  We analytically compute the effects that a mass variation rate \dot M/M of a
pulsar may have on the changes \Delta\tau in the times of arrival of its pulses
due to test particle companions, and on their orbital dynamics. We apply our
results to the planetary system of the PSR B1257+12 pulsar, located in the
Galaxy at 600 pc from us, to phenomenologically constrain a putative accretion
of non-annihilating dark matter on the hosting neutron star. (Abridged)
