Abstract
Signal detection theory has influenced the behavioural sciences for over 50 years. The theory provides a simple equation that indicates numerous 'intuitive' results; e.g. prey should be more prone to take evasive action (in response to an ambiguous cue) if predators are more common. Here, we use analytical and computational models to show that, in numerous biological scenarios, the standard results of signal detection theory do not apply; more predators can result in prey being less responsive to such cues. The standard results need not apply when the probability of danger pertains not just to the present, but also to future decisions. We identify how responses to risk should depend on background mortality and autocorrelation, and that predictions in relation to animal welfare can also be reversed from the standard theory.