Not yet reviewed by Pith; the record is open.

Observations of long gamma-ray bursts (LGRBs) offer a unique opportunity for probing the cosmic star formation history, although whether or not LGRB rates are biased tracers of star formation rate history is highly debated. Based on an extensive sample of LGRBs compiled by Robertson & Ellis (2012), we analyze various models of star formation rate and the possible effect of the evolution of cosmic metallicity under the assumption that LGRBs tend to occur in low-metallicity galaxies. The models of star formation rate tested in this work include empirical fits from observational data as well as a self-consistent model calculated in the framework of the hierarchical structure formation. Comparing with the observational data, we find a relatively higher metallicity cut of $Z\gtrsim0.6Z_{\odot}$ for the empirical fits and no metallicity cut for the self-consistent model. These results imply that there is no strong metallicity preference for the host galaxy of LGRBs, in contrast to previous work which suggest a cut of $Z\sim0.1-0.3Z_{\odot}$, and that the inferred dependencies of LGRBs on their host galaxy properties are strongly related to the specific models of star formation rate. Furthermore, a significant fraction of LGRBs occur in small dark matter halos down to $3\times10^{8}\,\mathrm{M_{\odot}}$ can provide an alternative explanation for the discrepancy between the star formation rate history and LGRB rate history.