  The observed properties of long gamma-ray burst (GRB) host galaxies show them
to often be of a rather low metallicity and/or of high specific star formation
rate (SFR). It is not clear which of these properties is a dominant factor in
determining if a galaxy will host a GRB or not. In fact there are indications,
at least in the local Universe, that the two may be anticorrelated and that the
metallicity is the deciding parameter. Here, we consider GRB production models
dependent on both quantities and show that when compared to the best available
data, the respective star formation fractions appear indistinguishable out to
redshift of $z\sim 4$. However, the fraction of galaxies hosting a GRB, as
determined by the specific SFR, is less at tension with the observed host
galaxy fraction than the corresponding metallicity determined fraction, but
this conclusion is model dependent. Well established galaxy stellar mass and
star formation rate functions at high redshift are crucial in breaking the
apparent degeneracy between the specific rate and metallicity in GRB production
probability.
