Fish Frank E, Kolpas Allison, Crossett Andrew, Dudas Michael A, Moored Keith W, Bart-Smith Hilary
Department of Biology, West Chester University, West Chester, PA 19383, USA
Department of Mathematics, West Chester University, West Chester, PA 19383, USA.
J Exp Biol. 2018 Mar 22;221(Pt 6):jeb166041. doi: 10.1242/jeb.166041.
For aquatic animals, turning maneuvers represent a locomotor activity that may not be confined to a single coordinate plane, making analysis difficult, particularly in the field. To measure turning performance in a three-dimensional space for the manta ray (), a large open-water swimmer, scaled stereo video recordings were collected. Movements of the cephalic lobes, eye and tail base were tracked to obtain three-dimensional coordinates. A mathematical analysis was performed on the coordinate data to calculate the turning rate and curvature (1/turning radius) as a function of time by numerically estimating the derivative of manta trajectories through three-dimensional space. Principal component analysis was used to project the three-dimensional trajectory onto the two-dimensional turn. Smoothing splines were applied to these turns. These are flexible models that minimize a cost function with a parameter controlling the balance between data fidelity and regularity of the derivative. Data for 30 sequences of rays performing slow, steady turns showed the highest 20% of values for the turning rate and smallest 20% of turn radii were 42.65±16.66 deg s and 2.05±1.26 m, respectively. Such turning maneuvers fall within the range of performance exhibited by swimmers with rigid bodies.
对于水生动物而言，转向动作是一种运动活动，可能并不局限于单一坐标平面，这使得分析变得困难，尤其是在野外环境中。为了测量蝠鲼（一种大型远洋游泳动物）在三维空间中的转向性能，我们收集了按比例缩放的立体视频记录。对头叶、眼睛和尾基部的运动进行跟踪，以获取三维坐标。对坐标数据进行数学分析，通过数值估计蝠鲼在三维空间中的轨迹导数，计算出作为时间函数的转向速率和曲率（1/转弯半径）。主成分分析用于将三维轨迹投影到二维转弯上。对这些转弯应用平滑样条。这些是灵活的模型，通过一个控制数据保真度和导数正则性之间平衡的参数来最小化一个代价函数。对30个蝠鲼进行缓慢、稳定转弯序列的数据显示，转弯速率最高的20%的值和转弯半径最小的20%的值分别为42.65±16.66度/秒和2.05±1.26米。这种转弯动作属于具有刚体的游泳者所表现出的性能范围。
