A method of deriving and using merging history trees of dark matter galaxy haloes directly from pure gravity N-body simulations is presented .
This combines the full non-linearity of N-body simulations with the flexibility of the semi-analytical approach .

Merging history trees derived from power-law initial perturbation spectrum simulations ( for indices n = -2 and n = 0 ) by [ Warren et al . ] ( 1992 ) are shown .
As an example of a galaxy formation model , these are combined with evolutionary stellar population synthesis , via simple scaling laws for star formation rates , showing that if most star formation occurs during merger-induced bursts , then a nearly flat faint-end slope of the galaxy luminosity function may be obtained in certain cases .

Interesting properties of hierarchical halo formation are noted : ( 1 ) In a given model , merger rates may vary widely between individual haloes , and typically 20 % \sim 30 % of a halo ’ s mass may be due to infall of uncollapsed material .
( 2 ) Small mass haloes continue to form at recent times : as expected , the existence of young , low redshift , low metallicity galaxies ( e.g. , [ Izotov et al . ] 1997 ) is consistent with hierarchical galaxy formation models .
( 3 ) For n = -2 , the halo spatial correlation function can have a very high initial bias due to the high power on large scales .