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]
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