Alternative prey can change model-mimic dynamics between parasitism and mutualism

Classical (conventional) Mullerian mimicry theory predicts that two (or more) defended prey sharing the same signal always benefit each other despite the fact that one species can be more toxic than the other. The quasi-Batesian (unconventional) mimicry theory, instead, predicts that the less defended partner of the mimetic relationship may act as a parasite of the signal, causing a fitness loss to the model. Here we clarify the conditions for parasitic or mutualistic relationships between aposematic prey, and build a model to examine the hypothesis that the availability of alternative prey is crucial to Mullerian and quasi-Batesian mimicry. Our model is based on optimal behaviour of the predator. We ask if and when it is in the interest of the predator to learn to avoid certain species as prey when there is alternative (cryptic) prey available. Our model clearly shows that the role of alternative prey must be taken into consideration when studying model-mimic dynamics. When food is scarce it pays for the predator to test the models and mimics, whereas if food is abundant predators should leave the mimics and models untouched even if the mimics are quite edible. Dynamics of the mimicry tend to be classically Mullerian if mimics are well defended, while quasi-Batesian dynamics are more likely when they are relatively edible. However, there is significant overlap: in extreme cases mimics can be harmful to models (a quasi-Batesian case) even if the species are equally toxic. A crucial parameter explaining this overlap is the search efficiency with which indiscriminating vs. discriminating predators find cryptic prey. Quasi-Batesian mimicry becomes much more likely if discrimination increases the efficiency with which the specialized predator finds cryptic prey, while the opposite case tends to predict Mullerian mimicry. Our model shows that both mutualistic and parasitic relationship between model and mimic are possible and the availability of alternative prey can easily alter this relationship.