对代谢“3/4定律”的再认识
Re-examination of the "3/4-law" of Metabolism
摘要：
我们研究的比例法则$B \propto M^α$连接有机体代谢率$B$与有机体质量$M$，其中$α$通常被认为是3/4。由于简单的维度分析表明$α=2/3$，我们认为这是一个零假设检验的实证研究。我们重新分析了Heusner、Bennett和Harvey、Bartels、Hemmingsen、Brody和Kleiber编制的哺乳动物和鸟类数据集，发现几乎没有证据表明$α=2/3$被$α=3/4$取代。对于哺乳动物，我们发现一个可能的故障，反映在一个系统的增加$α$的规模较大的群众。我们还回顾了$α=3/4$基于维度分析，营养供应网络和四维生物学的理论依据。我们发现，目前的理论$α=3/4$需要的假设，使他们无法令人信服的拒绝零假设，$α=2/3$。
英文摘要：
We examine the scaling law $B \propto M^α$ which connects organismal metabolic rate $B$ with organismal mass $M$, where $α$ is commonly held to be 3/4. Since simple dimensional analysis suggests $α=2/3$, we consider this to be a null hypothesis testable by empirical studies. We re-analyze data sets for mammals and birds compiled by Heusner, Bennett and Harvey, Bartels, Hemmingsen, Brody, and Kleiber, and find little evidence for rejecting $α=2/3$ in favor of $α=3/4$. For mammals, we find a possible breakdown in scaling for larger masses reflected in a systematic increase in $α$. We also review theoretical justifications of $α=3/4$ based on dimensional analysis, nutrient-supply networks, and four-dimensional biology. We find that present theories for $α=3/4$ require assumptions that render them unconvincing for rejecting the null hypothesis that $α=2/3$.
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