Division of Biomechanics and Research Development, Department of Biomechanics, Center for Research in Human Movement Variability, University of Nebraska at Omaha, Omaha, NE, 68182, USA.
Graduate School of Engineering Science, Osaka University, Osaka, 560-8531, Japan.
Sci Rep. 2024 Aug 28;14(1):19957. doi: 10.1038/s41598-024-69199-5.
Various animal and plant species exhibit allometric relationships among their respective traits, wherein one trait undergoes expansion as a power-law function of another due to constraints acting on growth processes. For instance, the acknowledged consensus posits that tree height scales with the two-thirds power of stem diameter. In the context of human development, it is posited that body weight scales with the second power of height. This prevalent allometric relationship derives its nomenclature from fitting two variables linearly within a logarithmic framework, thus giving rise to the term "power-law relationship." Here, we challenge the conventional assumption that a singular power-law equation adequately encapsulates the allometric relationship between any two traits. We strategically leverage quantile regression analysis to demonstrate that the scaling exponent characterizing this power-law relationship is contingent upon the centile within these traits' distributions. This observation fundamentally underscores the proposition that individuals occupying disparate segments of the distribution may employ distinct growth strategies, as indicated by distinct power-law exponents. We introduce the innovative concept of "multi-scale allometry" to encapsulate this newfound insight. Through a comprehensive reevaluation of (i) the height-weight relationship within a cohort comprising 7, 863, 520 Japanese children aged 5-17 years for which the age, sex, height, and weight were recorded as part of a national study, (ii) the stem-diameter-height and crown-radius-height relationships within an expansive sample of 498, 838 georeferenced and taxonomically standardized records of individual trees spanning diverse geographical locations, and (iii) the brain-size-body-size relationship within an extensive dataset encompassing 1, 552 mammalian species, we resolutely substantiate the viability of multi-scale allometric analysis. This empirical substantiation advocates a paradigm shift from uni-scaling to multi-scaling allometric modeling, thereby affording greater prominence to the inherent growth processes that underlie the morphological diversity evident throughout the living world.
各种动植物物种在其各自的特征之间表现出异速生长关系，其中一个特征由于生长过程中的限制而以幂律函数的形式扩展。例如，公认的共识是，树高与茎直径的三分之二次方成正比。在人类发展的背景下，有人认为体重与身高的二次方成正比。这种普遍的异速生长关系因其在对数框架内线性拟合两个变量而得名，因此产生了“幂律关系”一词。在这里，我们挑战了一个单一幂律方程足以描述任何两个特征之间异速生长关系的传统假设。我们巧妙地利用分位数回归分析来证明，描述这种幂律关系的标度指数取决于这些特征分布中的百分位数。这一观察结果从根本上强调了这样一个观点，即个体占据分布的不同部分可能采用不同的生长策略，这表现为不同的幂律指数。我们引入了“多尺度异速生长”的创新概念来封装这一新的发现。通过对（i）日本 5-17 岁儿童的身高-体重关系进行全面重新评估，该研究对 7863520 名儿童进行了研究，记录了他们的年龄、性别、身高和体重，这些数据是国家研究的一部分；（ii）一个包含 498838 个地理位置和分类标准化的个体树木记录的广泛样本的茎直径-高度和树冠半径-高度关系；以及（iii）一个包含 1552 种哺乳动物物种的广泛数据集的大脑大小-身体大小关系进行全面重新评估，我们坚决证实了多尺度异速生长分析的可行性。这种实证证实提倡从单尺度到多尺度异速生长建模的范式转变，从而更加突出了潜在的生长过程，这些过程是整个生命世界中明显的形态多样性的基础。
