  We simulated the long-term collisional depletion of debris disks around
solar-type (G2V) stars with our code. The numerical results were supplemented
by, and interpreted through, a new analytic model. A few general scaling rules
for the disk evolution are suggested. The timescale of the collisional
evolution is inversely proportional to the initial disk mass and scales with
radial distance as r^4.3 and with eccentricities of planetesimals as e^-2.3.
Further, we show that at actual ages of debris disks between 10 Myr and 10 Gyr,
the decay of the dust mass and the total disk mass follow different laws. The
reason is that the collisional lifetime of planetesimals is size-dependent. At
any moment, there exists a transitional size, which separates larger objects
that still have the ``primordial'' size distribution set in the growth phase
from small objects whose size distribution is already set by disruptive
collisions. The dust mass and its decay rate evolve as that transition affects
objects of ever-larger sizes. Under standard assumptions, the dust mass,
fractional luminosity, and thermal fluxes all decrease as t^xi with xi =
-0.3...-0.4. Specific decay laws of the total disk mass and the dust mass,
including the value of xi, largely depend on a few model parameters, such as
the critical fragmentation energy as a function of size, the primordial size
distribution of largest planetesimals, as well as the characteristic
eccentricity and inclination of their orbits. With standard material
prescriptions and a distribution of disk masses and extents, a synthetic
population of disks generated with our analytic model agrees quite well with
the observed Spitzer/MIPS statistics of 24 and 70 micron fluxes and colors
versus age.
