Rajiform locomotion: three-dimensional kinematics of the pectoral fin surface during swimming by freshwater stingray Potamotrygon orbignyi

Abstract

SUMMARYRajiform locomotion in fishes is dominated by distinctive undulations of expanded pectoral fins. Unlike other fishes, which typically interact with the fluid environment via multiple fins, undulating rays modulate a single control surface, the pectoral disc, to perform pelagic locomotion, maneuvering and other behaviors. Complex deformations of the broad, flexible pectoral fins occur as the undulating wave varies in three dimensions; pectoral fin kinematics and changes in waveform with swimming speed cannot be fully quantified by two-dimensional analyses of the fin margin. We present the first three-dimensional analysis of undulatory rajiform locomotion in a batoid, the freshwater stingray Potamotrygon orbignyi. Using three cameras (250framess -1 ), we gathered three-dimensional excursion data from 31 points on the pectoral fin during swimming at 1.5 and 2.5disclengthss -1 , describing the propulsive wave and contrasting waveforms between swimming speeds. Only a relatively small region of the pectoral fin (~25%) undulates with significant amplitude (>0.5cm). Stingrays can maintain extreme lateral curvature of the distal fin margin in opposition to induced hydrodynamic loads, ʻcuppingʼ the edge of the pectoral fin into the flow, with potential implications for drag reduction. Wave amplitude increases across both anteroposterior and mediolateral fin axes. Along the anteroposterior axis, amplitude increases until the wave reaches mid-disc and then remains constant, in contrast to angulliform patterns of continuous amplitude increase. Increases in swimming speed are driven by both wave frequency and wavespeed, though multivariate analyses reveal a secondary role for amplitude. Supplementary material available online at

Batoid locomotion: effects of speed on pectoral fin deformation in the little skate, Leucoraja erinacea

“…2) during three independent (non-consecutive) fin beats (or swimming sequences) from each of the three individuals at the two speeds every 20 ms (total finbeats=18). Fin beats were defined as a complete cycle of disc wave, from the anterior to the posterior edge (Blevins and Lauder, 2012). We used natural markings on the dorsal surface of each skate left wing to track the nine points and determine the 3D deformation of the wing by analyzing the x, y and z coordinates of each point in time.…”

“…To date, only a few studies have attempted to quantify swimming kinematics of batoids (e.g. Fish et al, 2016;Fontanella et al, 2013;Parson et al, 2011;Rosenblum et al, 2011), and threedimensional deformation of the wing during swimming has only been described in one species, the freshwater stingray, Potamotrygon orbignyi (Blevins and Lauder, 2012). Although the extreme morphology of batoids renders the wing disc essentially two-dimensional in shape, the disc assumes a complex threedimensional conformation during swimming that can be effectively described only using three-dimensional kinematic analyses (Blevins and Lauder, 2012;Lauder and Jayne, 1996).…”

“…The availability of correlated analyses of metabolic and detailed kinematic data are rare for any fish species, and observed changes in patterns of wing deformation with swimming speed may help explain previous data showing the inability of this fish to sustain swimming at higher speeds (>1.25 BL s −1 ) for more than a few minutes. Second, three-dimensional kinematic data are only available for one other batoid species, the specialized freshwater stingray (Blevins and Lauder, 2012). A secondary purpose of this paper is to provide comparative data to allow at least a preliminary assessment of the diversity of batoid wing kinematics in non-pelagic species.…”

Skating by: low energetic costs of swimming in a batoid fish

“…Moreover, metabolic costs typically increase at higher speeds as drag forces increase to the square of velocity (Webb, 1998). Although swimming kinematics have been analyzed in a number of batoids (Blevins and Lauder, 2012;Rosenberger, 2001;Rosenberger and Westneat, 1999), no study has yet quantified the energetic costs of swimming in a batoid, nor whether different speeds require aerobic or anaerobic metabolism (Lauder and Di Santo, 2015). This is despite a long-standing recognition that locomotor performance and the associated metabolic costs are traits linked to fitness because they determine the capacity to endure migrations, escape predators, explore the environment and forage over long distances (Bennett and Huey, 1990).…”

Numerical Research on Amplitude of Batoid

“…Highly maneuverable fish have fins that are very effective at manipulating fluid and producing forces in threedimension [5][6][7]. The propulsion performance of the pectoral fins is affected by various parameters, including the geometry of the fin, the length and the flexibility of the fins, as well frequency and wavespeed etc [8][9][10].…”