On estimating the exponent of power-law frequency distributions. Ecology 89, 905-912

Department of Biology and the Ecology Center, Utah State University, Logan, Utah 84322, USA.
Ecology (Impact Factor: 5). 05/2008; 89(4):905-12. DOI: 10.1890/07-1288.1
Source: PubMed

ABSTRACT 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 used 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 outperforms 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.

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Available from: Brian J. Enquist, Aug 29, 2015
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    • "The tail behaviour, as well as the difference of scaling behaviours between the sites in Saskatchewan and the site in Alberta (Figure 3), might be linked to the climate as consequences of its spatial variability. While there are several methods available for estimating the exponent of power-law distributions from empirical data, the maximum likelihood estimation outperforms other methods in both accuracy and precision (White et al. 2008). Generally, one can Figure 2 Inter-annual variability of spring wheat yield, from left to right, at the Census Agricultural Region, Ecodistrict, and Rural Municipality scales for the Canadian Prairie provinces (i.e. "
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    • "A constant bin-width of 10 3 m 2 was chosen based on the observations range and on a trade-off between frequency distribution resolution and accuracy in the studied oak woodlands, given the FC resolution maps. These oak woodland patch sizeefrequency distributions were then fitted to two different models for abundance distribution of oak woodlands: 1) a power law (K efi et al., 2007; White et al., 2008) NðSÞ ¼ cS l (3) "
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