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The presence of self-organized criticality in biology is often evidenced by apower-law scaling of event size distributions, which can be measured by linearregression on logarithmic axes. We show here that such a procedure does notnecessarily mean that the system exhibits self-organized criticality. We firstprovide an analysis of multisite local field potential (LFP) recordings ofbrain activity and show that event size distributions defined as negative LFPpeaks can be close to power-law distributions. However, this result is notrobust to change in detection threshold, or when tested using more rigorousstatistical analyses such as the Kolmogorov-Smirnov test. Similar power-lawscaling is observed for surrogate signals, suggesting that power-law scalingmay be a generic property of thresholded stochastic processes. We nextinvestigate this problem analytically, and show that, indeed, stochasticprocesses can produce spurious power-law scaling without the presence ofunderlying self-organized criticality. However, this power-law is only apparentin logarithmic representations, and does not survive more rigorous analysissuch as the Kolmogorov-Smirnov test. The same analysis was also performed on anartificial network known to display self-organized criticality. In this case,both the graphical representations and the rigorous statistical analysis revealwith no ambiguity that the avalanche size is distributed as a power-law. Weconclude that logarithmic representations can lead to spurious power-lawscaling induced by the stochastic nature of the phenomenon. This apparentpower-law scaling does not constitute a proof of self-organized criticality,which should be demonstrated by more stringent statistical tests.

Can power-law scaling and neuronal avalanches arise from stochastic dynamics?