Except in honey bees we have the highest rate of recombination of any animal - when subjected to Natural Selection, heterozygosity and recombination work to increase the frequency of the alleles suitable to survival - thus an 'additive' accumulation of the appropriate genes.
This is why Tom noted that the resurgence of feral bees would be our 'tell' that Natural Selection is bringing the appropriate alleles forward.
True enough.
The mean may shift toward more or less resistance.
The standard deviation may become larger or smaller as the number of variations available for each gene that has resistant variants increases or decreases.
But the distribution will be Gaussian. It is inescapable.
Convolution of a number of distributions of nearly any shape results in a gaussian distribution.
So the goal of selective breeding is to increase the mean (average tolerance) while reducing the standard deviation.
To do that, you need to reduce the number of variants of genes that affect the desired result - getting rid of the bad variants.
You also need to increase the number of good variants. A bee with 200 gene variants that code for resistance (200 locations) is more resistant than a bee with 100 gene variants that code for resistance (100 locations).
At the same time, you need to maintain as many variants as possible everywhere else to avoid inbreeding.
You want bees that are effectively partially inbred in very specific ways.
One challenge is that the offspring of an outcross with a non-resistant drone will produce some offspring which are fully resistant compared with the mother, and some that are fully non-resistant with the father. But those are the tails of the distribution. Most will be about half-resistant.
But it gets worse.
Imagine that you have your adequately resistant stock. The average bee is about 1 standard deviation above the mean of the resistance needed to be TF. And imagine that you have done this while maintaining diversity generally, so that you can mate your queens with your drones without the problem of inbreeding. You have maybe 20 surviving matrilines in your population by careful selection not just for resistance but for diverse resistance.
You sell mated queens. Their daughter workers are good bees. TF!
BUT
Your customers raise queens from your queens. Open mated with non-resistant drones.
On average, those queens after mating will produce daughters that have half of the resistant genes that their mothers had. And they will be highly variable. But the only way to figure out how good they are is to try them. Some will be quite good. Others quite bad. But by the time they figure out which is which, your customers will have done a lot of mite monitoring and lost a few colonies. Not something the average backyarder or commercial beekeeper has the time or inclination to do.
The model that works is to requeen with your queens in every case that a queen is needed.
Over time, if enough people do that, the effect of the drones produced by those queens will improve the quality of the local bees pretty much everywhere.
However, it will be expensive. And beekeepers are an independent lot,
The only way this can work, I think, is first to make the resistant queens available at no cost. Second to make the use of other queens illegal. Third to start a public service / propaganda campaign explaining how good people use the good bees, and bad people don't.
More practically, you need to get people who are politically connected to invest in your bee breeding experiment. It would be a natural avenue for the pharmaceutical companies to expand into. They are good at making money off of stuff like that.
You could even enforce this. Genetic testing of drones from a hive will show conclusively if it has "your" queen. If not, the colony would be destroyed, and the keeper fined and/or imprisoned.
Monsanto is famous for using these methods on people who violate their roundup-ready patents...
How do YOU spell dystopia?