Asteroid families represent the outcomes of major collisional events in the
asteroid Main Belt. These events produced in some cases huge numbers of fr
agments, down to sizes of at least I km in diameter. In this paper we show
that these families produce a significant increase in the "local" collision
rate by as much as an order of magnitude relative to the average collision
rate of the entire Belt. This fact should be taken into account in future
studies of the collisional evolution of the Main Belt. (C) 2001 Academic Pr
ess.