Mass–gas phase metallicity and fundamental metallicity relations: Left: MZR relation for M0416 cluster members and field galaxies using the O3N2 metallicity calibration of Kewley et al. (2013). The symbols are the same as in Fig. 4 and in addition, we also show the M0416 cluster sample from Maier et al. (2016), observed with VLT/VIMOS, as light grey crosses. The black points and curves represent the local SDSS relation from the latter authors, consistently derived using the O3N2 calibration, with its 1σ scatter. The MZR for the SDSS sample was extrapolated down to lower masses of log(M/M_⊙) = 8, by assuming that the slope remains constant for log(M/M_⊙) < 9.2. The cross in the lower right corner shows the mean value of the measurement errors. Right: difference between the measured (O/H)s for M0416 cluster and field galaxies, using the O3N2 metallicity calibration and the expected (O/H)s from the formulations of Lilly et al. (2013) for different infall metallicities Z₀, relative to the yield, y, as a function of the stellar mass of the systems. The models assuming a primordial metallicity for the inflowing gas, Z₀/y = 0, are depicted by the bright data points, whereas the models assuming a metal-enriched gas inflow, Z₀/y = 0.1, are depicted by the faint data points. The symbols are the same as in the plot from the left-hand side.