Optimal eradication: when to stop looking for an invasive plant

The notion of being sure that you have completely eradicated an invasive species is
fanciful because of imperfect detection and persistent seed banks. Eradication is
commonly declared either on an ad hoc basis, on notions of seed bank longevity, or on
setting arbitrary thresholds of 1% or 5% confidence that the species is not present.
Rather than declaring eradication at some arbitrary level of confidence, we take an
economic approach in which we stop looking when the expected costs outweigh the
expected benefits. We develop theory that determines the number of years of absent
surveys required to minimize the net expected cost. Given detection of a species is
imperfect, the optimal stopping time is a trade-off between the cost of continued
surveying and the cost of escape and damage if eradication is declared too soon. A
simple rule of thumb compares well to the exact optimal solution using stochastic
dynamic programming. Application of the approach to the eradication programme of
Helenium amarum reveals that the actual stopping time was a precautionary one given the ranges for each parameter.