  We describe a simple spatial model of urban growth for systems of cities at
the macroscopic scale, which combines direct interaction between cities and an
indirect effect of physical network flows as population growth drivers. The
model is parametrized on population data for the French system of cities
between 1831 and 1999, which strong non-stationarity in correlation patterns
suggest to apply the model on local time windows. The corresponding calibration
of the model using genetic algorithms provide the evolution of interaction
processes and network effects in time. Furthermore, the fit improvement when
adding network module appears effective when controlling for additional
parameters, what confirms the ability of the model to unveil network effects in
the system of cities.
