Lunge filter feeding biomechanics constrain rorqual foraging ecology across scale.

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 filtering it through baleen plates. However, as engulfment capacity increases with body length (engulfment volume∝body length3.57), the surface area of the baleen filter does not increase proportionally (baleen area∝body length1.82), and thus the filtration time of larger rorquals predictably increases as 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 length1.75). We tested this hypothesis on four rorqual species using multi-sensor tags with corresponding unoccupied aircraft systems-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 with smaller whales if they do not match their engulfment capacity to the size of targeted prey aggregations.