Rorqual Lunge-Feeding Energetics Near and Away from the Kinematic Threshold of Optimal Efficiency

Abstract

Humpback and blue whales are large baleen-bearing cetaceans which use a unique prey-acquisition strategy - lunge feeding - to engulf entire patches of large plankton or schools of forage fish and the water in which they are embedded. Dynamically, and while foraging on krill, lunge-feeding incurs metabolic expenditures estimated at up to 20.0 MJ. Because of prey abundance and its capture in bulk, lunge feeding is carried out at high acquired-to-expended energy ratios of up to 30 at the largest body sizes (∼27m). We use bio-logging tag data and the work-energy theorem to show that when krill-feeding at depth while using a wide range of prey approach swimming speeds (2 to 5m/s), rorquals generate significant and widely varying metabolic power output during engulfment, typically ranging from 10 to 50 times the basal metabolic rate of land mammals. At equal prey field density, such output variations lower their feeding efficiency 2- to 3-fold at high foraging speeds, thereby allowing slow and smaller rorquals to feed more efficiently than fast and larger rorquals. The analysis also shows how the slowest speeds of harvest so far measured may be connected to the biomechanics of the buccal cavity and the prey’s ability to collectively avoid engulfment. Such minimal speeds are important as they generate the most efficient lunges.

Scaling of oscillatory kinematics and Froude efficiency in baleen whales

“…Mean mass-specific thrust power output increased with the transition from routine to lunge-associated swimming modes (Fig. 4A-B), and to values in agreement with an alternative approach based on the work-energy theorem (Potvin et al, 2021). There was a positive effect of swimming speed on mass-specific thrust power output during both routine and lunge-associated swimming (routine: ŷ = 0.381x -1.215; R 2 = 0.38; p < 0.001; lunge-associated: ŷ = 0.320x -0.804; R 2 = 0.57; p < 0.001; Fig 4A).…”

“…Foraging lunges were detected manually using a series of defined kinematic parameters that have been validated using tag video ( Cade et al, 2016 ). These events typically involve an increase in speed during prey approach, followed by a rapid deceleration as an animal opens its mouth to engulf prey ( Potvin et al, 2009 ; Goldbogen et al, 2011 ; Cade et al, 2016 ; Potvin et al, 2021 ). We standardized the period from 10 to 0 s prior to the lunge deceleration (which typically coincides with the period of mouth opening) as the lunge-associated period.…”

“…where the mean acceleration is given by , with U f as the final speed at the end of the tailbeat, U i the initial speed at its beginning, and T beat as its duration. Given the high degree of body streamlining, the mean drag force ( ; N ) is expressed as follows ( Goldbogen et al, 2019 ; Potvin et al, 2020 ; Segre et al, 2020 ; Potvin et al, 2021 ): …”

“…a result involving the corresponding ‘mean drag coefficient’ across the duration of the tailbeat ( C D ). The parameter k added is an acceleration reaction coefficient set at 0.03 for blue whales and minke whales and 0.05 for humpback whales ( Potvin et al, 2020 , 2021 ). Merging Eqns 5–7 and solving for the drag coefficient results in: …”

“…All of the species included in our study are lunge feeders, which open their mouth wide prior to engulfing a large volume of water into a highly expansible throat pouch ( Goldbogen et al, 2017b ). This behavior requires the efficient achievement of high swimming speeds in order to maintain a favorable energetic balance ( Potvin et al, 2009 , 2020 , 2021 ). We hypothesize that the kinematic and hydrodynamic parameters of swimming scale similarly between small and large cetaceans and will lead to high (>75%) Froude efficiencies for even the largest animals.…”