Abstract
Rorqual whales (crown Balaenopteridae) are unique among aquatic vertebrates in their ability to lunge-feed. During a single lunge, rorquals rapidly engulf a large volume of prey-laden water at high speed, which they then filter to capture suspended prey. Engulfment biomechanics are mostly governed by the coordinated opening and closing of the mandibles at large gape angles, which differentially exposes the floor of the oral cavity to oncoming flow. Mouth area in rorquals is delimited by unfused bony mandibles that form kinetic linkages to each other and with the skull. The relative scale and morphology of these skeletal elements have profound consequences for the energetic efficiency of foraging in these gigantic predators. Here we performed a morphometric study of rorqual mandibles using a dataset derived from a survey of museum specimens. Across adult specimens of extant balaenopterids, mandibles range in size from ~1-6 m in length, and at their upper limit they represent the single largest osteological element of any vertebrate, living or extinct. Our analyses determined that rorqual mandibles exhibit positive allometry, whereby the relative size of these mandibles becomes greater with increasing body size. These robust scaling relationships allowed us to predict mandible length for fragmentary remains (e.g., incomplete and/or fossil specimens), as we demonstrated for two partial mandibles from the latest Miocene of California, U.S.A., and for mandibles from previously described fossil balaenopterids. Furthermore, we showed the allometry of mandible length to body size in extant mysticetes, which hints at fundamental developmental constraints in mysticetes despite their ecomorphologic differences in the feeding styles. Lastly, we outlined how our findings can be used to test hypotheses about the antiquity and evolution of lunge-feeding.