> If a daughter from a pure VSH mother mates with drone with zero VSH is the colony back to ground zero on mite control?

This is a very important point, which is seldom addressed sufficiently. I recently published an article in the ABJ on the future of bee breeding and in the process of researching for it became somewhat familiar with the problems associated with honey bee "improvement". I suggest  to anyone with more than a passing interest to read that article and the one on the history of bee breeding. I can email pdfs to anyone who wishes them. 

It is very difficult for new trait to become established in bee colonies because of several factors. We don't understand the genetic underpinning of behavior but we do know it is extremely complex. There is no such thing as a "gene for aggression" for example. Behaviors are caused by multiple factors and the same behavior may be produced by different genetic and environmental factors in different colonies. These factors may or may not be heritable. 

Honey bees have a very high rate of recombination, which tends to dilute traits rather than reinforce them. For a trait to become dominant in honey bee colonies it appears (to me) that it has to become dominant in an entire population. In other words, it has to be so common that the chance of the allele or allelic combination being passed on is almost guaranteed. I think that the breeding population under control by the breeder has to be very large and the selective pressure must be very strong for significant and permanent change to be affected. 

I would point to the following examples where this has taken place. I submit that Danny Weaver has created a large and consistent population of mite resistant bees by working with a very large population and a ruthless approach at get the most vigorous bee possible, irrespective of other traits. Another example would be in certain feral populations, where natural selection has created survivor stock. 

I must caution that survivor stock does not develop every time a swarm heads for the woods. That is a myth which dies hard. I submit there must be a significantly large and isolated population for this to occur; that it is not automatic nor guaranteed; and that these bees may not do as well if transplanted to other regions where they would be subjected to different sets of factors.

PLB

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