following cosmology throughout this paper: $H_0$ = 100 $h~\textrm{km}~s^{-1}~\textrm{Mpc}^{-1}$, $\Omega_\textrm{m}$= 0.3, and $\Omega_{\Lambda}$ = 0.7. We adopt the Hubble constant $h$ = 0.7 when calculating rest-frame magnitudes. We use a Salpeter initial mass function (IMF) when deriving stellar masses and SFRs. All magnitudes are given in the AB system.

Data
====

The galaxy and group sample analyzed in this work are the same as was used in [@lin14] with an $i$-band selection cut, $i$ $<$ 24.0. We briefly describe the data here. The detailed description of the galaxy sample can be found in S. Foucaud et al. (2017, in preparation) and in [@lin14], and for that of the group/cluster sample is described in [@jian14].

Galaxy Sample
-------------

Our galaxy sample is based on images and photometry from the Pan-STARRS1 [PS1; @kai10] Medium-Deep (MD) Field survey with ${{\ensuremath{g_{\rm P1}}}{\ensuremath{r_{\rm P1}}}{\ensuremath{i_{\rm P1}}}{\ensuremath{z_{\rm P1}}}{\ensuremath{y_{\rm P1}}}}$ filters [@stu10; @ton12] plus the Canada$-$France$-$Hawaii$-$Telescope (CFHT) MEGACAM $u^*$ band from archival data from a program lead by Eugene Magnier as part of the PS1 efforts to produce deep stacks in six bands and associated catalogs. Data taken in two PS1 MD fields, MD04 and MD07, are adopted for use (S. Foucaud et al. 2017, in preparation).

With 