Background/Question/Methods
Economic impacts of invasive species worldwide are substantial. Management strategies have been incorporated in population models to assess their effectiveness at reducing density, with the implicit assumption that impact of the invasive species will also decline. The optimal management effort will be that which minimizes the sum of the cost of management and the cost of impact. The relationship between population density and impact is rarely examined in a management context and it could take several non-linear forms. We derive generalizations about population dynamics and density-impact curves for which 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 under-investment in management can be large.

Results/Conclusions
By calculating the increase of the total costs due to mis-specification of the density-impact curve, and subsequent over- or under-investment in management, we discovered 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. This knowledge problem is most acute for the invaders that cause high impact at low density, for these management will be too little, too late. For species which are only problematic at high density, ignorance of the impact-density curve will lead to too much management with little reduction in impact.