Many species find themselves isolated from the predators with which they evolved. This situation commonly occurs with island biota, and is similar to moving from the dangerous inner-city to the suburbs. Economic thinking tells us that we should expect costly antipredator behaviour to be lost if it is no longer beneficial. The loss of antipredator behaviour has important consequences for those seeking to translocate or reintroduce individuals from predator-free islands back to the predator-rich mainland, but we have neither a detailed understanding of the mechanisms of loss nor information on the time course of relaxed selection. Some antipredator behaviours are experience-dependent: experience with predators is required for their proper performance. In these cases, antipredator behaviour is lost after only a single generation of isolation, but it should be able to be regained following exposure to predators. Other behaviours may be more `hard-wired'. The evolutionary loss of antipredator behaviour may occur over as few as several generations, but behaviours may also persist for many thousands of years of predator-free living.