In recent years, fertility in developed countries has drastically fallen towards replacement levels, so that further changes play an increasing role in determining the dynamics of population systems. In this paper, the dynamics of multiregional populations are analyzed when occasional perturbations resulting from changes in social and economic conditions exist. A perturbation theory for population models is introduced and the increasing effect of changes in demographic rates in determining the spatial component of the multiregional population growth is shown. Critical situations in which perturbations produce drastic changes are outlined. A numerical experiment is discussed: an oversimplified model of the Italian population is given and it is shown how the theory can be applied to focus the short-run and the long-run effects of changes in demographic rates.