  By comparing relative rates of supernovae versus formation rates of single
radio pulsars, recycled pulsars, binary pulsars and X-ray binaries we put
strong limits on the progenitors of radio pulsars and on the requirement of an
asymmetry in the supernova. The assumption that radio pulsars are only formed
in type Ib and type Ic supernovae from interacting binaries (Iben & Tutukov
1996) breaks down on the implication that in that case either the formation
rate of binary pulsars (double neutron stars) should be of the order of 20%, of
the single pulsar birthrate or, alternatively, almost all single pulsars (85%
to 98%) should originate from Thorne-Zytkow stars. In the latter case the
pulsar velocity distribution is inconsistent with observations. Also, in that
case the difference between the supernova rate and the pulsar formation rate
would be about one order of magnitude, i.e.: much larger than observed.
  Allowing type II supernovae from single stars and non-interacting binaries to
form radio pulsars solves this conundrum, but then a kick is required in order
to explain the high velocities of single radio pulsars. A kick is also required
to understand the small birthrate, relative to the supernova rate, of binary
pulsars consisting of two neutron stars.
