From my understanding of insect evolution in insects, it's a *slow*
process.  Researchers specifically use *Drosophila melanogaster *to study
evolution.  After many hundreds, to many thousands of generations, a trait
such as resistance to dehydration may improve by 40%.  That's the better
part of a number of years, drosophila is bred in a laboratory setting,
non-stop.  Drosophila have a generation time of approximately 7 days.

For Example: *Physiological mechanisms of evolved desiccation resistance in
Drosophila melanogaster.*
  https://jeb.biologists.org/content/200/12/1821.short

With bees, how many beekeepers are breeding more than 2 generations a year?
Perhaps in very warm climates, 8 or so generations would be possible (and a
lot of work) per annum.  A generation in bees is defined by the time from
egg to mature mated queen.

However, the "trait" we are trying to breed is not easily definable.  How
do we define, and more importantly, how do we quantify "varroa resistant
bees"?  What are the controls for comparison?

I'm also not aware of any definitions of the premise.  Is there any
evidence that behavior in insects is a heritable trait that can be
selectively bred?

Interestingly, research has indicated that the Asian Honey bee has evolved
the behavioral trait to remove mites from brood, and sophisticated hygienic
"rituals" to survive Varroa infestations:  The resistance mechanism of the
Asian Honey bee

*The resistance mechanism of the Asian honey bee, Apis cerana Fabr., to an
ectoparasitic mite, Varroa jacobsoni Oudemans*

https://www.sciencedirect.com/science/article/abs/pii/002220118790125X
<https://www.sciencedirect.com/science/article/abs/pii/002220118790125X>

There also appears to be resistance to mites by simply not uncapping the
drone brood after succumbing to mites in:

*OBSERVATIONS ON MITES OF THE ASIAN HONEYBEE SPECIES *


https://www.apidologie.org/articles/apido/pdf/1983/03/Apidologie_0044-8435_1983_14_3_ART0005.pdf

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