  Motivated by recent observations of the star formation rate density function
out to z~7, we describe a simple model for the star formation rate density
function at high redshift based on the extended Press-Schechter formalism. This
model postulates a starburst following each major merger, lasting for a time
t_SF and converting at most f_star of galactic gas into stars. We include a
simple physical prescription for supernovae feedback that suppresses star
formation in low mass galaxies. Constraining t_SF and f_star to describe the
observed star formation rate density at high redshifts, we find that individual
starbursts were terminated after a time t_SF~10^7 years. This is comparable to
the main-sequence lifetimes of supernova progenitors, indicating that high
redshift starbursts are quenched once supernovae feedback had time to develop.
High redshift galaxies convert ~10% of their mass into stars for galaxies with
star formation rates above ~1 solar mass per year, but a smaller fraction for
lower luminosity galaxies. Our best fit model successfully predicts the
observed relation between star formation rate and stellar mass at z>~4, while
our deduced relation between stellar mass and halo mass is also consistent with
data on the dwarf satellites of the Milky Way. We find that supernovae feedback
lowers the efficiency of star formation in the lowest mass galaxies and makes
their contribution to reionization small. As a result, photo-ionization
feedback on low mass galaxy formation does not significantly affect the
reionization history. Using a semi-analytic model for the reionization history,
we infer that approximately half of the ionizing photons needed to complete
reionization have already been observed in star-forming galaxies.
