Optimal spatial and temporal management of invasive species: general principles for eradication and suppression

Background/Question/Methods

Choosing effective management strategies for invasive species is a global challenge. The invasive species problem comprises a huge number of species, and modelling every invasive species to determine appropriate management strategies is impractical. There is a pressing need to provide general guidelines for invasive species managers that can easily be applied in a range of locations and scenarios. We use a reaction-diffusion model and optimal control theory to determine optimal management strategies in a range of invasive species scenarios. We demonstrate how to adjust control effort through time for an island eradication; how control efforts should vary through space around high-value conservation assets; and how to vary control efforts through space and time to eradicate a new invasion. By estimating relatively few parameters, our solutions give managers a strong platform on which to base strategic decisions. Our methods can also be applied to specific situations, and we demonstrate this with a case study of a tropical fire ant (Solenopsis geminata) eradication on Ashmore Reef.

Results/Conclusions

Our results show a very clear relationship between population spread rate, population growth rate and the diminishing returns of control effectiveness. For island eradications we find that it is optimal to start with a relatively small amount of control and increase through time. The optimal eradication time depends on growth rate and the diminishing returns parameter. If a population grows quickly or large control efforts can be applied effectively, then it is best to eradicate it quickly. Otherwise, longer eradications result in lower overall costs. For spatial suppression around high conservation assets, the most important quantity is the ratio of the spread and growth rates. If the ratio is large, then it is optimal to target a large section of the surrounding landscape, while if the ratio is small it is best to focus control efforts near the conservation asset. Controlling a spreading invasion incorporates principles from both temporal eradication and spatial control problems. Control efforts should initially be focussed at the main infestation and then increased in the surrounding region through time.