Uncertainty in allometric exponent estimation: a case study in scaling metabolic rate with body mass

Many factors could influence the allometric scaling exponent beta estimation, but have not been explored systematically. We investigated the influences of three factors on the estimate of beta based on a data set of 626 species of basal metabolic rate and mass in mammals. The influence of sampling error was tested by re-sampling with different sample sizes using a Monte Carlo method. Small random errors were introduced to measured data to examine their influence on parameter estimations. The influence of analysis method was also evaluated by applying nonlinear and linear regressions to the original data. Results showed that a relative large sample size was required to lower statistical inference errors. When sample size n was 10% of the base population size (n=63), 35% of the samples supported beta=2/3, 39% supported beta=3/4, and 15% rejected beta=0.711, even though the base population had a beta=0.711. The controversy surrounding the estimation of beta in the literature could be partially attributable to such small sample sizes in many studies. Measurement errors in body mass and base metabolic rate, especially in body mass, could largely increase alpha and beta errors. Analysis methods also affected parameter estimations. Nonlinear regressions provided better estimates of the scaling exponent that were significantly higher than these commonly estimated by linear regressions. This study demonstrated the importance of the quantity and quality of data as well as analysis method in power law analysis, raising caution in interpreting power law results. Meta-data synthesis using data from independent studies seems to be a proper approach in the future, but caution should be taken to make sure that such measurements are made using similar protocols.