Universal distribution of component frequencies in biological and technological systems

Abstract

Bacterial genomes and large-scale computer software projects both consist of a large number of components (genes or software packages) connected via a network of mutual dependencies. Components can be easily added or removed from individual systems, and their use frequencies vary over many orders of magnitude. We study this frequency distribution in genomes of ∼500 bacterial species and in over 2 million Linux computers and find that in both cases it is described by the same scale-free power-law distribution with an additional peak near the tail of the distribution corresponding to nearly universal components. We argue that the existence of a power law distribution of frequencies of components is a general property of any modular system with a multilayered dependency network. We demonstrate that the frequency of a component is positively correlated with its dependency degree given by the total number of upstream components whose operation directly or indirectly depends on the selected component. The observed frequency/dependency degree distributions are reproduced in a simple mathematically tractable model introduced and analyzed in this study.