一種生物的代謝率與其身體質量之間的關系，自Max Kleiber在1932年首次提出不同物種代謝率隨身體質量按3/4次方增加的觀點以來,，一直讓生物學家著迷,。
這一“標度指數”自那時以來被重新計算了很多次,，其中有些人估計該指數接近2/3，而另一些人則估計其接近 3/4,。一項新的分析表明,，這種關系在對數標度上并不遵從一條直線，所以根本不遵守冪律（指數定律）,。
試圖將一條直線應用于實際上是一條曲線的情形,，會產生高度依賴于所使用數據的“標度指數”。以小生物為主的數據集傾向于產生2/3的指數,，而以大生物為主的數據集則會產生3/4的指數,。(生物谷Bioon.com)
生物谷推薦原文出處：
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.
