENT OF AN INVASIVE METAPOPULATION TIFFANY BOGICH 1,3 AND KATRIONA SHEA 2 1 Conservation Science Group, Department of Zoology, University of Cambridge, Downing Street, Cambridge CB2 3EJ United Kingdom 2 Department of Biology, 208 Mueller Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802 USA Abstract. Management of invasive species involves choosing between different manage- ment strategy options, but often the best strategy for a particular scenario is not obvious. We illustrate the use of optimization methods to determine the most efficient management strategy using one of the most devastating invasive forest pests in North America, the gypsy moth (Lymantria dispar), as a case study. The optimization approach involves the application of stochastic dynamic programming (SDP) to a metapopulation framework with different infestation patch sizes, with the goal of minimizing infestation spread. We use a novel ‘‘moving window’’ approach as a way to address a spatially explicit problem without being explicitly spatial. We examine results for two cases in order to develop general rules of thumb for management. We explore a model with limited parameter information and then assess how strategies change with specific parameterization for the gypsy moth. The model results in a complex but stable, state-dependent management strategy for a multiyear management program that is robust even under situations of uncertainty. The general rule of thumb for the basic model consists of three strategies: eradicating medium-density infestations, reducing large-density infestations, and reducing the colonization rate from the main infestation, depending on the state of the system. With specific gypsy moth parameterization, reducing colonization decreases in importance relative to the other two strategies. The application of this model to gypsy moth management emphasizes the importance of managing based on the state of the system, and if applied to a specific geographic area, has the potential to substantially improve the efficiency and cost-effectiveness of current gypsy moth eradication programs, helping to slow the spread of this pest. Additionally, the approach used for this particular invasive species can be extended to the optimization of management programs for the spread of other invasive and problem species exhibiting metapopulation dynamics. Key words: decision theory; gypsy moth; invasive species management; Lymantria dispar; mainland– island metapopulation; optimization; stochastic dynamic programming (SDP). INTRODUCTION Biological invasions of pest species pose a threat to the stability of ecosystems, both natural and managed (Liebhold et al. 1995). Invasive species can alter habitats, through both direct and indirect competitive effects on other species, and can completely restructure a wide range of ecosystems (Mack et al. 2000). Addition- ally, invasive species are a threat to economies, societies, and ecosystems across the globe, costing countries billions of U.S. dollars per year in direct management costs in addition to the indirect costs of environmental damage, trade disruption, and disease risk (Global Invasive Species Programme 2005, Lodge et al. 2006). Because of the significance in both cost and ecological impact of invasive species, we are interested in deter- mining the optimal management strategy for invasive species through the use of quantitative methods. Mathematical models, particularly optimization mod- els, in conjunction with experimental research, can contribute to a more cost-efficient and practical ap- proach to investigating and recommending management decisions for invasive species. Setting the stage, Moody and Mack (1988) developed a simple, one-time control model and found, for invasions radiating out of a few large, isolated infestations, it is best to control the smaller, satellite populations than the larger foci, contrary to typical management practice at the time. Their rule of thumb, to continually remove the small, new infestations, has been revisited by several recent studies (Taylor and Hastings 2004, Grevstad 2005, Hastings et al. 2006, Whittle et al. 2007). Most recently, Whittle et al. (2007) updated the original model and found a new optimal decision to focus on both the larger and satellite infestations, where the relative focus depends on the cost of managing vs. doing nothing. Using different quanti- tative methods, other studies have found modified optimal solutions including eradicating low-density (faster growing) subpopulations first, depending on the available budget (Taylor and Hastings 2004), attacking Manuscript received 20 April 2007; revised 30 August 2007; accepted 22 October 2007. Corresponding Editor: J. A. Powell. 3 E-mail: tlb24@cam.ac.uk 748