When is predator's opportunism remunerative?

When an opportunistic predator is looking for a given type of prey and encounters another one from different species, it tries to utilize this random opportunity. We characterize the optimal levels of this opportunism in the framework of stochastic models for the two prey-one predator case. We consider the spatial dispersal of preys and the optimal diet choice of predator as well. We show that when both preys have no handling time, the total opportunism provides maximal gain of energy for the predator. When handling times differ with prey, we find a conditional optimal behavior: for small density of both prey species the predator prefers the more valuable one and is entirely opportunistic. However, when the density of the more valuable prey is higher than that of the other species, then the predator prefers the first one and intentionally neglects the other. Furthermore, when the density of the less valuable prey is high and that of the other one is small, then predator will look for the less valuable prey and is therefore totally opportunistic. We demonstrate that prey preference is remunerative whenever the advantage of a proper prey preference is larger than the average cost of missed prey preference. We also propose a dynamics which explicitly contains two sides of shared predation: apparent mutualism and apparent competition, and we give conditions when the rare prey goes extinct.