With the first metal enrichment by Population III (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, Pops II and III co-evolve 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, to a rate per comoving volume of ≲ 10- 4 M⊙ yr- 1 Mpc- 3, compared to the case in which this radiation is not included. However, we find that the effect of Lyman-Werner (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⊙ 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 ˜ 105 M⊙ black holes.