  The influence of crowding on the diffusion of tagged particles in a dense
medium is investigated in the framework of a mean-field model, derived in the
continuum limit from a microscopic stochastic process with exclusion. The
probability distribution function of the tagged particles obeys to a nonlinear
Fokker-Planck equation, where the drift and diffusion terms are determined
self-consistently by the concentration of crowders in the medium. Transient
sub-diffusive or super-diffusive behaviours are observed, depending on the
selected initial conditions, that bridge normal diffusion regimes characterized
by different diffusion coefficients. These anomalous crossovers originate from
the microscopic competition for space and reflect the peculiar form of the
non-homogeneous advection term in the governing Fokker-Planck equation. Our
results strongly warn against the overly simplistic identification of crowding
with anomalous transport {\em tout court}.
