  We describe a methodology to accurately compute halo mass functions,
progenitor mass functions, merger rates and merger trees in non-cold dark
matter universes using a self-consistent treatment of the generalized extended
Press-Schechter formalism. Our approach permits rapid exploration of the
subhalo population of galactic halos in dark matter models with a variety of
different particle properties or universes with rolling, truncated, or more
complicated power spectra. We make detailed comparisons of analytically derived
mass functions and merger histories with recent warm dark matter cosmological
N-body simulations, and find excellent agreement. We show that, once the
accretion of smoothly distributed matter is accounted for, coarse-grained
statistics such as the mass accretion history of halos can be almost
indistinguishable between cold and warm dark matter cases. However, the halo
mass function and progenitor mass functions differ significantly, with the warm
dark matter cases being strongly suppressed below the free-streaming scale of
the dark matter. We demonstrate the importance of using the correct solution
for the excursion set barrier first-crossing distribution in warm dark matter -
if the solution for a flat barrier is used instead the truncation of the halo
mass function is much slower, leading to an overestimate of the number of low
mass halos.
