  We present a semi-analytic, computationally inexpensive model to identify
halos capable of forming a Population III star in cosmological simulations
across a wide range of times and environments. This allows for a much more
complete and representative set of Population III star forming halos to be
constructed, which will lead to Population III star formation simulations that
more accurately reflect the diversity of Population III stars, both in time and
halo mass. This model shows that Population III and chemically enriched stars
coexist beyond the formation of the first generation of stars in a cosmological
simulation until at least z~10, and likely beyond, though Population III stars
form at rates that are 4-6 orders of magnitude lower than chemically enriched
stars by z=10. A catalog of more than 40,000 candidate Population III forming
halos were identified, with formation times temporally ranging from z=30 to
z=10, and ranging in mass from 2.3x10^5 M_sun to 1.2x10^10 M_sun. At early
times, the environment that Population III stars form in is very similar to
that of halos hosting chemically enriched star formation. At later times
Population III stars are found to form in low-density regions that are not yet
chemically polluted due to a lack of previous star formation in the area.
Population III star forming halos become increasingly spatially isolated from
one another at later times, and are generally closer to halos hosting
chemically enriched star formation than to another halo hosting Population III
star formation by z~10.
