  We study the propagation of pulled fronts in the $A <-> \leftrightarrow A+A$
microscopic reaction-diffusion process using Monte Carlo (MC) simulations. In
the mean field approximation the process is described by the deterministic
Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation. In particular we
concentrate on the corrections to the deterministic behavior due to the number
of particles per site $\Omega$. By means of a new hybrid simulation scheme, we
manage to reach large macroscopic values of $\Omega$ which allows us to show
the importance in the dynamics of microscopic pulled fronts of the interplay of
microscopic fluctuations and their macroscopic relaxation.
