Statistical tools to interpret risks that arise from rare events in host specificity testing

► One C. japonicas developed to pupation on a native plant during non-target host testing. ► One larva pupated on the native plant in 0.0037 of reps, cf. 98.7 % on the target weed. ► Effect sizes less probable than 0.020 will be undetectable at a sample size <300. ► A survival model predicted only 0.6 % of larvae will survive >13 days on the native plant. ► The risk to the native plant, Hebe speciosa, is now defined as very low.