Schematic representation of the selection procedure and tracking of progenitor halos. The selection criteria were applied only once at the ɀ_ref = 0.56, resulting in the S1 and S2 from the entire population of CMASS mock galaxies catalogue. The progenitors of these samples are then identified at the subsequent simulation snapshot using their unique identification number, resulting in the progenitor sub-samples Sla corresponding to S1-sample and S2a to S2-sample. This step is repeated and we subsequently move towards higher redshifts (S1x and S2x). This process is repeated as we progress to higher redshifts, generating S1x and S2x. This approach represents the conventional method for extracting information on the redshift evolution of galaxies in simulations.