  We consider a multidimensional monostable reaction-diffusion equation whose
nonlinearity involves periodic heterogeneity. This serves as a model of
invasion for a population facing spatial heterogeneities. As a rescaling
parameter tends to zero, we prove the convergence to a limit interface, whose
motion is governed by the minimal speed (in each direction) of the underlying
pulsating fronts. This dependance of the speed on the (moving) normal direction
is in contrast with the homogeneous case and makes the analysis quite involved.
Key ingredients are the recent improvement \cite{A-Gil} of the well-known
spreading properties \cite{Wein02}, \cite{Ber-Ham-02}, and the solution of a
Hamilton-Jacobi equation.
