An Empirical Study of the Relationship between Ly{\alpha} and UV
  selected Galaxies: Do Theorists and Observers `Select' the Same Objects?
  Lyman Alpha Emitters (LAEs) are galaxies that have been selected on the basis
of a strong Ly{\alpha} emission line in their spectra. Observational campaigns
have dramatically increased the sample of known LAEs, which now extends out to
z=7. These discoveries have motivated numerous theoretical studies on the
subject, which usually define LAEs in their models based on sharp Ly{\alpha}
luminosity and equivalent width (EW) cuts. While broadly representative, this
procedure does not mimic the selection from observational programs in detail,
which instead use cuts in various colour-spaces. We investigate what
implications this disjoint may have for studies that aim to model LAEs. We
construct an empirical model for the number density of star forming galaxies as
a function of their UV and Ly{\alpha} luminosity, utilising measured
constraints on the luminosity functions (LFs) of drop-out galaxies, and their
luminosity dependent probability distribution function of Ly{\alpha} EW. In
particular, we investigate whether the LAE LFs can be reproduced by defining
LAEs using a (z-dependent) Ly{\alpha} luminosity and EW threshold. While we are
able to reproduce the observed distribution of Ly{\alpha} EW among LAEs out to
restframe EW 200 A, we find that our formalism over-predicts both the UV and
Ly{\alpha} LFs of LAEs by a factor of 2-3, and is inconsistent with
observations at the ~95% level. This tension is partially resolved if we assume
the Ly{\alpha} EW-distribution of drop-out galaxies to be truncated at
restframe EW>150 A. However the overprediction indicates that modeling LAEs
with simple REW and luminosity cuts does not accurately mimic observed
selection criteria, and can lead to uncertainties in the predicted number
density of LAEs. On the other hand, the predicted z-evolution is not affected.
We apply our formalism to drop-out galaxies at z>6, and predict the LFs of LAEs
at z=7-9.
