Variation in rachis (central shaft) morphology in individual remiges (flight feathers) within and among species reflects adaptations to requirements imposed by aerodynamic forces, but the fine-scale variation of feather morphology across remiges is not well known. Here we describe how the shape of the rachis, expressed by the height/width ratio, changes along the longitudinal and lateral axis of the wing in four bird species with different flight styles: flapping-soaring (white storks), flapping-gliding (common buzzards), passerine-type (house sparrows) and continuous flapping (pygmy cormorants). Overall, in each wing feather, irrespective of species identity, rachis shape changed from circular to rectangular, from the base towards the feather tip. The ratio between the height and width of the calamus was similar across remiges in all species, whereas the ratio at the base, middle and tip of the rachis changed among flight feathers and species. In distal primaries of white storks and common buzzards, the ratio decreased along the feather shaft, indicating a depressed (wider than high) rachis cross section towards the feather tip, whereas the inner primaries and secondaries became compressed (higher than wide). In house sparrows, the rachis was compressed in each of the measurement points, except at the distal segment of the two outermost primary feathers. Finally, in pygmy cormorants, the width exceeds the height at each measurement point, except at the calamus. Our results may reflect the resistance of the rachis to in-plane and out-of-plane aerodynamic forces that vary across remiges and across study species. A link between rachis shape and resistance to bending from aerodynamic forces is further indicated by the change of the second moment of areas along the wing axes.

中文翻译：

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不同飞行方式的四种鸟类飞行羽毛杆的形态学表征

物种内部和物种之间的单个迁徙（飞行羽毛）中的棘齿（中心轴）形态变化反映了对空气动力施加的要求的适应性，但是跨迁徙的羽毛形态的精细尺度变化尚不为人所知。在这里，我们描述了以高度/宽度比表示的棘突的形状如何在四种鸟类中以不同的飞行方式沿机翼的纵轴和横轴变化：拍打ar翔（白鹳），拍打滑翔（常见uzz，雀形目（麻雀）和连续扑动（侏儒cor）。总体而言，在每只翼羽中，无论根的种类如何，从根部到羽尖的轴形都从圆形变为矩形。在所有物种的迁徙中，cal蒲的高度与宽度之间的比例相似，而根际，中部和顶端的比率在飞羽和物种之间变化。在白鹳和普通秃鹰的远侧初级原毛中，该比率沿羽毛轴下降，表明朝向羽尖的凹陷的脊柱横截面呈凹形（宽于高），而内部初级和次级则被压缩（高于宽）。在麻雀中，除了两个最外面的主要羽毛的远侧部分以外，在每个测量点上均压缩了脊柱。最后，在侏儒cor中，除了the蒲以外，每个测量点的宽度都超过了高度。我们的结果可能反映了rachis对不同迁徙者和不同研究物种的平面内和平面外空气动力的抵抗力。