  We have developed a semi-analytic framework to model the large-scale
evolution of the first Population III (Pop III) stars and the transition to
metal-enriched star formation. Our model follows dark matter halos from
cosmological N-body simulations, utilizing their individual merger histories
and three-dimensional positions, and applies physically motivated prescriptions
for star formation and feedback from Lyman-Werner (LW) radiation, hydrogen
ionizing radiation, and external metal enrichment due to supernovae winds. This
method is intended to complement analytic studies, which do not include
clustering or individual merger histories, and hydrodynamical cosmological
simulations, which include detailed physics, but are computationally expensive
and have limited dynamic range. Utilizing this technique, we compute the
cumulative Pop III and metal-enriched star formation rate density (SFRD) as a
function of redshift at $z \geq 20$. We find that varying the model parameters
leads to significant qualitative changes in the global star formation history.
The Pop III star formation efficiency and the delay time between Pop III and
subsequent metal-enriched star formation are found to have the largest impact.
The effect of clustering (i.e. including the three-dimensional positions of
individual halos) on various feedback mechanisms is also investigated. The
impact of clustering on LW and ionization feedback is found to be relatively
mild in our fiducial model, but can be larger if external metal enrichment can
promote metal-enriched star formation over large distances.
