  Scale independence is a ubiquitous feature of complex systems which implies a
highly skewed distribution of resources with no characteristic scale. Research
has long focused on why systems as varied as protein networks, evolution and
stock actions all feature scale independence. Assuming that they simply do, we
focus here on describing how this behaviour emerges, in contrast to more
idealized models usually considered. We arrive at the conjecture that a minimal
model to explain the growth towards scale independence involves only two
coupled dynamical features: the first is the well-known preferential attachment
principle and the second is a general form of delayed temporal scaling. While
the first is sufficient, the second is present in all studied data and appears
to maximize the speed of convergence to true scale independence. The delay in
this temporal scaling acts as a coupling between population growth and
individual activity. Together, these two dynamical properties appear to pave a
precise evolution path, such that even an instantaneous snapshot of a
distribution is enough to reconstruct the past of the system and predict its
future. We validate our approach and confirm its usefulness on diverse spheres
of human activities ranging from scientific and artistic productivity, to
sexual relations and online traffic.

Physics and Society