  A model for the formation and evolution of binary millisecond radio pulsars
in systems with low mass companions (< 0.1 Msun) is investigated using a binary
population synthesis technique. Taking into account the non conservative
evolution of the system due to mass loss from an accretion disk as a result of
propeller action and from the companion via ablation by the pulsar, the
transition from the accretion powered to rotation powered phase is
investigated. It is shown that the operation of the propeller and ablation
mechanisms can be responsible for the formation and evolution of black widow
millisecond pulsar systems from the low mass X-ray binary phase at an orbital
period of ~0.1 day. For a range of population synthesis input parameters, the
results reveal that a population of black widow millisecond pulsars
characterized by orbital periods as long as ~0.4 days and companion masses as
low as ~0.005 Msun can be produced. The orbital periods and minimum companion
mass of this radio millisecond pulsar population critically depend on the
thermal bloating of the semi-degenerate hydrogen mass losing component, with
longer orbital periods for a greater degree of bloating. Provided that the
radius of the companion is increased by about a factor of 2 relative to a fully
degenerate, zero temperature configuration, an approximate agreement between
observed long orbital periods and theoretical modeling of hydrogen rich donors
can be achieved. We find no discrepancy between the estimated birth rates for
LMXBs and black widow systems, which on average are $\sim~1.3\times10^{-5} {\rm
yr}^{-1}$ and $1.3\times10^{-7} {\rm yr}^{-1}$ respectively.
