Optimal spatial control of biological invasions Rebecca S. Epanchin-Niell a,n , James E. Wilen b a Resources for the Future, 1616 P Street NW, Washington, DC 20036, USA b Department of Agricultural and Resource Economics, University of California, Davis, CA 95616, USA article info Article history: Received 28 December 2009 Available online 6 November 2011 Keywords: Invasive species Spatial–dynamic processes Spatial spread Reaction–diffusion Management Cellular automaton Eradication Containment Spatial control Integer programming abstract This study examines the spatial nature of optimal bioinvasion control. We develop a spatially explicit two-dimensional model of species spread that allows for differential control across space and time, and we solve for optimal spatial–dynamic control strategies. The qualitative nature of optimal strategies depends in interesting ways on aspects of landscape and invasion geometry. For example, reducing the extent of exposed invasion edge, through spread, removal, or strategically employing landscape features, can be optimal because it reduces long-term containment costs. Optimal invasion control is spatially and temporally ‘‘forward-looking’’ in the sense that strategies should be targeted to slow or prevent the spread of an invasion in the direction of greatest potential long-term damages. These spatially explicit characteriza- tions of optimal policies contribute insights and intuition to the largely nonspatial literature on controlling invasions and to understanding control of spatial–dynamic processes in general. & 2011 Elsevier Inc. All rights reserved. 1. Introduction Much of the economic research on bioinvasion management frames the issue as a pest control problem, in which the population density of the invader is controlled. This literature has generally focused on the aggregate pest population, without consideration of its spatial characteristics [1–3]. But a critical feature of invasion problems is that they unfold over time and space and are thus driven by spatial–dynamic processes, rather than by simpler dynamic processes. Existing analytical work generally abstracts away from the spatial features of invasions, focusing on when and how much to control [4–6]. There is less understanding about where to optimally allocate control efforts or the effect of spatial characteristics of the invasion or landscape on optimal control choices. This paper develops a bioeconomic model of bioinvasions that incorporates a spatial–dynamic spread process and that allows various aspects of space to be characterized explicitly. We examine optimal policies over a range of bioeconomic parameters, spatial configurations, and initial invasion types. The more interesting results show how the geometry of the initial invasion and landscape influences the qualitative characteristics of optimal policies. Optimal solutions often utilize landscape features or alter the shape of the initial invasion in order to reduce the length of exposed invasion front, thereby reducing long term control costs. Optimal policies also exhibit classic forward-looking behavior that not only anticipates impacts over time, but also looks forward over space to slow and steer the invasion front away from the direction of greatest potential damages, or in the direction where the costs of achieving control are low. Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/jeem Journal of Environmental Economics and Management 0095-0696/$ - see front matter & 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.jeem.2011.10.003 n Corresponding author. Fax: þ1 202 939 3460. E-mail address: epanchin-niell@rff.org (R.S. Epanchin-Niell). Journal of Environmental Economics and Management 63 (2012) 260–270