  With the advent of wide-area submillimeter surveys, a large number of
high-redshift gravitationally lensed dusty star-forming galaxies (DSFGs) has
been revealed. Due to the simplicity of the selection criteria for candidate
lensed sources in such surveys, identified as those with $S_{500\mu m} > 100$
mJy, uncertainties associated with the modelling of the selection function are
expunged. The combination of these attributes makes submillimeter surveys ideal
for the study of strong lens statistics. We carried out a pilot study of the
lensing statistics of submillimetre-selected sources by making observations
with the Atacama Large Millimetre Array (ALMA) of a sample of strongly-lensed
sources selected from surveys carried out with the Herschel Space Observatory.
We attempted to reproduce the distribution of image separations for the lensed
sources using a halo mass function taken from a numerical simulation which
contains both dark matter and baryons. We used three different density
distributions, one based on analytical fits to the halos formed in the EAGLE
simulation and two density distributions (Singular Isothermal Sphere (SIS) and
SISSA) that have been used before in lensing studies. We found that we could
reproduce the observed distribution with all three density distributions, as
long as we imposed an upper mass transition of $\sim$$10^{13} M_{\odot}$ for
the SIS and SISSA models, above which we assumed that the density distribution
could be represented by an NFW profile. We show that we would need a sample of
$\sim$500 lensed sources to distinguish between the density distributions,
which is practical given the predicted number of lensed sources in the Herschel
surveys.
