A major challenge for invasive species managers is deciding when an eradication program can be deemed successful. Declaring eradication and ceasing to monitor when the invasive species is still present can lead to a re-emergence, with resulting ecological and economic impacts. However, continuing to monitor when the species has already been eradicated is a waste of resources. Regan et al. (2006) were the first to pose this problem in an economic way, and minimise the net expected cost of the decision. They find the optimal time to declare eradication, based on the number of consecutive surveys in which the species is not found (absent surveys). Their formulation requires estimates of detectability and persistence—parameters that are often difficult to estimate. We eliminate the need to estimate these parameters by instead using Solow’s equation (Solow 1993) to calculate the probability the invasive species is still present from the more readily available sighting record. We derive a rule of thumb and an approximation, and also find the exact optimal results with a stochastic dynamic program (SDP). We apply these three methods to the example of bitterweed (Helenium amarum), which enables a direct comparison with the results in Regan et al. (2006).
The results calculated with the rule of thumb and approximation are close to the exact optimal results from the SDP. The approximation is a simple calculation requiring only the sighting record, a cost ratio, and a prior probability that the weed is present. This makes it an accessible tool that could be applied by decision-makers and managers of weed eradication programs. All three methods we used found that H. amarum should be declared eradicated after 11 years of absent surveys, whereas Regan et al. (2006) found it should be declared after 3 years. Using the same data, Solow’s equation produces much higher values for the probability the weed is extant than either the SDP or the rule of thumb methods in Regan et al. (2006). These higher probabilities translate into a more conservative optimal solution. Aside from Solow’s equation, there are numerous other methods for calculating the probability of species presence from sighting data. We are currently examining the range of results that might be achieved given plausible alternative models for how the probability of presence declines with the number of consecutive absent surveys.
Regan et al. 2006. Ecology Letters 9:759-766. Solow 1993. Ecology, 74(3):962-64.