How can automimicry persist when predators can preferentially consume undefended mimics?

It is common for species that possess toxins or other defences to advertise these defences to potential predators using aposematic ("warning") signals. There is increasing evidence that within such species, there are individuals that have reduced or non-existent levels of defence but still signal. This phenomenon (generally called automimicry) has been a challenge to evolutionary biologists because of the need to explain why undefended automimics do not gain such as a fitness advantage by saving the physiological costs of defence that they increase in prevalence within the population, hence making the aposematic signal unreliable. The leading theory is that aposematic signals do not stop all predatory attacks but rather encourage predators to attack cautiously until they have identified the defence level of a specific individual. They can then reject defended individuals and consume the undefended. This theory has recently received strong empirical support, demonstrating that high-accuracy discrimination appears possible. However, this raises a new evolutionary problem: if predators can perfectly discriminate the defended from the undefended and preferentially consume the latter, then how can automimicry persist? Here, we present four different mechanisms that can allow non-trivial levels of automimics to be retained within a population, even in the extreme case where predators can differentiate defended from undefended individuals with 100% accuracy. These involve opportunity costs to the predator of sampling carefully, temporal fluctuation in predation pressure, predation pressure being correlated with the prevalence of automimicry, or developmental or evolutionary constraints on the availability of defence. These mechanisms generate predictions as to the conditions where we would expect aposematically signalling populations to feature automimicry and those where we would not.