Robust decisions for declaring eradication of invasive species.
Invasive species threaten biodiversity, and their eradication is desirable whenever possible. Deciding whether an invasive species has been successfully eradicated is difficult because of imperfect detection. Two previous studies [Regan et al., Ecology Letters, 9 (2006), 759; Rout et al., Journal of Applied Ecology, 46 (2009), 110] have used a decision theory framework to minimize the total expected cost by finding the number of consecutive surveys without detection (absent surveys) after which a species should be declared eradicated. These two studies used different methods to calculate the probability that the invasive species is present when it has not been detected for a number of surveys. However, neither acknowledged uncertainty in this probability, which can lead to suboptimal solutions. We use info-gap theory to examine the effect of uncertainty in the probability of presence on decision-making. Instead of optimizing performance for an assumed system model, info-gap theory finds the decision among the alternatives considered that is most robust to model uncertainty while meeting a set performance requirement. This is the first application of info-gap theory to invasive species management. We find the number of absent surveys after which eradication should be declared to be relatively robust to uncertainty in the probability of presence. This solution depends on the nominal estimate of the probability of presence, the performance requirement and the cost of surveying, but not the cost of falsely declaring eradication. More generally, to be robust to uncertainty in the probability of presence, managers should conduct at least as many surveys as the number that minimizes the total expected cost. This holds for any nominal model of the probability of presence. Synthesis and applications. Uncertainty is pervasive in ecology and conservation biology. It is therefore crucial to consider its impact on decision-making; info-gap theory provides a way to do this. We find a simple expression for the info-gap solution, which could be applied by eradication managers to make decisions that are robust to uncertainty in the probability of presence.