Optimal diving: patch quality, depth, and marginal value.

The Marginal Value Theorem, a widely used model of how long an animal should spend foraging on a given patch, has often been invoked in the context of diving animals to predict optimal underwater foraging time. Here, we highlight and address two main issues regarding using the Marginal Value Theorem in this context. First, we show that the theorem's central assumption of diminishing returns from foraging may not always be correct or necessary, and provide an analysis demonstrating that both ecological and physiological influences on patch residency time-based on prey abundance and aerobic capacity, respectively-which have sometimes been presented as alternatives are, in fact, both important and interacting. Second, we attempt to clarify common confusions around interpreting how environmental quality should affect optimal foraging time, in the cases of homogeneous and heterogenous habitats, for which the effect of quality differ. Finally, we discuss a case in which the foraging gain depends on both foraging time and depth, and prove that the optimal foraging depth is not necessarily the depth at which the energetic rate of gain peaks. Altogether, the clarifications and general proofs we provide should improve future interpretations of models of optimal foraging in diving animals.