  Successful innovations achieve large geographical coverage by spreading
across settlements and distances. For decades, spatial diffusion has been
argued to take place along the urban hierarchy such that the innovation first
spreads from large to medium cities then later from medium to small cities.
Yet, the role of geographical distance, the other major factor of spatial
diffusion, was difficult to identify in hierarchical diffusion due to missing
data on spreading events. In this paper, we exploit spatial patterns of
individual invitations on a social media platform sent from registered users to
new users over the entire life cycle of the platform. This enables us to
disentangle the role of urban hierarchy and the role of distance by observing
the source and target locations of flows over an unprecedented timescale. We
demonstrate that hierarchical diffusion greatly overlaps with diffusion to
close distances and these factors co-evolve over the life cycle; thus, their
joint analysis is necessary. Then, a regression framework is applied to
estimate the number of invitations sent between pairs of towns by years in the
life cycle with the population sizes of the source and target towns, their
combinations, and the distance between them. We confirm that hierarchical
diffusion prevails initially across large towns only but emerges in the full
spectrum of settlements in the middle of the life cycle when adoption
accelerates. Unlike in previous gravity estimations, we find that after an
intensifying role of distance in the middle of the life cycle a surprisingly
weak distance effect characterizes the last years of diffusion. Our results
stress the dominance of urban hierarchy in spatial diffusion and inform future
predictions of innovation adoption at local scales.

Physics and Society