  Absorption spectra of high redshift quasars exhibit an increasingly thick
Ly-alpha forest towards z~6. However, the interpretation of these spectra is
complicated by the fact that the Ly-alpha optical depth is already large for
neutral hydrogen fractions in excess of 10^-4, and also because quasars are
expected to reside in dense regions of the IGM. We present a model for the
evolution of the ionization state of the IGM which is applicable to the dense,
biased regions around high-redshift quasars as well as more typical regions in
the IGM, and combine this with numerical radiative transfer simulations. Our
model is able to simultaneously reproduce the observed Ly-alpha forest opacity
at 4<z<6, the ionizing photon mean-free-path at z~4 and the rapid evolution of
highly ionized near-zone sizes around high-redshift quasars at 5.8<z<6.4. We
find that within 5 physical Mpc of a high redshift quasar, the evolution of the
ionization state of the IGM precedes that in more typical regions by around 0.3
redshift units. More importantly, when combined with the rapid increase in the
ionizing photon mean-free-path expected shortly after overlap, this offset
results in an ionizing background near the quasar which exceeds the value in
the rest of the IGM by a factor of ~2-3. We further find that in the
post-overlap phase of reionization the size of the observed quasar near-zones
is not directly sensitive to the neutral hydrogen fraction of the IGM. Instead,
these sizes probe the level of the background ionization rate and the
temperature of the surrounding IGM. The observed rapid evolution of the quasar
near-zone sizes at 5.8<z<6.4 can thus be explained by the rapid evolution of
the ionizing background, which in our model is caused by the completion of
overlap at the end of reionization by 6<z<7.
