  The orbits of asteroids from the MPC catalogue of May 31, 2020 with absolute
magnitudes H < 16m, in the 3:1, 5:2 and 2:1 mean motion resonances (MMRs) with
Jupiter were selected. The number of the orbits in the 2:1 MMR is dozens times
greater than in the other two resonances.
  There are fragments of parent bodies of neighbour asteroid families, in
particular the Themis family, among bodies in the 2:1 MMR.
  Numerical calculations were performed to evaluate the evolution of the
selected orbits over hundreds of thousand years. Perturbations from all eight
major planets and the relativistic effects of orbital perihelion displacement
were taken into account. For all orbits in the 3:1 and 5:2 MMRs an increase in
the orbit eccentricities, which are sufficient for the bodies to approach Mars,
was obtained. In the 2:1 MMR, a sufficient increase in the orbit eccentricities
was not detected.
  An increase in orbit eccentricities in this resonance can occur due to the
action of non-gravitational effects (NGEs). The action of the Yarkovsky effect
can explain the exit of an asteroid with a size of 5 km from the 2:1 MMR over a
period about 1 billion years or more. More than 2 billion years ago, there were
dozens of bodies over 50 km in size in the 2:1 gap. To form the gap in the 2:1
resonance at the very beginning, the physical conditions in the asteroid belt
had to be significantly different from the today ones. In particular, the
intensity of the solar radiation in the early Solar system could be much higher
as compared to the today one.
