> If you have a mesh floor you go to the colony from  the back side
 
Hmmm.  We have four hives on a pallet, so there is a problem with back
access.  Side access also would be a problem in that some hives have the
left available, and some the right.
 
Moreover, we have also spent a lot of money building the floors we
currently use.
 
>  I found a diagram of Imhoff et al about the natural mite fall in
> October over the varroa population in a colony (test of 90 colonies).
> With 1 mite per day the average was 500 mites in the colony, but the
> minimum was 200 and the maximum 1000.
 
Hmmm.  Again.  There are several factors here, and I guess we don't get to
see all the mites that fall, but that seems odd to me. When it appears a
large percentage are not recovered on the floor.
 
I forget how long a mother mite lives, but assume 50 days and that the
mites are evenly distributed as to age at any given time.  In that case,
with a stable mite population, we would expect to see one mite drop every
fifty days for each mite living in the hive.
 
Thus -- if we saw every mite that dropped dead -- we would deduce that 1
mite falling per 24 hours meant 50 mites living in the hive.  This is very
crude, but, I think the logic is there. Extending this, then 10 mites
would mean a population of 500 mites, etc.
 
Now we have a formula:
 
Drop=Population/Lifespan
 
We can refine this further to
 
Observed Drop = Recovering Eficiency X Drop
 
And then Population = Drop X Lifespan / Recovering Efficiency
 
This neglects changes in mite populations over the lifespan of one mite,
and probably several other minor (I think) factors.  And I am just
guessing here at typical mite lifespan.
 
Now, this brings into question the efficiency of recovery.  From empirical
data given we see that 1 mite/day observed using whatever means they used
(I'm assuming a sticky board about big enough to occupy the entire floor
area) means a 500 mite population.  Using my number from above, we see
that means we did not see 90% of the dropping mites.  They escaped our
sticky board.
 
Interesting.
 
If we reduce the area of our board to 1/4 of the hive floor size and
centre it, then we will miss up to 97.5% of the mites dropping instead of
90%, assuming that the mites are evenly distributed over the cross-section
of the hive (which they are not).
 
Nonetheless, over a number of hives, one quarter of the floor area should
be an adequate test for whether to treat the yard or not if the clusters
are reasonably strong and centred.
 
Shouldn't it?
 
Allen