And the numbers given assume mites never die off, not have multiple
generations of offspring. Evan at the lower reproduction rates, the # of
mites can increase explosively (if not quite exponentially).  Here is a
simple spreadsheet, based upon different reproduction rates (# viable
females per generation) which assumes each mite reproduces three times
(seems to be a good average).  Sorry about the formatting on the larger #'s.
As you can see, at the lower rate of 1.3, mites still get large (greater
than # of bees) populations after say 18 generations - but this is most of
the reproduction year at 12 days per generation (216 days). With perfect
reproduction of 3 mites per cell, the same levels are exceeded in 10
generations - only 120 days.

 Generation     Reproduction Rate
                 1.30    1.60    2.00    2.50    3.00
 1.00    1.00    1.00    1.00    1.00    1.00
 2.00    2.30    2.60    3.00    3.50    4.00
 3.00    5.29    6.76    9.00    12.25   16.00
 4.00    9.87    14.98   24.00   39.38   60.00
 5.00    19.70   34.78   66.00   129.06          228.00
 6.00    38.44   79.61   180.00          421.09          864.00
 7.00    77.89   185.61          495.00          1,378.89        3,280.00
 8.00    156.52          431.11          1,359.00        4,512.21        12,448.00
 9.00    316.90          1,004.33        3,735.00        14,770.63       47,248.00
 10.00   638.15          2,335.65        10,260.00       48,344.91       179,328.00
 11.00   1,286.89        5,434.40        28,188.00       158,240.57      680,640.00
 12.00   2,590.97        12,639.05       77,436.00       517,937.54      2,583,360.00
 13.00   5,220.36        29,400.11       212,733.00      1,695,271.39    9,805,120.00
 14.00   10,514.73       68,383.53       584,415.00      5,548,815.05    37,215,232.00
 15.00   21,184.50       159,065.09      1,605,501.00    18,161,913.29
141,250,048.00
 16.00   42,676.74       369,990.49      4,410,612.00    59,446,028.03
536,113,152.00
 17.00   85,979.46       860,618.37      12,116,790.00   194,573,695.28
2,034,812,160.00
 18.00   173,212.28      2,001,835.70    33,287,112.00   636,862,089.66
7,723,109,376.00
 19.00   348,956.09      4,656,366.78    91,446,003.00   2,084,522,912.21
29,312,985,088.00

-----Original Message-----
From: Blane White

Hold on there Jim, take a look at the published research on varroa
reproduction.  The real numbers are considerably less than 3 daughter mites
per mother per brood cycle.  The most published numbers are in the 1.6 - 1.3
range which frankly is a pretty low reproductive rate for a mite.  Now the
varroa generation time is the length of a capped brood cycle or about 10 to
12 days ...