We have developed a numerical algorithm to model the future collisiona
l evolution of the low-orbiting Earth debris population, accounting fo
r both the wide spectrum of masses (or sizes) of the orbiting objects,
and their different altitudes, which result in a variable efficiency
of the drag-induced decay. The evolution process has been assumed to b
e caused by a number of source and sink mechanisms, such as launches,
explosions, atmospheric drag, and mutual collisions. The collisional o
utcomes have been described through a semiempirical model for the frag
ment mass distributions, consistent with the available experimental ev
idence. A runaway exponential growth of collision fragments is always
found in our model. Although its timing and pace are sensitive to some
poorly known parameters, fairly plausible parameter choices predict t
hat the runaway growth will occur within the next century, starting in
the crowded shells between 700 and 1000 km of altitude and, somewhat
later, between 1400 and 1500 km. The runaway growth is delayed until a
few centuries in the future only if the catastrophic breakup threshol
d,in specific impact energy for orbiting objects exceeds that for natu
ral rocky bodies by at least a factor of 10. Our simulations show that
the sensitivity of the results to future launch and/or deorbiting and
removal policies is rather weak, so that drastic measures will need t
o be taken soon in order to significantly avoid or delay a catastrophi
c outcome.