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tokens: computed by Madau Dickinson ( 2014 ), after we converted it to a Kroupa IMF, and the red curve shows it multiplied by 0.4 to match roughly the SFR density history of the SCUBA-2 sources. However, once we also take into account the different FIR calibrations that were used in this work vs. in Madau Dickinson, we find that the SCUBA-2 data are only 0.29 times the Madau Dickinson curve. The red shaded region shows the 68% confidence range when allowance is made for the systematic uncertainties in the SFR calibrations. (b) Number density per unit comoving volume per unit SFR vs. SFR in five redshift intervals (see legend). The error bars in Figure 25 (a) are purely statistical. However, systematic errors in the SFR conversion and in the redshift estimates may also be important. In order to estimate these potential errors, we recomputed the SFR density history randomly, reassigning the SFRs and redshifts within the potential error ranges. Based on these Monte Carlo calculations, we computed the 68% error range produced by the systematics, which we show as the red shaded region. For the highest and lowest redshifts, where there are fewer objects, the systematic and statistical errors are similar, but for redshifts between 2 and 4, the systematic error dominates. In Figure 25 (b), we show the SCUBA-2 SFR density distribution functions computed for the same redshift intervals versus log SFR. Although the normalizations of the distribution functions are changing—they rise to reach a peak at before dropping at higher redshifts—the shapes over are remarkably similar; that is, the number density of high SFR galaxies relative to that of lower SFR galaxies is about the same in each redshift interval. However, at some point this similarity in shape must break down, as there cannot be large numbers of powerfully star-forming galaxies at very high redshifts. The present data show that this must occur at redshifts higher than . In Figure 26 , we show the SCUBA-2 distribution functions of Figure 25 (b) recomputed for the coarser redshift intervals , and 4–6 (colored circles; note that in the interval there are not enough sources to plot the two highest SFR bins). We compare these functions with those computed at lower SFRs from the extinction-corrected UV samples of Reddy Steidel ( 2009 ) and van der Burg et al. ( 2010 ) (small colored symbols and curves), assuming a Kennicutt ( 1998 ) conversion of UV luminosity to SFR for a Kroupa ( 2001 ) IMF. This emphasizes the disjoint nature of the SFRs of galaxies selected by UV and submillimeter observations (e.g., Barger et al. 2014 ): only submillimeter observations can find the most powerfully star-forming galaxies at redshifts . Both the UV and SCUBA-2 distribution functions have similar shapes in the interval. Thus, the number density of high SFR galaxies measured from the SCUBA-2 sample relative to that of lower SFR galaxies from UV-selected samples is about the same in this redshift interval. However, the