Energetics of the yo-yo dives of predatory sharks

Sharks zigzag vertically through the water in a series of alternating ascending and descending segments, changing depth by a few tens of meters over a period of a few hundred seconds. This 'yo-yo' like behavior has several characteristic patterns, identifiable by the way the swimming and vertical velocities vary along the dive. We suggest that these patterns represent different optimal strategies minimizing the cost of locomotion under different constraints; moreover, these constraints can be inferred by matching the pattern of a dive with a (standard) optimal swimming strategy for which the constraints are known. We used three sets of constraints and two definitions of the 'cost of locomotion' to analytically generate four standard optimal strategies; we have used high resolution tracking data from four tiger sharks to identify two different yo-yo diving patterns. These patterns seem to match two of the standard strategies: one that maximizes range, given an alternating power supply (e.g., swimming actively on ascents and lazily on descents); and the other that maximizes range, given an alternating vertical velocity (implying an 'intentional' up-and-down motion).