Relation between b and the metallicity derived from the empirical FMR relationship of Mannucci et al. (2010). The vertical error bars correspond to the statistical uncertainty on the number of LGRBs. The horizontal error bar attached to each symbol corresponds to the width of the bin used at the beginning of the method. The horizontal bar in the bottom-left part of the figure indicates a systematic uncertainty on abundance measurements of a typical factor 2. The top panel shows the results based on the SFR distribution function, and the bottom panels the results based on the stellar mass functions. Finally, the curve indicates the fraction of SN Ic-WO supernovae (with which LGRBs could be associated), according to the models of Georgy et al. (2009).