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We present a new self-consistent semi-analytic model of the first stars andgalaxies to explore the high-redshift ($z{>}15$) Population III (PopIII) andmetal-enriched star formation histories. Our model includes the detailed mergerhistory of dark matter halos generated with Monte Carlo merger trees. Wecalibrate the minimum halo mass for PopIII star formation from recenthydrodynamical cosmological simulations that simultaneously include thebaryon-dark matter streaming velocity, Lyman-Werner (LW) feedback, andmolecular hydrogen self-shielding. We find an overall increase in the resultingstar formation rate density (SFRD) compared to calibrations based on previoussimulations (e.g., the PopIII SFRD is over an order of magnitude higher at$z=35-15$). We evaluate the effect of the halo-to-halo scatter in this criticalmass and find that it increases the PopIII stellar mass density by a factor of${\sim}1.5$ at $z{>}15$. Additionally, we assess the impact of varioussemi-analytic/analytic prescriptions for halo assembly and star formationpreviously adopted in the literature. For example, we find that models assumingsmooth halo growth computed via abundance matching predict SFRDs similar to themerger tree model for our fiducial model parameters, but that they mayunderestimate the PopIII SFRD in cases of strong LW feedback. Finally, wesimulate sub-volumes of the Universe with our model both to quantify thereduction in total star formation in numerical simulations due to a lack ofdensity fluctuations on spatial scales larger than the simulation box, and todetermine spatial fluctuations in SFRD due to the diversity in halo abundancesand merger histories.

A Global Semi-Analytic Model of the First Stars and Galaxies Including Dark Matter Halo Merger Histories