Urban hierarchy and spatial diffusion over the innovation life cycle.

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. Yet, the role of geographical distance was difficult to identify in hierarchical diffusion due to missing data on spreading events. In this paper, we exploit spatial patterns of individual invitations sent from registered users to new users over the entire life cycle of a social media platform. We demonstrate that hierarchical diffusion overlaps with diffusion to close distances and these factors co-evolve over the life cycle. Therefore, we disentangle them in a regression framework that estimates the yearly number of invitations sent between pairs of towns. 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.