  Recently, the gravitational instability (GI) model of giant planet and brown
dwarf formation has been revisited and recast into what is often referred to as
the "tidal downsizing" hypothesis. The fragmentation of self-gravitating
protostellar discs into gravitationally bound embryos - with masses of a few to
tens of Jupiter masses, at semi major axes above 30 - 40 au - is followed by
grain sedimentation inside the embryo, radial migration towards the central
star and tidal disruption of the embryo's upper layers. The properties of the
resultant object depends sensitively on the timescales upon which each process
occurs. Therefore, GI followed by tidal downsizing can theoretically produce
objects spanning a large mass range, from terrestrial planets to giant planets
and brown dwarfs. Whether such objects can be formed in practice, and what
proportions of the observed population they would represent, requires a more
involved statistical analysis.
  We present a simple population synthesis model of star and planet formation
via GI and tidal downsizing. We couple a semi-analytic model of protostellar
disc evolution to analytic calculations of fragmentation, initial embryo mass,
grain growth and sedimentation, embryo migration and tidal disruption. While
there are key pieces of physics yet to be incorporated, it represents a first
step towards a mature statistical model of GI and tidal downsizing as a mode of
star and planet formation.
  We show results from four runs of the population synthesis model, varying the
opacity law and the strength of migration, as well as investigating the effect
of disc truncation during the fragmentation process. Our early results suggest
that GI plus tidal downsizing is not the principal mode of planet formation,
but remains an excellent means of forming gas giant planets, brown dwarfs and
low mass stars at large semimajor axes. (Abridged)
