  Searches for Lyman-alpha emission lines are among the most effective ways to
identify high-redshift galaxies. They are particularly interesting because they
probe not only the galaxies themselves but also the ionization state of the
intergalactic medium (IGM). The observed line strengths depend on the amount by
which each photon is able to redshift away from line center before encountering
neutral gas and hence on the size distribution of HII regions surrounding the
sources. Here, we use an analytic model of that size distribution to study the
effects of reionization on the luminosity function of Lyman-alpha emitters and
their observed spatial distribution. Our model includes the clustering of
high-redshift galaxies and thus contains ionized bubbles much larger than those
expected around isolated galaxies. As a result, Lyman-alpha emitting galaxies
remain visible earlier in reionization: we expect the number counts to decline
by only a factor ~2 (or 10) when the mean ionized fraction falls to x_i~0.75
(or 0.5) in the simplest model. Moreover, the absorption is not uniform across
the sky: galaxies remain visible only if they sit inside large bubbles, which
become increasingly rare as x_i decreases. Thus, the size distribution also
affects the apparent clustering of Lyman-alpha selected galaxies. On large
scales, it traces that of the large bubbles, which in our model are more biased
than the galaxies. On small scales, the clustering increases rapidly as x_i
decreases because large HII regions surround strong galaxy overdensities, so a
survey automatically selects only those galaxies with neighbours. The
transition between these two regimes occurs at the characteristic bubble size.
Hence, large Lyman-alpha galaxy surveys have the potential to measure directly
the size distribution of HII regions during reionization.
