  The effects of galaxy selection on our ability to constrain the nature of
weak Ly\alpha absorbers at low redshift are explored. Current observations
indicate the existence of a population of gas-rich, low surface brightness
(LSB) galaxies, and these galaxies may have large cross sections for Ly\alpha
absorption. Absorption arising in LSB galaxies may be attributed to HSB
galaxies at larger impact parameters from quasar lines of sight, so that the
observed absorption cross sections of galaxies may seem unreasonably large.
Thus it is not possible to rule out scenarios where LSB galaxies make
substantial contributions to Ly\alpha absorption using direct observations.
Less direct tests, where observational selection effects are taken into account
using simulations, should make it possible to determine the nature of Ly\alpha
absorbers by observing a sample of ~100 galaxies around quasar lines of sight
with well-defined selection criteria. Such tests, which involve comparing
simulated and observed plots of the unidentified absorber fractions and
absorbing galaxy fractions versus impact parameter, can distinguish between
scenarios where absorbers arise in particular galaxies and those where
absorbers arise in gas tracing the large scale galaxy distribution. Care must
be taken to minimize selection effects even when using these tests. Results
from such tests are likely to depend upon the limiting neutral hydrogen column
density. While not enough data are currently available to make a strong
conclusion about the nature of moderately weak absorbers, evidence is seen that
such absorbers arise in gas that is around or between galaxies that are often
not detected in surveys.
