Fat tails and and critical thinking – how frequent are power laws in nature?

Allow me this pun: there can be no doubt that power laws are abundant in Nature – rumor has it that finding scale-free (power-law) distributions in a system is a prime ingredient for a successful publication in this journal, as in its counterpart Science. As proof, see just a few recent articles about Levy walks of mussels during the formation of spatially patterned beds1), scaling laws of marine predator search behaviour or studies in social organization such as email communications or insurgency attacks (the latter line of research was continues in Science later, see the article on pattern in Escalations in Insurgent and Terrorist Activity), Japanese family names or scientific collaboration networks.

It seems that power laws are being found virtually everywhere. However, what does that mean regarding their role in nature? To understand what all the fuzz is about, we have to recall that a power law is not only simply a convenient description of some empirical data – exponential, log-normal or Weilbull or other distributions would often do the same job. Finding a power-law is so interesting because a “true” power-law may hint towards processes of self-organization such as self-organized criticality, preferential attachment or (although that is not really about criticality) optimal foraging such as in Levy flights (a good introduction to the mechanistic underpinning of power laws is Newman, 2005).

So, it is interesting to detect “real” power laws, and it has become something like a sport to find them in empirical data. The problem is that methods used by many studies are statistically questionable, and very often there is no mechanistic explanation at all that could suggest why a power law would be expected rather than, say, an exponential distribution. In particular, the tendency to find power laws is fueled by the still used, but very unfavorable methodology of linear regressions on log-log plots, although problems with this (bias, wrong significance levels) were repeatedly shown, as was the fact that log-log plots make nearly all decaying distributions look like a power law. A few people have taken it upon them in recent years to point out these statistical inconsistencies and also the lack of mechanistic explanations, for example Clauset et al. (2009), and its good to see that their warning voices finally made it from the more technical journals to the top, with the new publication of “Critical Truths About Power Laws” by Stumpf and Porter. As a side remark: Mason Porter also runs the power-law shop with fun T-shirts about power-law fits.

1) Addition 24.2.12: Interestingly, also this power law was questioned in a technical comment by Jansen et al.

One thought on “Fat tails and and critical thinking – how frequent are power laws in nature?

  1. Pingback: Universal species-area and endemics-area relationships at continental scales « theoretical ecology

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