  Negative magnetoresistivity is a special magnetotransport property associated
with chiral anomaly in four dimensional chiral anomalous systems, which refers
to the transport behavior that the DC longitudinal magnetoresistivity decreases
with increasing magnetic field. We calculate the longitudinal
magnetoconductivity in the presence of backreactions of the magnetic field to
gravity in holographic zero charge and axial charge density systems with and
without axial charge dissipation. In the absence of axial charge dissipation,
we find that the quantum critical conductivity grows with increasing magnetic
field when the backreaction strength is larger than a critical value, in
contrast to the monotonically decreasing behavior of quantum critical
conductivity in the probe limit. With axial charge dissipation, we find the
negative magnetoresistivity behavior. The DC longitudinal magnetoconductivity
scales as $B$ in the large magnetic field limit, which deviates from the exact
$B^2$ scaling of the probe limit result. In both cases, the small frequency
longitudinal magnetoconductivity still agrees with the formula obtained from
the hydrodynamic linear response theory, even in the large magnetic field
limit.
