  Rotation-powered millisecond radio pulsars have been spun up to their present
spin period by a $10^8$ - $10^9$ yr long X-ray-bright phase of accretion of
matter and angular momentum in a low-to-intermediate mass binary system.
Recently, the discovery of transitional pulsars that alternate cyclically
between accretion and rotation-powered states on time scales of a few years or
shorter, has demonstrated this evolutionary scenario. Here, we present a
thorough statistical analysis of the spin distributions of the various classes
of millisecond pulsars to assess the evolution of their spin period between the
different stages. Accreting sources that showed oscillations exclusively during
thermonuclear type I X-ray bursts (nuclear-powered millisecond pulsars) are
found to be significantly faster than rotation-powered sources, while accreting
sources that possess a magnetosphere and show coherent pulsations (accreting
millisecond pulsars) are not. On the other hand, if accreting millisecond
pulsars and eclipsing rotation-powered millisecond pulsars form a common class
of transitional pulsars, these are shown to have a spin distribution
intermediate between the faster nuclear-powered millisecond pulsars and the
slower non-eclipsing rotation-powered millisecond pulsars. We interpret these
findings in terms of a spin-down due to the decreasing mass-accretion rate
during the latest stages of the accretion phase, and in terms of the different
orbital evolutionary channels mapped by the various classes of pulsars. We
summarize possible instrumental selection effects, showing that even if an
unbiased sample of pulsars is still lacking, their influence on the results of
the presented analysis is reduced by recent improvements in instrumentation and
searching techniques.
