Allometric exponents support a 3/4-power scaling law

The relationship between metabolic rate and body mass follows a power function: B proportional to m(b) where B is the basal metabolic rate, in is the species mass, and b is the allometric exponent. Older models based on a consideration of surface to volume ratios predict an exponent b = 2/3, whereas more recent models based on efficient transport and fractal design predict an exponent b = 3/4. We analyzed 22 published allometric exponents to address the following questions: (1) Is the published allometric exponent correlated with number of species, average mass, or range of mass in the study? (2) What is the mean and confidence interval for published exponents, and do they vary among taxa? (3) Given the published exponent data, what is the likelihood that b = 2/3 vs. 3/4? We found that published exponents were not correlated with sample size, average mass, or log(difference in mass). For mammals and birds, the allometric exponents were tightly clustered, with means of 0.72 and 0.73, respectively. The reptile data spanned a wider range but had a mean of 0.74. Likelihood analysis suggests that b = 3/4 is significantly more probable than b = 2/3. We built a linear regression simulation with experimental error in mass and showed that such measurement error systematically lowers estimates of the allometric exponent. Measurement error probably contributes to the observation that published allometric exponents often fall short of b = 3/4 as predicted by theoretical models.