  We present an analysis of the predictions made by the Galform semi-analytic galaxy formation model for the evolution of the relationship between stellar mass and halo mass. We show that for the standard implementations of supernova feedback and gas reincorporation used in semi-analytic models, this relationship is predicted to evolve weakly over the redshift range 0<z<4. Modest evolution in the median stellar mass versus halo mass (SHM) relationship implicitly requires that, at fixed halo mass, the efficiency of stellar mass assembly must be almost constant with cosmic time. We show that in our model, this behaviour can be understood in simple terms as a result of a constant efficiency of gas reincorporation, and an efficiency of SNe feedback that is, on average, constant at fixed halo mass. We present a simple explanation of how feedback from active galactic nuclei (AGN) acts in our model to introduce a break in the SHM relation whose location is predicted to evolve only modestly. Finally, we show that if modifications are introduced into the model such that, for example, the gas reincorporation efficiency is no longer constant, the median SHM relation is predicted to evolve significantly over 0<z<4. Specifically, we consider modifications that allow the model to better reproduce either the evolution of the stellar mass function or the evolution of average star formation rates inferred from observations. 
The evolution of the stellar mass versus halo mass relationship