Looking over the literature, I find that some tests showed no beneficial effect and some tests showed mite reduction. It is interesting to note that in the second example, they attribute the reduction of varroa mites in hives on screens to the mites spending more time on the adults, not to mites falling through the screens. "This study focused on screen floors on hives, an *environmental condition* that affects percentage of mite population in brood cells." 

* * *

The test evaluating the benefits of extra top insulation [a layer of 25 lbs. (11.3 kg.) of dry oats above the hive] and of screened bottom boards did not show any clear colony survival advantage. The test did demonstrate that the screened bottom produced an increase in food consumption of about 20%, but that the additional insulation from the layer of oats did not significantly decrease food consumption. There was no significant effect of the type of bottom board or of the extra insulation on the final cluster volume of bees in April.

Overwintering of Russian honey bees in northeastern Iowa
José D. Villa, Thomas E. Rinderer and Manley Bigalk
Science of Bee Culture - Vol. 1, No. 2	21

* * *

Our objectives were to determine if screen floors could have a measurable effect on bees and varroa mites during a nine-week field test. We compared the effect of screen floors on honey consumption, brood production, the growth of bee populations, the growth of mite populations, and the distribution of a mite population within a colony (the number of mites in brood cells as compared to the number on adult bees). Our findings were consistent with earlier reports but also showed that colonies with open-screen floors had a lower percentage of their mite population in brood cells (P-MIB).

A lower P-MIB in hives with open-screen floors means that mites in those hives are remaining on adult bees for a longer time. In the combined data from both experiments (table 3), P-MIB averaged 57% for the open-screen floor and 74% for controls. This means that for the average varroa mite, the time span between leaving a brood cell and entering another cell (the time spent on adult bees) was 9.4 days in hives with an open-screen floor and 4.4 days in control hives.

Effect of screen floors on populations of honey bees and parasitic mites (Varroa destructor)
JOHN R HARBO AND JEFFREY W HARRIS
Journal of Apicultural Research 43(3): 114–117 (2004)

* * *

Yet in the final analysis, the consensus seems to be that bee breeding offers the most promise for mite reduction. Harbo again: 

"This study focused on screen floors on hives, an environmental condition that affects P-MIB. However, colony variation for P- MIB also has a strong heritable component in the honey bee. It is likely, therefore, that selective breeding of bees could reduce P-MIB."

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