We were interested in the time dependence of dispersion rates for the families we worked with.    Assumed that the standard deviation of changes in a was the following function of tiime:

we wanted to find how B changed with time.  Nesvorny' et al. (2001) found for its integration of 120 My of 300 asteroid a value of B of 0.63 (0.68 for asteroids with a > 2.5 AU, probably due to higher frequency  and lower mutual velocity of encounters with 1 Ceres).    The effect of close encounters did vary slower than linearly but faster than t^0.5(random walk).    The consequence  of close encounters is not necessarily a random walk, due to the possibility of encounters with repeated geometry, asymmetries in the perturbations, and lower mutual velocity for asteroids with orbital elements (inclination in particular) close to 1 Ceres.   Since the dispersion rates vary in different regions of the Main Belt, it is important to know how the value of B changes with asteroid location and time.   In the following figures we report the time evolution of B for the simulations involving close encounters. B was computed by a least square fit every 50 My.
 
 

For real members of Adeona B drops from an initial value of 0.71 to a minimum of 0.574 at t=150 My, and then slowly increases to ~0.63.   For members of the synthetic family B drops from its initial value of 0.71
to a minimum of 0.48 (less than a random walk) at the end of the simulation.
 
 

For members of the Gefion family, B oscillates 0.72,  while for the synthetic family  B decreases to a final value of 0.58.   Except for the integration with real members of Adeona, B is usually decreasing with time.