Stellar mass–stellar metallicity relation of mock galaxies from VANDELS cones, performed to reproduce the same sky area and redshift range targeted by our survey. The whole galaxy population is color-coded in two bins of local galaxy density, similarly to Fig. 4 top, and according to the overdensity flag and protocluster membership (second and third panels), assuming a radius of 15 cMpc. The theoretical MZR have been offset by −0.4 dex to match the observed global MZR normalization. The vertical error bars of the models represent the error on the median metallicity estimation in each bin.