Fundamental scaling relationships influence the physiology of vital rates, which in turn shape the ecology and evolution of organisms. For diving mammals, benefits conferred by large body size include reduced transport costs and enhanced breath-holding capacity, thereby increasing overall foraging efficiency. Rorqual whales feed by engulfing a large mass of prey-laden water at high speed and filter it through baleen plates. However, as engulfment capacity increases with body length across species (Engulfment Volume ∝ Body Length ^3.57), the surface area of the baleen filter does not increase proportionally (Baleen Area ∝ Body Length^1.82), and thus the filtration time of larger rorquals predictably increases because the baleen surface area must filter a disproportionally large amount of water. We predicted that filtration time should scale with body length to the power of 1.75 (Filter Time ∝ Body Length^1.75). We tested this hypothesis on four rorqual species using multi-sensor tags with corresponding unoccupied aerial systems (UAS) -based body length estimates. We found that filter time scales with body length to the power of 1.79 (95% CI: 1.61 - 1.97). This result highlights a scale-dependent trade-off between engulfment capacity and baleen area that creates a biomechanical constraint to foraging through increased filtration time. Consequently, larger whales must target high density prey patches commensurate to the gulp size to meet their increased energetic demands. If these optimal patches are absent, larger rorquals may experience reduced foraging efficiency compared to smaller whales if they do not match engulfment capacity to the size of targeted prey aggregations.

The morphometric data for engulfment capacity measurements was collected from the Discovery Reports (Mackintosh, 1929; Mackintosh, 1942; Matthews, 1937; Matthews, 1938). The baleen area data was collected from Werth et al., 2018.

The tag data was collected from 21 blue whales (Monterey Bay), three fin whales (Eastern Greenland and Monterey Bay), nine humpback whales (Antarctic Peninsula and Monterey Bay), and nine Antarctic minke whales (Antarctic Peninsula) between 2017 and 2019 using motion-sensing suction-cup attached tags. Whale body length measurements were taken from high-resolution aerial images using unoccupied aerial systems.

Data was processed using MATLAB, R, MorphoMetriX, and CollatriX.