  Motivated by the reported dearth of debris discs around M stars, we use
survival models to study the occurrence of planetesimal discs around them.
These survival models describe a planetesimal disc with a small number of
parameters, determine if it may survive a series of dynamical processes and
compute the associated infrared excess. For the WISE satellite, we demonstrate
that the dearth of debris discs around M stars may be attributed to the small
semi-major axes generally probed if either: 1. the dust grains behave like
blackbodies emitting at a peak wavelength coincident with the observed one; 2.
or the grains are hotter than predicted by their blackbody temperatures and
emit at peak wavelengths that are shorter than the observed one. At these small
distances from the M star, planetesimals are unlikely to survive or persist for
time scales of 300 Myr or longer if the disc is too massive. Conversely, our
survival models allow for the existence of a large population of low-mass
debris discs that are too faint to be detected with current instruments.
However, our interpretation becomes less clear and large infrared excesses are
allowed if only one of these scenarios holds: 3. the dust grains are hotter
than blackbody and predominantly emit at the observed wavelength; 4. or are
blackbody in nature and emit at peak wavelengths longer than the observed one.
Both scenarios imply that the parent planetesimals reside at larger distances
from the star than inferred if the dust grains behaved like blackbodies. In all
scenarios, we show that the infrared excesses detected at 22 and 70 microns
from AU Mic are easily reconciled with its young age. We elucidate the
conditions under which stellar wind drag may be neglected when considering dust
populations around M stars. The WISE satellite should be capable of detecting
debris discs around young M stars with ages on the order of 10 Myr.
