  With the first metal enrichment by Population (Pop) III supernovae (SNe), the
formation of the first metal-enriched, Pop II stars becomes possible. In turn,
Pop III star formation and early metal enrichment are slowed by the high energy
radiation emitted by Pop II stars. Thus, through the SNe and radiation they
produce, Populations II and III coevolve in the early Universe, one regulated
by the other. We present large (4 Mpc)^3, high resolution cosmological
simulations in which we self-consistently model early metal enrichment and the
stellar radiation responsible for the destruction of the coolants (H2 and HD)
required for Pop III star formation. We find that the molecule-dissociating
stellar radiation produced both locally and over cosmological distances reduces
the Pop III star formation rate at z > 10 by up to an order of magnitude
compared to the case in which this radiation is not included. However, we find
that the effect of LW feedback is to enhance the amount of Pop II star
formation. We attribute this to the reduced rate at which gas is blown out of
dark matter haloes by SNe in the simulation with LW feedback, which results in
larger reservoirs for metal-enriched star formation. Even accounting for metal
enrichment, molecule-dissociating radiation and the strong suppression of
low-mass galaxy formation due to reionization at z < 10, we find that Pop III
stars are still formed at a rate of ~ 10^-5 M_sun yr^-1 Mpc^-3 down to z ~ 6.
This suggests that the majority of primordial pair-instability SNe that may be
uncovered in future surveys will be found at z < 10. We also find that the
molecule-dissociating radiation emitted from Pop II stars may destroy H2
molecules at a high enough rate to suppress gas cooling and allow for the
formation of supermassive primordial stars which collapse to form ~ 100,000
solar mass black holes.
