In 0906.0590, Kistler et al investigate "The star formation rate in the reionization era as indicated by gamma-ray bursts". They make a compilation of high redshift long gamma ray bursts, deduce a correction factor as a function of redshift (at intermediate redshifts) between the rate of GRBs and the SFR and calculate the SFR(z), from GRBs. The result is the Lilly-Madua plot shown. The upper yellow points are results from the GRBs. Note that in all four bins there are just a few (1 in the last) GRBs used for the calculation. The grey points are the well known Hopkins & Beacom (2006) compilation, while the other, higher redshift, coloured points are deductions from UV luminosity functions from LBGs (Bouwens et al 2008) and Lyman alpha emitters (Ota et al 2008)

The grey lines with positive slope are the SFRDs necessary to keep the universe ionized according to Madau et al 1999. This seems to indicate that the star formation alone is enough to keep the universe ionized from z~8.