Semi-analytic models take the dark matter cosmological simulations and "add-in" gas physics using simple prescriptive formulae, such as how star formation depends on gas density, or how black-hole feedback removes gas. In all, about 10 gas-physics functions are used.
The figures show 4 stages in a dark matter calculation. The semi-analytic treatment determines where galaxies form and what their properties are. The colored dots show the location of galaxies, with bluer for higher star formation rates and younger populations.
These methods are able to reproduce many of the observed demographic features of the galaxian population.
The semi-analytic models are able to generate a galaxy mass (luminosity) function that matches quite closely the observed one. This is encouraging, though don't forget many of the free-parameters in the semi-analytic treatment are adjusted to optimize this fit.