different galaxy and halo samples we utilize. Finally, we describe the techniques used to characterise the galaxy and halo samples.

The semi-analytic model {#Sec:Sam}
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Semi-analytical modelling (SAMs) is one of the main tools used to study galaxy formation (see @Baugh:2006 [@Lacey:2016] for reviews). These models aim to follow the main physical processes involved in the formation and evolution of galaxies. Some of the processes modelled by the SAM are (i) the collapse and merging of dark matter haloes (ii) shock heating and radiative cooling of gas (iii) star formation (iv) supernovae, AGN, and photoionization feedback (v) chemical enrichment of gas and stars (vi) disc instabilities and (vii) galaxy mergers.

The SAM used here is that of Guo et al. (2013; hereafter G13). This model is a version of [L-GALAXIES]{} the SAM code developed by the Munich group [@DeLucia:2004; @Croton:2006; @DeLucia:2007; @Bertone:2007; @Guo:2011; @Henriques:2013; @Henriques:2015]. For an extended description of this model and its performance we refer the reader to Guo et al. (2013, see also @Guo:2016b and @C17). The outputs are publicly available from the Millennium Archive[^1]. G13 is the latest publicly available SAM of the Munich group that makes use of the Millennium-WMAP7 dark matter simulation. We will 