important to take the halo mass growth of the clusters into account when the stellar mass growth of BCGs is investigated, to ensure that that BCGs at high redshifts are compared to their likely descendants at lower redshifts. This idea has already been explored by other works in the literature [@Lidman2012; @Lin2013; @Oliva-Altamirano2014; @Zhang2016]. In our work we use an approach similar to that implemented by [@Lidman2012] to construct an evolutionary cluster sequence using evolving $M_{h}$ limits. We assume that the BCGs in this evolutionary sequence are progenitors/descendants of one another to derive the merger-inferred mass growth of the BCGs.

Briefly, we construct an evolutionary cluster sequence by identifying the low redshift descendants of the redMaPPer clusters in our highest redshift bin $(z=0.35)$. This is done by evolving the $M_{h}$ of these clusters forward in time using the mean mass accretion rates (MMAR) from the [-@Fakhouri2010] model (see their equation 2). Through these MMARs we are able to determine what the corresponding halo masses of these high redshift clusters will be at later times, allowing us to construct an evolving $M_{h}$ limit as a function of redshift. We divide the clusters into four equal sized redshift bins with a width 