  In this work, we investigate the evolution of a primordial belt of asteroids,
represented by a large number of massless test particles, under the
gravitational effect of migrating Jovian planets in the framework of the
jumping-Jupiter model. We perform several simulations considering test
particles distributed in the Main Belt, as well as in the Hilda and Trojan
groups. The simulations start with Jupiter and Saturn locked in the mutual 3:2
mean motion resonance plus 3 Neptune-mass planets in a compact orbital
configuration. Mutual planetary interactions during migration led one of the
Neptunes to be ejected in less than 10 Myr of evolution, causing Jupiter to
jump by about 0.3 au in semi-major axis. This introduces a large scale
instability in the studied populations of small bodies. After the migration
phase, the simulations are extended over 4 Gyr, and we compare the final
orbital structure of the simulated test particles to the current Main Belt of
asteroids with absolute magnitude $H<9.7$. The results indicate that, in order
to reproduce the present Main Belt, the primordial belt should have had a
distribution peaked at $\sim10^{\circ}$ in inclination and at $\sim0.1$ in
eccentricity. We discuss the implications of this for the Grand Tack model. The
results also indicate that neither primordial Hildas, nor Trojans, survive the
instability, confirming the idea that such populations must have been implanted
from other sources. In particular, we address the possibility of implantation
of Hildas and Trojans from the Main Belt population, but find that this
contribution should be minor.
