I'm happy to address some excellent questions, and glad to see that some
are checking my math...

>A 20 day gap in egg-laying does not directly lead to a 20 day gap in mite
reproduction.

Yes Mike, you over complicated it : )  Wagnitz created a 20-day break
during which no eggs were laid.  What that leads to (beginning 8 days
later) is a 20-day gap during which no mites are able to enter cells in
order to reproduce.  Thus, equivalent to a 20-day gap in mite
reproduction.  The overlaps that you detailed do not affect the
calculation.  Without invasion into cells for reproduction, then only the
negative r for mite mortality applies.

>Randy, is "e" in this equation a factor you used for the rate of emerging
brood, or is it something else?

"e" is the natural logarithm.  It is used in biology to calculate growth
rates from instantaneous rate of change.  e raised to the power of r x t
(rate of change x number of relative units of time) gives you the
percentage increase over that period of time.  I'm no mathematician, but
after practicing enough, I'm now pretty comfortable calculating values of r
from data, and then applying it to model varroa growth.  I find that it is
a very informative tool!

>What happens if you remove the first brood to be sealed after the brood
break?

This same question occurred to me last night. Trapping of mites by offering
them only a single frame containing brood of the appropriate age for
invasion (8 days post egglaying for worker brood) is a well-documented
effective method for varroa management.

*A Simple Method for Treatment-Free Mite Management*

What occurred to me would be a very simple technique for mite control that
could be used by the recreational beekeeper who didn't want to use
treatments.  He/she could build a frame holder from queen excluder material
(we commonly use these in commercial queen production), and instead of
removing the queen, simply place her in the excluder cage with a frame of
drawn comb,

Then allow her to continue to lay eggs for 12 days, at which point release
her back into the hive.  No reason to keep her confined longer, since after
12 days, any eggs that she laid wouldn't be able to develop far enough by
20 days for varroa to invade.

Back to her confinement.  After 8 days of her confinement, there would be
no worker brood outside of her cage that were of the age window for varroa
invasion, so any invading mites would get sealed into the brood *within the
cage*.  This would continue for another 12 days.  8 +12 = 20.  At 20 days,
worker brood in the cage would begin to emerge.  So remove the trap frame
at that time (20 days after first caging, 12 days after her release). * It
would contain all varroa that invaded brood for that 12-day period.*

Thus, you'd not only have created a 12-day brood break, but you would also
have trapped a large proportion of the mites in the colony.  Repeat a
couple of times a season--perhaps no other treatments necessary.

Anyone on the List with a number of hives at their disposal who wants to
work with me to collect data on the efficacy of the method?  Email me if
you're serious, and I'll write up a protocol.
---

The other thing that occurred to me last night is the huge value of
mite-grooming behavior.  Previous studies found that during the winter
brood break, about a half of 1% of mites are lost per day.  If, by
selecting for bees that were better groomers, we might be able to double or
triple that rate--which would greatly decrease the mite population in the
hive during any brood break.


-- 
Randy Oliver
Grass Valley, CA
www.ScientificBeekeeping.com

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