Polygenic traits of the Honeybee
Most important traits of bees are controlled by more than one gene, so are termed polygenic. Hygienic behavior is a trait by which bees uncap and remove diseased larva from their cells. It is thought to be controlled by at least 2 recessive genes, one for uncapping the cell and one for removing the diseased larva. Actually this model which dates back to the 1960’s and Walter Rothenbuhler is now thought to be too simple. 
There are probably more like 7 genes involved so it is probably more complex than this. Nonetheless, many breeders have bred hygienic bees successfully, using a simple assay of the removal of killed brood.
This figure shows that progress with recessive traits is slow at first until the gene frequency builds up in the population. But once the genes become fixed in the population, all the bees are resistant to American foulbrood and chalkbrood. It’s possible to reach this level using instrumental insemination. But it’s much more difficult through natural mating.
But this is where our knowledge of bee genetics is useful. We know that the drones get all their genes from the queen. So any daughter queens raised from hygienic breeder queens will produce pure hygienic drones. No matter who she mated with, and even if her own colony doesn't’t express the behavior, the drones transmit the good genes to the next generation. This is good to know when you’re trying to breed bees through natural mating.
I consider hygienic behavior to be one of the greatest accomplishments of bee breeding. It is the trait which by seeing with my own eyes and experience has convinced me of the effectiveness of genetic control of honeybee diseases. All of the bees that we use in our program are hygienic and I have seen the almost complete disappearance of chalk brood and AFB in our colonies.
Varroa Sensitive Hygiene (VSH)
Varroa sensitive hygiene or VSH was defined by Dr. John Harbo and Dr. Jeffery Harris at the USDA. It was first called SMR or suppressed mite reproduction but has been renamed VSH or varroa sensitive hygiene.
This diagram by Harbo shows that if a mite begins to lay eggs and reproduce, the bees bred with the VSH trait will uncap and remove the mite family along with the bee pupae. However if a mite fails to reproduce in the cell, the cell will not be uncapped.
In Dr. Harbo and Harris’s original assay to select for this trait, they observed that there was a higher percentage of non-reproductive mites in the total number of mites they counted. They surmised that something in the bee must be causing the mites not to reproduce, and the trait was named SMR. However with further observations Marla Spivak realized that the reason that there appeared to be a higher percentage of non reproductive mites was because the reproductive mites were being removed by hygienic behavior. This was a great observation which Harbo quickly verified as true and decided the name should be changed to VSH to be more accurate.
This is a form of hygienic behavior that targets varroa. Although they also remove chalkbrood and AFB as well as regular hygienic bee, VSH bees are remarkably more resistant to varroa mites. Exactly how VSH differs from regular hygienic behavior is not completely clear right now, but it is being studied.
Selection for the trait is tedious, counting mite families in infested cells. But it is very easy to cross any line with a pure VSH breeder queen and get a good amount of resistance in a single generation.

Dr. Harbo believes that the VSH trait is controlled by an unknown number of additive genes. Additive genes are polygenic that lack dominance. Simply put, the more of these genes are present, the more the trait is expressed.
This slide shows that the 50% level is reached in one generation. A cross of about 50% VSH seems to be a good productive and mite resistant bee. Note again that pure VSH drones are produced from any pure VSH queen, no matter who she mated with. As more drones start to carry the trait, more of the trait will be expressed.
The only drawback with VSH is that when the bees have much more than 50% VSH in them, their brood rearing ability seems impaired for some reason, maybe it’s an over expression of the trait. Colonies holding 100% VSH breeder queens are sustained with the addition of brood from other colonies.
The VSH project is still a work in progress. But I think it holds the greatest promise for a sustainable solution to varroa.

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