  Characterizing the spatial organization of urban systems is a challenge which
points to the more general problem of describing marked point processes in
spatial statistics. We propose a non-parametric method that goes beyond
standard tools of point pattern analysis and which is based on a mapping
between the points and a "dominance tree", constructed from a recursive
analysis of their Voronoi tessellation. Using toy models, we show that the
height of a node in this tree encodes both its mark and the structure of its
neighborhood, reflecting its importance in the system. We use historical
population data in France (1876-2018) and the US (1880-2010) and show that the
method highlights multiscale urban dynamics experienced by these countries.
These include non-monotonous city trajectories in the US, as revealed by the
evolution of their height in the tree. We show that the height of a city in the
tree is less sensitive to different statistical definitions of cities than its
rank in the urban hierarchy. The method also captures the attraction basins of
cities at successive scales, and while in both countries these basin sizes
become more homogeneous at larger scales, they are also more heterogeneous in
France than in the US. Finally, we introduce a simple graphical representation
- the height clock - that monitors the evolution of the role of each city in
its country.
