Total radio LFs at different cosmic epochs. Black points show LFs derived using the V_max method (see Sect. 3.1). The blue and red shaded areas show the ± 3σ ranges of the best-fit evolution for the individual SF and AGN populations, respectively (outlined in Sect. 3.2). The black line is the fit to the total radio LF, as explained in Sect. 3.3. Other models used are indicated in the legend. In all of these models we assume the local (z ≈ 0) LFs from the respective papers and fit for the PLE parameters as in Eq. (5). The only exception is model 4, where the shape of the faint slope of the SF LF changes with redshift. The vertical gray shaded area shows the luminosity decade that contributes to the radio source counts between 1 and 10 μJy.