  The large cross-section of the Lyman alpha (Lya) line makes it a sensitive
probe of the ionization state of the intergalactic medium (IGM). Here we
present the most complete study to date of the IGM Lya opacity, and its
application to the redshift evolution of the 'Lya fraction', i.e. the fraction
of color-selected galaxies with a detectable Lya emission line. We use a tiered
approach, which combines large-scale semi-numeric simulations of reionization
with moderate-scale hydrodynamic simulations of the ionized IGM. This allows us
to simultaneously account for evolution in both: (i) the opacity from an
incomplete (patchy) reionization, parameterized by the filling factor of
ionized regions, Q_HII; and (ii) the opacity from self-shielded systems in the
ionized IGM, parameterized by the average photo-ionization rate inside HII
regions, \Gamma. In contrast to recent empirical models, attenuation from
patchy reionization has a unimodal distribution along different sightlines,
while attenuation from self-shielded systems is more bimodal. We quantify the
average IGM transmission in our (Q_HII, \Gamma) parameter space, which can
easily be used to interpret new data sets. Using current observations, we
predict that the Lya fraction cannot drop by more than a factor of ~2 with IGM
attenuation alone, even for HII filling factors as low as Q_HII>0.1. Larger
changes in the Lya fraction could result from a co-evolution with galaxy
properties. Marginalizing over \Gamma, we find that current observations
constrain Q_HII < 0.6 at z=7 [68% confidence level (C.L.)]. However, all of our
parameter space is consistent with observations at 95% C.L., highlighting the
need for larger observational samples at z >= 6.
