Optimal prey switching: Predator foraging costs provide a mechanism for functional responses in multi-prey systems

Foragers must balance the costs and gains inherent in the pursuit of their next meal. Classical functional response formulations describe consumption rates driven by prey density and are naive to predator foraging costs. Here, we integrated foraging costs into functional responses to add mechanism and precision to foundational ideas. Specifically, using a model system with a single predator and two prey, we express a functional response emerging from variable energy and time costs of each predation phase: searching, attacking, or consuming prey. The utility of our model is explored through a focused example where prey can exert variable influence on predator foraging costs through antipredator traits. Dissimilarity between prey in their foraging costs influence the energy gain rate of the predator through optimal prey switching. We found that a small subset of prey antipredator traits and density conditions generated a stabilizing Type III (sigmoidal) functional response-the pattern often thought to typify a generalist predator switching between prey species. The sigmoid functional response occurred for highly profitable prey only when the costly prey (1) were at a high density and (2) their antipredator traits increased energy or time costs following an encounter. We outline testable predictions regarding foraging costs from our model. We provide guidance on how to apply optimal foraging theory to empirical scenarios where predator foraging costs vary due to prey type, predator type, or environmental conditions. Our framework represents a synergy of foundational and contemporary theory across disciplines, facilitating the discovery of shared principles and context-dependent variation across varied predator-prey systems.