State-dependent risk-taking by predators in systems with defended prey

Even defended prey items may contain nutrients that can sustain predators in times of energetic need. Conversely, a well-fed predator might be expected to avoid attacking prey items that have a chance of being defended, particularly if there is an abundance of familiar palatable prey to support it. To further understand the implications of optimal state-dependent foraging behaviour by predators in systems that contain defended prey, I developed a stochastic dynamic programming model. This state-dependent approach formally accounts for the trade-off between avoiding starvation and minimising harm from attacking defended prey. It predicts that the mean attack probability of predators on defended models and their undefended mimics should decline in a sigmoidal fashion with increasing availability of alternative undefended prey, and that the foraging decisions of predators should in general be relatively insensitive to the probability that a potentially defended prey item is indeed defended. Some implications of these predictions are that conspicuous warning signals are more likely to evolve in systems that contain an abundance of alternative undefended prey, and that imperfect mimicry will provide almost complete protection to the mimic when predators are readily supported by alternative food sources. Somewhat surprisingly, increasing the density of nutritious undefended mimics while keeping the densities of all other prey types constant tended to decrease the attack rates of predators on encounter with mimics and their defended models. This increase in dietary conservatism arose because in these cases there would be more prey available to sustain the predator if it ever found itself critically low in energy.