  We use the redshift evolution of the lyman-alpha forest mean transmitted flux
at z>2.5 to infer the evolution of the intensity of the ionizing background,
using theoretical predictions for the density distribution of the intergalactic
gas giving rise to the lyman-alpha forest. The proper background intensity
declines gradually with redshift, decreasing by a factor \sim 3 between z=3 and
z=5.
  The gravitational structure formation theory of the lyman-alpha forest
implies that, given the observed mean transmitted flux of \bar{F}=0.1 in the
highest redshift quasar (with a mean lyman-alpha forest redshift z=5.2), only
about 3% of the lyman-alpha spectrum should have a flux higher than 50% of the
continuum, and less than 0.5% of pixels should have flux above 75% of the
continuum, assuming a uniform ionizing background intensity. We show that this
is consistent with the spectrum shown in Fan et al.
