Ecological Applications, 19(2), 2009, pp. 376–386 Ó 2009 by the Ecological Society of America Managing the impact of invasive species: the value of knowing the density–impact curve HIROYUKI YOKOMIZO, 1,2,4 HUGH P. POSSINGHAM, 2 MATTHEW B. THOMAS, 3 AND YVONNE M. BUCKLEY 1,2 1 CSIRO Sustainable Ecosystems, 306 Carmody Road, St. Lucia, Queensland 4067 Australia 2 The Ecology Centre, School of Integrative Biology, University of Queensland, St. Lucia, Queensland 4072 Australia 3 Center for Infectious Disease Dynamics and Department of Entomology Chemical Ecology Lab, Pennsylvania State University, University Park, Pennsylvania 16802 USA Abstract. Economic impacts of invasive species worldwide are substantial. Management strategies have been incorporated in population models to assess the effectiveness of management for reducing density, with the implicit assumption that economic impact of the invasive species will also decline. The optimal management effort, however, is that which minimizes the sum of both the management and impact costs. The relationship between population density and economic impact (what we call the ‘‘density–impact curve’’) is rarely examined in a management context and could take several nonlinear forms. Here we determine the effects of population dynamics and density–impact curves of different shapes on optimal management effort and discover cases where management is either highly effective or a waste of resources. When an inaccurate density–impact curve is used, the increase in total costs due to over- or underinvestment in management can be large. We calculate the increase in total costs incurred if the density–impact curve is incorrect and find that the greater the maximum impact caused by an invasive species, the more important it is not only to reduce its density, but also to know the shape of the density–impact relationship accurately. Lack of information regarding the relationship between density and economic impact causes the most acute problems for invaders that cause high impact at low density, where management typically will be too little, too late. For species that are only problematic at high density, ignorance of the density–impact curve can lead to overinvestment in management with little reduction in impact. Key words: cost of impact; density dependence; invasive species; modeling economic impact of pests and their control; stochastic dynamic programming; value of information; weed management. INTRODUCTION Invasive species have substantial negative environ- mental and economic impacts worldwide (U.S. Congress 1993, Manchester and Bullock 2000, Sinden et al. 2004). While studies of population dynamics are necessary to determine ecologically appropriate strategies for reduc- ing invader population density (e.g., Buckley et al. 2001, 2007, Taylor and Hastings 2004, Shea et al. 2006), there are only a few studies in which optimal management strategies are derived with explicit consideration of the relationship between ecological or economic impact of invaders and their population density (Finnoff et al. 2005, Whittle et al. 2007). This makes it unclear how one management strategy compares with another in relation to the total costs of both management and impact (Regan et al. 2006). Commonly, insufficient information exists to describe the relationship between density of an invasive popula- tion and economic impacts (Parker et al. 1999). Where this has been explored, both linear and nonlinear relationships between density and cost of impact have been found (Medd et al. 1985, Bobbink and Willems 1987, Standish et al. 2001, Alvarez and Cushman 2002, Hester et al. 2006). It is likely that the optimal management effort for an invasive species that minimiz- es costs due to management and impact will depend on the shape of the relationship between density and economic impact, what we call here the ‘‘density–impact curve.’’ Management strategies that incorporate this curve thereby consider the cost–benefit ratio for reductions in density, however, this has not been well examined. For example Whittle et al. (2007) assume that the impact of an invader is proportional to the invaded area, i.e., that impact of an invader has constant per capita costs. Finnoff et al. (2005) apply a particular nonlinear density–impact curve for management of zebra mussels (Dreissena polymorpha) but do not examine the dependence of management strategies on the shape of the density–impact curve. If the per capita economic impact of an invader is a function of its population density, the reduction in impact of removing one individual will depend on the population density at that time. In Fig. 1 we propose three basic nonlinear shapes that the density–impact Manuscript received 5 March 2008; revised 4 June 2008; accepted 12 June 2008. Corresponding Editor: R. A. Hufbauer. 4 E-mail: Hiroyuki.Yokomizo@csiro.au 376