  In the MW bulge, metal-rich stars form a strong bar and are more
peanut-shaped than metal-poor stars. It has been recently claimed that this
behavior is driven by the initial in-plane radial velocity dispersion of these
populations, rather than by their initial vertical random motions. This has led
to the suggestion that a thick disc is not necessary to explain the
characteristics of the MW bulge. We rediscuss this issue by analyzing two
dissipationless N-body simulations of boxy/peanut (b/p)-shaped bulges formed
from composite stellar discs, made of kinematically cold and hot stellar
populations, and we conclude that initial vertical random motions are as
important as in-plane random motions in determining the relative contribution
of cold and hot disc populations with height above the plane, the metallicity
and age trends. Previous statements emphasizing the dominant role of in-plane
motions in determining these trends are not confirmed. However, differences
exist in the morphology and strength of the resulting b/p-shaped bulges: a
model where disc populations have initially only different in-plane random
motions, but similar thickness, results into a b/p bulge where all populations
have a similar peanut shape, independently on their initial kinematics, or
metallicity. We discuss the reasons behind these differences, and also predict
the signatures that these two extreme initial conditions would leave on the
vertical age and metallicity gradients of disc stars, outside the bulge region.
We conclude that a metal-poor, kinematically (radial and vertical) hot
component, that is a thick disc, is necessary in the MW before bar formation,
supporting the scenario traced in previous works. [abridged]
