To sample or eradicate? A cost minimization model for monitoring and managing an invasive species

1. Considerable effort is expended by national and local governments to exclude alien species via detection and eradication of invading populations, but these efforts are not necessarily designed in the most economically or biologically efficient manner. 2. Using the invasion of the European strain of the gypsy moth Lymantria dispar into the USA as a case study, we develop an analytical model to determine the optimal trap density for detecting isolated infestations. Most models focus on monitoring or eradication costs only; our model considers the costs of both detection and eradication when determining the best monitoring strategy. 3. The model assumes that all isolated populations must be located and eradicated by the conclusion of a programme. For programmes lasting longer than 1 year, it is more worthwhile to proactively monitor and manage rather than to wait until the programme is over. 4. For a management programme of a given length, optimal trap density is most influenced by the growth rate of the infestation. Optimal trap densities are lowest for infestations with very low growth rates (because they remain small and therefore are less expensive to eradicate) or very high growth rates (because they are easier to detect), and highest for infestations with moderate growth rates (because they are neither inexpensive to eradicate nor easy to detect). 5. Our model is useful in setting a baseline level of monitoring for isolated incidents of gypsy moth invasion. Analysis of data in two US states show that actual trap densities are far higher than the optimal densities from the model. The difference suggests risk aversion may play a role in real systems. 6. Synthesis and applications. Our model suggests that we can improve the efficiency of detection and eradication programmes for isolated infestations by optimizing detection effort relative to infestation growth rates and management programme duration. It also clearly demonstrates the importance of balancing the costs and benefits of both detection and eradication when developing invasive species monitoring programmes.