  Long gamma-ray burst's (LGRB's) association to the death of massive stars
suggest they could be used to probe the cosmic star formation history (CSFH)
with high accuracy, due to their high luminosities. We utilise cosmological
simulations from the First Billion Years project to investigate the biases
between the CSFH and the LGRB rate at z>5, assuming various different models
and constraints on the progenitors of LGRBs. We populate LGRBs using a
selection based on environmental properties and demonstrate that the LGRB rate
should trace the CSFH to high redshifts. The measured LGRB rate suggests that
LGRBs have opening angles of theta_jet=0.1 deg, although the degeneracy with
the progenitor model cannot rule out an underlying bias. We demonstrate that
proxies that relate the LGRB rate with global LGRB host properties do not
reflect the underlying LGRB environment, and are in fact a result of the host
galaxy's spatial properties, such that LGRBs can exist in galaxies of solar
metallicity. However, we find a class of host galaxies that have low stellar
mass and are metal-rich, and that their metallicity dispersions would not allow
low-metallicity environments. Detection of hosts with this set of properties
would directly reflect the progenitor's environment. We predict that 10% of
LGRBs per year are associated with this set of galaxies that would have
forbidden line emission that could be detected by instruments on the James Webb
Space Telescope. Such a discovery would place strong constraints on the
collapsar model and suggest other avenues to be investigated.
