Extrinsic vs Intrinsic Criticality In Systems With Many Components*

Some biological systems with many components exhibit seemingly critical behaviors, causes of which are unclear. Here we argue that although signatures of criticality are indicative of atypically large fluctuations coupled to observable degrees of freedom, they are agnostic about the origins of such fluctuations. We provide a definition of intrinsic and extrinsic criticalities, based on whether large critical fluctuations originate from within the systems, and offer a unifying way of describing the mechanism behind both types of criticalities. We study how the fluctuation variance, system size, subsampled system size and sample size affect the observability of Zipf's law—oft-used empirical evidence of criticality based on a power-law rank-frequency distribution of the states of the systems. We argue that intrinsic fluctuations are usually too small to explain empirically observed Zipf behaviors and extrinsically driven criticality is a more robust explanation. Finally we explore how specially designed models may induce intrinsic fluctuations large enough to generate Zipf-like distributions that extend adequately far into the observable range of rank-frequency plots.