Optimal diving under the risk of predation

Many air-breathing aquatic foragers may be killed by aerial or subsurface predators while recovering oxygen at the surface; yet the influence of predation risk on time allocation during dive cycles is little known in spite of numerous studies on optimal diving. We modeled diving behavior under the risk of predation at the surface. The relationship between time spent at the surface and the risk of death is predicted to influence the optimal surface interval, regardless of whether foragers accumulate energy at a constant rate while at the food patch, deplete food resources over the course of the dive, or must search for food during the dive. When instantaneous predation risk during a single surface interval decreases with time spent at the surface, a diver should increase its surface interval relative to that which maximizes energy intake, thereby increasing dive durations and reducing the number of surfacings per foraging bout. When instantaneous risk over a single surface interval does not change or increases with increasing time at the surface, divers should decrease their surface interval (and consequently their dive duration) relative to that which maximizes energy intake resulting in more dives per foraging bout. The fitness consequences of selecting a suboptimal surface interval vary with the risk function and the way divers harvest energy when at depth. Finally, predation risk during surface intervals should have important consequences for habitat selection and other aspects of the behavioral ecology of air-breathing aquatic organisms.