The optimal sampling strategy for unfamiliar prey

Precisely how predators solve the problem of sampling unfamiliar prey types is central to our understanding of the evolution of a variety of antipredator defenses, ranging from Müllerian mimicry to polymorphism. When predators encounter a novel prey item then they must decide whether to take a risk and attack it, thereby gaining a potential meal and valuable information, or avoid such prey altogether. Moreover, if predators initially attack the unfamiliar prey, then at some point(s) they should decide to cease sampling if evidence mounts that the type is on average unprofitable to attack. Here, I cast this problem as a "two-armed bandit," the standard metaphor for exploration-exploitation trade-offs. I assume that as predators encounter and attack unfamiliar prey they use Bayesian inference to update both their beliefs as to the likelihood that individuals of this type are chemically defended, and the probability of seeing the prey type in the future. I concurrently use dynamic programming to identify the critical informational states at which predator should cease sampling. The model explains why predators sample more unprofitable prey before complete rejection when the prey type is common and explains why predators exhibit neophobia when the unfamiliar prey type is perceived to be rare.