Using sighting records to declare eradication of an invasive species.
A major challenge for eradication managers is deciding when a programme can be deemed successful. Regan et al. (2006) were the first to pose this problem within a decision theory framework, minimizing the net expected cost of the decision. The optimal time to declare eradication was based on the number of consecutive surveys in which the species was not found ('absent surveys'). Their formulation used estimates of detectability and persistence - parameters that are often difficult to estimate - to calculate the probability that the invasive species is still present. Here we use a similar decision-making framework but instead predict presence based on the pattern of sightings, using a method developed by Solow (1993a) that assumes a constant sighting rate. This method does not require estimates of detectability and persistence. We find the number of absent surveys after which eradication should be declared, using three approaches: a stochastic dynamic program, which finds the exact optimal solution, a rule of thumb, and an approximation. We then compare these results with a method assuming a declining sighting rate. Both the rule of thumb and approximation give results that are close to the exact optimal solution. The rule of thumb with the declining sighting rate method generally gives a larger optimal number of absent surveys. Synthesis and applications. Analysing this problem within a decision theory framework enables us to minimize the expected cost of declaring eradication. By using the more readily available sighting data, we make this framework applicable to a wider range of invasive species. Our approximation is a simple calculation, making it an accessible tool that could be applied by managers of eradication programmes for invasive species.