Ecological Society of America
Power-law frequency distributions characterize a wide array of natural phenomena. In ecology, biology, and many physical and social sciences, the exponents of these power-laws are estimated to draw inference about the processes underlying the phenomenon, to test theoretical models, and to scale up from local observations to global patterns. Therefore, it is essential that these exponents be estimated accurately. Unfortunately, the binning-based methods traditionally utilized in ecology and other disciplines perform quite poorly. Here we discuss more sophisticated methods for fitting these exponents based on cumulative distribution functions and maximum likelihood estimation. We illustrate their superior performance at estimating known exponents and provide details on how and when ecologists should use them. Our results confirm that maximum likelihood estimation out-performs other methods in both accuracy and precision. Because of the use of biased statistical methods for estimating the exponent, the conclusions of several recently published papers should be revisited.
White, E.P., B.J. Enquist, and J.L. Green. 2008. On estimating the exponent of powerlaw frequency distributions. Ecology 89:905912.