Feldman H A, McMahon T A
Respir Physiol. 1983 May;52(2):149-63. doi: 10.1016/0034-5687(83)90002-6.
The scaling law eta = alpha Mb is used to model basal energy metabolism (eta) in terms of body mass (M). The exponent b = 3/4 has commonly been applied to either inter-specific or intra-specific variation of body mass (the 'Brody-Kleiber law'). Heusner recently demonstrated that the exponent 2/3 provided a better description of intra-specific variation in a set of animal data from the literature and dismissed the value 3/4 as a 'statistical artifact.' Using the same data, we recast the statistical analysis in mathematically equivalent form and show that 3/4 nonetheless emerges as a precise numerical estimate of the mass exponent for inter-specific variation. We relate this finding to the theory of elastic similarity and demonstrate that there is both experimental and theoretical justification for the use of both exponents in describing the variation of basal energy metabolism among animals of different size and species.
标度律η = αM^b用于根据体重（M）对基础能量代谢（η）进行建模。指数b = 3/4通常应用于种间或种内体重变化（“布罗迪-克莱伯定律”）。休斯纳最近证明，指数2/3能更好地描述文献中一组动物数据的种内变化，并摒弃了3/4这个值，认为它是“统计假象”。我们使用相同的数据，以数学等价形式重新进行统计分析，结果表明，对于种间变化，3/4仍然是质量指数的精确数值估计。我们将这一发现与弹性相似性理论联系起来，并证明在描述不同大小和物种的动物基础能量代谢变化时，使用这两个指数都有实验和理论依据。
