The optimal allocation of time during the diving cycle

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Abstract
Previous research has used a “marginal value” approach to determine how long a diver should spend on the surface obtaining oxygen if it is to maximize the proportion of time in the foraging area. In this paper we develop an explicit and general version of this model and show how it results in predictions about both time on the surface and time under water. We also extend the analysis to include the maximization of the net rate of energetic gain and the maximization of energetic efficiency. We show that the various currencies can be distinguished qualitatively in terms of the way in which their predictions depend on the parameters that characterize the animal and its environment. A general feature of the results is that the time in the foraging area should first increase and then decrease as round-trip travel time, т, from the surface to the foraging area and back again increases.

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