"This leaves me with some questions regarding screened bottom boards
and IPM for varroa.  Basically, should I use them with a closed
bottom board, or should my only bottom board be the screened one?"

I have used Screened Bottom Boards for two years now. The version I use is
from BetterBee and has a screen over an open drawer arrangement. Within this
open drawer area goes a monitoring tray (cafeteria tray). The idea is that
you have a built in, reusable and easily monitored catch-all for anything
small enough to fall through the mesh floor. The tray is pulled out from the
back of the hive which does not interrupt the front entrance nor the bees
above the floor. I like this arrangement better than sticky boards because
the tray is always in place, I can check on its contents anytime and I do
not have to fool around with the front entrance to retrieve it. I do monitor
mite thresholds this way and after each reading I simply scrape or brush off
the dead mites and any other debris. The separation between the mesh and the
tray prevents any bees from coming into contact with the fallen mites and
the mites die when separated from their food source. Also, you mentioned new
data showing hive temperatures affecting mite densities, while I have not
seen this actual study, if this is the case, the Betterbee Varroa Screen
arrangement does allow you to minimize the bottom board inside area to the
outside ambient temperature. The tray fits in tightly enough to essentially
close off the drawer to the outside. Additionally, if added ventilation is
desired in the summer, the tray can be removed or pulled out slightly to
provide free air movement. By the way, I firmly believe and practice OMF's
as only a part of my IPM strategy.

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Ken Haller
Viking Honey Farm
Arlington Heights, Illinois USA
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AIM Screen Name: kenhaller