We present a comparison of nine galaxy formation models , eight semi-analytical and one halo occupation distribution model , run on the same underlying cold dark matter simulation ( cosmological box of co-moving width 125 h ^ { -1 } { Mpc } , with a dark-matter particle mass of 1.24 \times 10 ^ { 9 } h ^ { -1 } { { M _ { \odot } } } ) and the same merger trees .
While their free parameters have been calibrated to the same observational data sets using two approaches , they nevertheless retain some ‘ memory ’ of any previous calibration that served as the starting point ( especially for the manually-tuned models ) .
For the first calibration , models reproduce the observed z = 0 galaxy stellar mass function ( SMF ) within 3 - \sigma .
The second calibration extended the observational data to include the z = 2 SMF alongside the z \sim 0 star formation rate function , cold gas mass and the black hole-bulge mass relation .
Encapsulating the observed evolution of the SMF from z = 2 to z = 0 is found to be very hard within the context of the physics currently included in the models .
We finally use our calibrated models to study the evolution of the stellar-to-halo mass ( SHM ) ratio .
For all models we find that the peak value of the SHM relation decreases with redshift .
However , the trends seen for the evolution of the peak position as well as the mean scatter in the SHM relation are rather weak and strongly model dependent .
Both the calibration data sets and model results are publicly available .