Many complex systems are hierarchical in nature; social groups, economic and
biological ecosystems, transportation infrastructures, languages, they all
develop hierarchies of their constitutive elements that emerge from networked
interactions within the system and with the external world. These hierarchies
change in time according to system-dependent mechanisms of interaction, such as
selection in evolutionary biology, or rules of performance in human sports, and
reflect the relevance or ability of the element in performing a function in the
system. However, it is still unclear whether the temporal evolution of
hierarchies solely depends on the driving forces and characteristics of each
system, or if there are generic features of hierarchy stability that allow us
to model and predict patterns of hierarchical behaviour without considering the
particularities of the system. We explore this question by analysing over 30
datasets of social, nature, economic, infrastructure, and sports systems in a
wide range of sizes (10^2 − 10^5) and time scales (from days to centuries) and
find that, despite their various origins, the elements in these systems show
remarkably similar stability depending on their position in the hierarchy. By
classifying systems from closed to increasingly open, we manage to reproduce
their hierarchy evolution in a minimal model with no system-dependent
mechanisms of interaction. This allows us to make predictions on unobserved
data, such as the likelihood of an unknown element climbing high in the
hierarchy, or the time scale over which an element can maintain its relevance
in the system. Our results may be crucial in further understanding why
hierarchies evolve similarly in seemingly unrelated areas, and give clues on
how to promote stability in the complex socio-technical systems of our day.

* Carlos Pineda, Instituto de Fisica, Universidad Nacional Autonoma de Mexico