Meyer Thomas H, Rittenhouse Tracy A G, Elbroch L Mark, Pozdnyakov Vladimir, Yan Jun, Hu Chaoran, Félix Fernando, Guzmán Héctor M, Meynecke Jan-Olaf
Department of Natural Resources and the Environment, University of Connecticut, Storrs, Connecticut, USA.
Panthera, Kelly, Wyoming, USA.
Ecology. 2025 Jul;106(7):e70167. doi: 10.1002/ecy.70167.
Animals move in three dimensions, yet movement models do not capture the third dimension when data are collected as longitude and latitude coordinates (only) and models are developed in two dimensions. Here, we ask the question to what extent topography and the shape of the Earth-its ellipsoidal shape-affect the quantification of animal movement. To answer this question, we draw from the fields of ecology and geodesy: geodesy provides the mathematics to solve the problem on the curved surface of the Earth exactly, as opposed to using a map projection, because all map projections impart a scale distortion that systematically enlarges or shrinks the distances between points in space. We provide mathematical derivations to solve this problem in two different ways and show that they are equivalent. We also provide analyses of data from pumas (Puma concolor) and humpback whales (Megaptera novaeangliae) to discuss the impact of not accounting for the macroscopic, ellipsoidal shape of the Earth nor for topography when quantifying animal movements. In short, if the vertical extent of the movement is small compared to the horizontal extent, then the difference is de minimis. Conversely, if an animal moves vertically as much, or more, than how far it moves horizontally, then the difference is not negligible. Using map-projection coordinates without corrections systematically increases and/or decreases distances and, therefore, speeds.
动物在三维空间中移动，但当仅将经度和纬度坐标作为数据收集且在二维空间中建立运动模型时，这些模型无法捕捉到第三维度。在此，我们提出一个问题：地形以及地球的形状——其椭球体形状——在多大程度上会影响动物运动的量化。为回答这个问题，我们借鉴了生态学和大地测量学领域的知识：大地测量学提供了精确解决地球曲面问题的数学方法，这与使用地图投影不同，因为所有地图投影都会产生比例失真，从而系统地放大或缩小空间中各点之间的距离。我们提供了两种不同的数学推导来解决这个问题，并证明它们是等效的。我们还对美洲狮（美洲狮）和座头鲸（大翅鲸）的数据进行了分析，以讨论在量化动物运动时未考虑地球宏观椭球体形状和地形的影响。简而言之，如果运动的垂直范围与水平范围相比很小，那么差异可以忽略不计。相反，如果动物垂直移动的距离与水平移动的距离一样多，甚至更多，那么这种差异就不可忽略。使用未经校正的地图投影坐标会系统地增加和/或减小距离，进而影响速度。
