一种生物的代谢率与其身体质量之间的关系，自Max Kleiber在1932年首次提出不同物种代谢率随身体质量按3/4次方增加的观点以来，一直让生物学家着迷。
这一“标度指数”自那时以来被重新计算了很多次，其中有些人估计该指数接近2/3，而另一些人则估计其接近 3/4。一项新的分析表明，这种关系在对数标度上并不遵从一条直线，所以根本不遵守幂律（指数定律）。
试图将一条直线应用于实际上是一条曲线的情形，会产生高度依赖于所使用数据的“标度指数”。以小生物为主的数据集倾向于产生2/3的指数，而以大生物为主的数据集则会产生3/4的指数。(生物谷Bioon.com)
生物谷推荐原文出处：
Nature doi:10.1038/nature08920
Curvature in metabolic scaling
Tom Kolokotrones1, Van Savage2, Eric J. Deeds1 & Walter Fontana1
Harvard Medical School, Boston, Massachusetts 02115, USA
David Geffen School of Medicine at the University of California at Los Angeles, Los Angeles, California 90024, USA
For more than three-quarters of a century it has been assumed1 that basal metabolic rate increases as body mass raised to some power p. However, there is no broad consensus regarding the value of p: whereas many studies have asserted that p is 3/4 (refs 1–4; ‘Kleiber’s law’), some have argued that it is 2/3 (refs 5–7), and others have found that it varies depending on factors like environment and taxonomy6, 8, 9, 10, 11, 12, 13, 14, 15, 16. Here we show that the relationship between mass and metabolic rate has convex curvature on a logarithmic scale, and is therefore not a pure power law, even after accounting for body temperature. This finding has several consequences. First, it provides an explanation for the puzzling variability in estimates of p, settling a long-standing debate. Second, it constitutes a stringent test for theories of metabolic scaling. A widely debated model17 based on vascular system architecture fails this test, and we suggest modifications that could bring it into compliance with the observed curvature. Third, it raises the intriguing question of whether the scaling relation limits body size.
