Time-variant payoffs and signal detection theory

“Better safe than sorry” summarises the principle that strong responses to rare events may be appropriate if the outcome is important enough. The calculation of optimal bias in signal detection theory (McMillan & Creelman, 1991) formalises this idea and is often used to explain the evolution of response biases. However, signal detection theory assumes that payoffs are stable over time. Trimmer et al. (2017) showed that when payoffs change across trials, the optimal bias may have the opposite sign compared to the case of invariant payoffs. Here, we show that the same can happen when payoffs change within trials. We argue that such changes over time are plausible for evolutionary scenarios to which signal detection theory has been applied, and that conclusions drawn from signal detection theory are not always valid when the assumption of time-invariant payoffs is violated.