  Blue Large-Amplitude Pulsators (BLAPs) are a recently discovered class of
pulsating star, believed to be proto-white dwarfs, produced by mass stripping
of a red giant when it has a small helium core. An outstanding question is why
the stars in this class of pulsator seem to form two distinct groups by surface
gravity, despite predictions that stars in the gap between them should also
pulsate. We use a binary population synthesis model to identify potential
evolutionary pathways that a star can take to become a BLAP. We find that BLAPs
can be produced either through common envelope evolution or Roche lobe
overflow, with a Main Sequence star or an evolved compact object being
responsible for the envelope stripping. The mass distribution of the inferred
population indicates that fewer stars would be expected in the range of masses
intermediate to the two known groups of pulsators, suggesting that the lack of
observational discoveries in this region may be a result of the underlying
population of pre-white dwarf stars. We also consider metallicity variation and
find evidence that BLAPs at $Z = 0.010$ (half-Solar) would be pulsationally
unstable and may also be more common. Based on this analysis, we expect the
Milky Way to host around 12000 BLAPs and we predict the number density of
sources expected in future observations such as the Legacy Survey of Space and
Time at the Vera Rubin Observatory.
