  The coupling between population growth and transport accessibility has been
an elusive problem for more than 60 years now. Due to the lack of theoretical
foundations, most of the studies that considered how the evolution of
transportation networks impacts the population growth are based on regression
analysis in order to identify relevant variables. The recent availability of
large amounts of data allows us to envision the construction of new approaches
for understanding this coupling between transport and population growth. Here,
we use a detailed dataset for about 36000 municipalities in France from 1968
until now. In the case of large urban areas such as Paris, we show that growth
rate statistical variations decay in time and display a trend towards
homogeneization where local aspects are less relevant. We also show that growth
rate differences due to accessibility are very small and can mostly be observed
for cities that experienced very large accessibility variations. This suggests
that the relevant variable for explaining growth rate variations is not the
accessibility but its temporal variation. We propose a model that integrates
the stochastic internal variation of the municipalitie's population and an
inter-urban migration term that we show to be proportional to the accessibility
variation and has a limited time duration. This model provides a simple
theoretical framework that allows to go beyond econometric studies and sheds a
new light on the impact of transportation modes on city growth.
